Mandelbrot set

From Rosetta Code
This page uses content from Wikipedia. The original article was at Mandelbrot_set. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Mandelbrot set
You are encouraged to solve this task according to the task description, using any language you may know.


Task

Generate and draw the Mandelbrot set.


Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .

11l

Translation of: Python
F mandelbrot(a)
   R (0.<50).reduce(0i, (z, _) -> z * z + @a)

F step(start, step, iterations)
   R (0 .< iterations).map(i -> @start + (i * @step))

V rows = (step(1, -0.05, 41).map(y -> (step(-2.0, 0.0315, 80).map(x -> (I abs(mandelbrot(x + 1i * @y)) < 2 {‘*’} E ‘ ’)))))
print(rows.map(row -> row.join(‘’)).join("\n"))

ACL2

(defun abs-sq (z)
   (+ (expt (realpart z) 2)
      (expt (imagpart z) 2)))

(defun round-decimal (x places)
   (/ (floor (* x (expt 10 places)) 1)
      (expt 10 places)))

(defun round-complex (z places)
   (complex (round-decimal (realpart z) places)
            (round-decimal (imagpart z) places)))

(defun mandel-point-r (z c limit)
   (declare (xargs :measure (nfix limit)))
   (cond ((zp limit) 0)
         ((> (abs-sq z) 4) limit)
         (t (mandel-point-r (+ (round-complex (* z z) 15) c)
                            c
                            (1- limit)))))

(defun mandel-point (z iters)
   (- 5 (floor (mandel-point-r z z iters) (/ iters 5))))

(defun draw-mandel-row (im re cols width iters)
   (declare (xargs :measure (nfix cols)))
   (if (zp cols)
       nil
       (prog2$ (cw (coerce
                    (list
                     (case (mandel-point (complex re im)
                                         iters)
                           (5 #\#)
                           (4 #\*)
                           (3 #\.)
                           (2 #\.)
                           (otherwise #\Space))) 'string))
               (draw-mandel-row im
                                (+ re (/ (/ width 3)))
                                (1- cols)
                                width iters))))

(defun draw-mandel (im rows width height iters)
   (if (zp rows)
       nil
       (progn$ (draw-mandel-row im -2 width width iters)
               (cw "~%")
               (draw-mandel (- im (/ (/ height 2)))
                            (1- rows)
                            width
                            height
                            iters))))

(defun draw-mandelbrot (width iters)
   (let ((height (floor (* 1000 width) 3333)))
        (draw-mandel 1 height width height iters)))
Output:
> (draw-mandelbrot 60 100)
                                        #                   
                                     ..                     
                                   .####                    
                            .     # .##.                    
                             ##*###############.            
                           #.##################             
                          .######################.          
                 ######.  #######################           
               ##########.######################            
##############################################              
               ##########.######################            
                 ######.  #######################           
                          .######################.          
                           #.##################             
                             ##*###############.            
                            .     # .##.                    
                                   .####                    
                                     ..                     

Ada

Library: Lumen

mandelbrot.adb:

with Lumen.Binary;
package body Mandelbrot is
   function Create_Image (Width, Height : Natural) return Lumen.Image.Descriptor is
      use type Lumen.Binary.Byte;
      Result : Lumen.Image.Descriptor;
      X0, Y0 : Float;
      X, Y, Xtemp : Float;
      Iteration   : Float;
      Max_Iteration : constant Float := 1000.0;
      Color : Lumen.Binary.Byte;
   begin
      Result.Width := Width;
      Result.Height := Height;
      Result.Complete := True;
      Result.Values := new Lumen.Image.Pixel_Matrix (1 .. Width, 1 .. Height);
      for Screen_X in 1 .. Width loop
         for Screen_Y in 1 .. Height loop
            X0 := -2.5 + (3.5 / Float (Width) * Float (Screen_X));
            Y0 := -1.0 + (2.0 / Float (Height) * Float (Screen_Y));
            X := 0.0;
            Y := 0.0;
            Iteration := 0.0;
            while X * X + Y * Y <= 4.0 and then Iteration < Max_Iteration loop
               Xtemp := X * X - Y * Y + X0;
               Y := 2.0 * X * Y + Y0;
               X := Xtemp;
               Iteration := Iteration + 1.0;
            end loop;
            if Iteration = Max_Iteration then
               Color := 255;
            else
               Color := 0;
            end if;
            Result.Values (Screen_X, Screen_Y) := (R => Color, G => Color, B => Color, A => 0);
         end loop;
      end loop;
      return Result;
   end Create_Image;

end Mandelbrot;

mandelbrot.ads:

with Lumen.Image;

package Mandelbrot is

   function Create_Image (Width, Height : Natural) return Lumen.Image.Descriptor;

end Mandelbrot;

test_mandelbrot.adb:

with System.Address_To_Access_Conversions;
with Lumen.Window;
with Lumen.Image;
with Lumen.Events;
with GL;
with Mandelbrot;

procedure Test_Mandelbrot is

   Program_End : exception;

   Win : Lumen.Window.Handle;
   Image : Lumen.Image.Descriptor;
   Tx_Name : aliased GL.GLuint;
   Wide, High : Natural := 400;

   -- Create a texture and bind a 2D image to it
   procedure Create_Texture is
      use GL;

      package GLB is new System.Address_To_Access_Conversions (GLubyte);

      IP : GLpointer;
   begin  -- Create_Texture
      -- Allocate a texture name
      glGenTextures (1, Tx_Name'Unchecked_Access);

      -- Bind texture operations to the newly-created texture name
      glBindTexture (GL_TEXTURE_2D, Tx_Name);

      -- Select modulate to mix texture with color for shading
      glTexEnvi (GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE);

      -- Wrap textures at both edges
      glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
      glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);

      -- How the texture behaves when minified and magnified
      glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
      glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);

      -- Create a pointer to the image.  This sort of horror show is going to
      -- be disappearing once Lumen includes its own OpenGL bindings.
      IP := GLB.To_Pointer (Image.Values.all'Address).all'Unchecked_Access;

      -- Build our texture from the image we loaded earlier
      glTexImage2D (GL_TEXTURE_2D, 0, GL_RGBA, GLsizei (Image.Width), GLsizei (Image.Height), 0,
                    GL_RGBA, GL_UNSIGNED_BYTE, IP);
   end Create_Texture;

   -- Set or reset the window view parameters
   procedure Set_View (W, H : in Natural) is
      use GL;
   begin  -- Set_View
      GL.glEnable (GL.GL_TEXTURE_2D);
      glClearColor (0.8, 0.8, 0.8, 1.0);

      glMatrixMode (GL_PROJECTION);
      glLoadIdentity;
      glViewport (0, 0, GLsizei (W), GLsizei (H));
      glOrtho (0.0, GLdouble (W), GLdouble (H), 0.0, -1.0, 1.0);

      glMatrixMode (GL_MODELVIEW);
      glLoadIdentity;
   end Set_View;

   -- Draw our scene
   procedure Draw is
      use GL;
   begin  -- Draw
      -- clear the screen
      glClear (GL_COLOR_BUFFER_BIT or GL_DEPTH_BUFFER_BIT);
      GL.glBindTexture (GL.GL_TEXTURE_2D, Tx_Name);

      -- fill with a single textured quad
      glBegin (GL_QUADS);
      begin
         glTexCoord2f (1.0, 0.0);
         glVertex2i (GLint (Wide), 0);

         glTexCoord2f (0.0, 0.0);
         glVertex2i (0, 0);

         glTexCoord2f (0.0, 1.0);
         glVertex2i (0, GLint (High));

         glTexCoord2f (1.0, 1.0);
         glVertex2i (GLint (Wide), GLint (High));
      end;
      glEnd;

      -- flush rendering pipeline
      glFlush;

      -- Now show it
      Lumen.Window.Swap (Win);
   end Draw;

   -- Simple event handler routine for keypresses and close-window events
   procedure Quit_Handler (Event : in Lumen.Events.Event_Data) is
   begin  -- Quit_Handler
      raise Program_End;
   end Quit_Handler;

   -- Simple event handler routine for Exposed events
   procedure Expose_Handler (Event : in Lumen.Events.Event_Data) is
      pragma Unreferenced (Event);
   begin  -- Expose_Handler
      Draw;
   end Expose_Handler;

   -- Simple event handler routine for Resized events
   procedure Resize_Handler (Event : in Lumen.Events.Event_Data) is
   begin  -- Resize_Handler
      Wide := Event.Resize_Data.Width;
      High := Event.Resize_Data.Height;
      Set_View (Wide, High);
--        Image := Mandelbrot.Create_Image (Width => Wide, Height => High);
--        Create_Texture;
      Draw;
   end Resize_Handler;

begin
   -- Create Lumen window, accepting most defaults; turn double buffering off
   -- for simplicity
   Lumen.Window.Create (Win           => Win,
                        Name          => "Mandelbrot fractal",
                        Width         => Wide,
                        Height        => High,
                        Events        => (Lumen.Window.Want_Exposure  => True,
                                          Lumen.Window.Want_Key_Press => True,
                                          others                      => False));

   -- Set up the viewport and scene parameters
   Set_View (Wide, High);

   -- Now create the texture and set up to use it
   Image := Mandelbrot.Create_Image (Width => Wide, Height => High);
   Create_Texture;

   -- Enter the event loop
   declare
      use Lumen.Events;
   begin
      Select_Events (Win   => Win,
                     Calls => (Key_Press    => Quit_Handler'Unrestricted_Access,
                               Exposed      => Expose_Handler'Unrestricted_Access,
                               Resized      => Resize_Handler'Unrestricted_Access,
                               Close_Window => Quit_Handler'Unrestricted_Access,
                               others       => No_Callback));
   end;
exception
   when Program_End =>
      null;
end Test_Mandelbrot;
Output:

ALGOL 68

Plot part of the Mandelbrot set as a pseudo-gif image.

 
INT pix = 300, max iter = 256, REAL zoom = 0.33 / pix;
[-pix : pix, -pix : pix] INT plane;
COMPL ctr = 0.05 I 0.75 # center of set #;

# Compute the length of an orbit. #
PROC iterate = (COMPL z0) INT:
  BEGIN COMPL z := 0, INT iter := 1;
        WHILE (iter +:= 1) < max iter # not converged # AND ABS z < 2 # not diverged #
        DO z := z * z + z0
        OD;
        iter
  END;

# Compute set and find maximum orbit length. #     
INT max col := 0;
FOR x FROM -pix TO pix
DO FOR y FROM -pix TO pix
   DO COMPL z0 = ctr + (x * zoom) I (y * zoom);
      IF (plane [x, y] := iterate (z0)) < max iter
      THEN (plane [x, y] > max col | max col := plane [x, y])
      FI
   OD
OD;

# Make a plot. #
FILE plot;
INT num pix = 2 * pix + 1;
make device (plot, "gif", whole (num pix, 0) + "x" + whole (num pix, 0));
open (plot, "mandelbrot.gif", stand draw channel);
FOR x FROM -pix TO pix
DO FOR y FROM -pix TO pix
   DO INT col = (plane [x, y] > max col | max col | plane [x, y]);
      REAL c = sqrt (1- col / max col); # sqrt to enhance contrast #
      draw colour (plot, c, c, c);
      draw point (plot, (x + pix) / (num pix - 1), (y + pix) / (num pix  - 1))
   OD
OD;
close (plot)

ALGOL W

Generates an ASCII Mandelbrot Set. Translated from the sample program in the Compiler/AST Interpreter task.

begin
    % -- This is an integer ascii Mandelbrot generator, translated from the   %
    % -- Compiler/AST Interpreter Task's ASCII Mandelbrot Set example program %
    integer leftEdge, rightEdge, topEdge, bottomEdge, xStep, yStep, maxIter;
    leftEdge   := -420;
    rightEdge  :=  300;
    topEdge    :=  300;
    bottomEdge := -300;
    xStep      :=    7;
    yStep      :=   15;
 
    maxIter    :=  200;
 
    for y0 := topEdge step - yStep until bottomEdge do begin
        for x0 := leftEdge step xStep until rightEdge do begin
            integer x, y, i;
            string(1) theChar;
            y := 0;
            x := 0;
            theChar := " ";
            i := 0;
            while i < maxIter do begin
                integer x_x, y_y;
                x_x := (x * x) div 200;
                y_y := (y * y) div 200;
                if x_x + y_y > 800 then begin
                    theChar := code( decode( "0" ) + i );
                    if i > 9 then theChar := "@";
                    i := maxIter
                end;
                y := x * y div 100 + y0;
                x := x_x - y_y + x0;
                i := i + 1
            end while_i_lt_maxIter ;
            writeon( theChar );
        end for_x0 ;
        write();
    end for_y0
end.
Output:
1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333222222222222222222222222222222222222222
1111111111111222222222233333333333333333333333344444456655544443333332222222222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
11111111111222222333333333333333333333334444444445555679@@@@7654444443333333222222222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98755544444433333332222222222222222222222222
1111111122223333333333333333333333344444444445556668@@@    @@@76555544444333333322222222222222222222222
1111111222233333333333333333333344444444455566667778@@      @987666555544433333333222222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@    @@@@@@877779@5443333333322222222222222222222
1111112233333333333333333334444455555556679@   @@@               @@@@@@ 8544333333333222222222222222222
1111122333333333333333334445555555556666789@@@                        @86554433333333322222222222222222
1111123333333333333444456666555556666778@@ @                         @@87655443333333332222222222222222
111123333333344444455568@887789@8777788@@@                            @@@@65444333333332222222222222222
111133334444444455555668@@@@@@@@@@@@99@@@                              @@765444333333333222222222222222
111133444444445555556778@@@         @@@@                                @855444333333333222222222222222
11124444444455555668@99@@             @                                 @655444433333333322222222222222
11134555556666677789@@                                                @86655444433333333322222222222222
111                                                                 @@876555444433333333322222222222222
11134555556666677789@@                                                @86655444433333333322222222222222
11124444444455555668@99@@             @                                 @655444433333333322222222222222
111133444444445555556778@@@         @@@@                                @855444333333333222222222222222
111133334444444455555668@@@@@@@@@@@@99@@@                              @@765444333333333222222222222222
111123333333344444455568@887789@8777788@@@                            @@@@65444333333332222222222222222
1111123333333333333444456666555556666778@@ @                         @@87655443333333332222222222222222
1111122333333333333333334445555555556666789@@@                        @86554433333333322222222222222222
1111112233333333333333333334444455555556679@   @@@               @@@@@@ 8544333333333222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@    @@@@@@877779@5443333333322222222222222222222
1111111222233333333333333333333344444444455566667778@@      @987666555544433333333222222222222222222222
1111111122223333333333333333333333344444444445556668@@@    @@@76555544444333333322222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98755544444433333332222222222222222222222222
11111111111222222333333333333333333333334444444445555679@@@@7654444443333333222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
1111111111111222222222233333333333333333333333344444456655544443333332222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333222222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111

The entry for m4 also is based on Rosetta Code's "compiler" task suite.

Amazing Hopper

El siguiente programa genera el conjunto de Mandelbrot directamente en pantalla. Ha sido adaptado desde Wikipedia.

Se ejecutó con:

rxvt -g 500x250 -fn "xft:FantasqueSansMono-Regular:pixelsize=1" -e hopper3 jm/mandel.jambo

 
#!/usr/bin/hopper
#include <jambo.h>

Main

Initialize '300, ancho, alto'

Set '-2,0.47,-1.12,1.12' Init 'min real, max real, min complex, max complex'

Init zero 'submaxRminR, submaxCminC'

Let ( submaxRminR := 'max real' Minus 'min real') 
Let ( submaxCminC := 'maxcomplex' Minus 'mincomplex' )

Init zero 'a2,b2,a,b,ta'

Loop for (i=1, Less equal(i, ancho),++i)

   Let ( ta := Add(min real, Div ( Mul( submaxRminR, Minus one(i)), Minus one(ancho) )) )

   Loop for (j=1, Less equal (j, alto),++j)

       Let ( b := Add( min complex, Div ( Mul (submaxCminC, Minus one(j)), Minus one(alto))) )

       a=ta, a2=a, b2=b
   
       k=1000, color=256
       Loop if (Sqradd (a,b) Is less than (4), And (k) )
            Add(Sqrdiff(a,b), a2), 
            Add(b2, Mul(2, Mul(a, b)))

            Move to (b), Move to (a)

            --color
            --k
       Back
       Color back (color), Print("O")
   Back
   Prnl
Back
Pause

End
Output:

Arturo

Translation of: Nim
inMandelbrot?: function [c][
    z: to :complex [0 0]
    do.times: 50 [
        z: c + z*z
        if 4 < abs z -> return false
    ]
    return true
]

mandelbrot: function [settings][
    y: 0
    while [y < settings\height][
        Y: settings\yStart + y * settings\yStep
        x: 0
        while [x < settings\width][
            X: settings\xStart + x * settings\xStep
            if? inMandelbrot? to :complex @[X Y] -> prints "*"
            else -> prints " "
            x: x + 1
        ]
        print ""
        y: y + 1
    ]
]

mandelbrot #[ yStart: 1.0 yStep: neg 0.05 
              xStart: neg 2.0 xStep: 0.0315
              height: 40 width: 80 ]
Output:
                                                           **                   
                                                         ******                 
                                                       ********                 
                                                         ******                 
                                                      ******** **   *           
                                              ***   *****************           
                                              ************************  ***     
                                              ****************************      
                                           ******************************       
                                            *******************************     
                                         ************************************   
                                *         **********************************    
                           ** ***** *     **********************************    
                           ***********   ************************************   
                         ************** ************************************    
                         ***************************************************    
                     ******************************************************     
************************************************************************        
                     ******************************************************     
                         ***************************************************    
                         ************** ************************************    
                           ***********   ************************************   
                           ** ***** *     **********************************    
                                *         **********************************    
                                         ************************************   
                                            *******************************     
                                           ******************************       
                                              ****************************      
                                              ************************  ***     
                                              ***   *****************           
                                                      ******** **   *           
                                                         ******                 
                                                       ********                 
                                                         ******                 
                                                           **

ATS

A non-interactive program that writes a PPM image

Translation of: JavaScript
(* The algorithm is borrowed from Wikipedia. The graphics is a
   modification of the display made by the JavaScript entry. Output
   from the program is a Portable Pixmap file. *)

#include "share/atspre_staload.hats"
staload "libats/libc/SATS/math.sats"
staload _ = "libats/libc/DATS/math.dats"

fn
mandel_iter {max_iter : nat}
            (cx       : double,
             cy       : double,
             max_iter : int max_iter)
    :<> intBtwe (0, max_iter) =
  let
    fun
    loop {iter : nat | iter <= max_iter}
         .<max_iter - iter>.
         (x    : double,
          y    : double,
          iter : int iter) :<> intBtwe (0, max_iter) =
      if iter = max_iter then
        iter
      else if 2.0 * 2.0 < (x * x) + (y * y) then
        iter
      else
        let
          val x = (x * x) - (y * y) + cx
          and y = (2.0 * x * y) + cy
        in
          loop (x, y, succ iter)
        end
  in
    loop (0.0, 0.0, 0)
  end

fn                (* Write a Portable Pixmap of the Mandelbrot set. *)
write_mandelbrot_ppm (outf       : FILEref,
                      width      : intGte 0,
                      height     : intGte 0,
                      xmin       : double,
                      xmax       : double,
                      ymin       : double,
                      ymax       : double,
                      max_iter : intGte 0) : void =
  let
    prval [width : int] EQINT () = eqint_make_gint width
    prval [height : int] EQINT () = eqint_make_gint height

    macdef output (r, g, b) =
      let
        val r = min ($UNSAFE.cast{int} ,(r), 255)
        and g = min ($UNSAFE.cast{int} ,(g), 255)
        and b = min ($UNSAFE.cast{int} ,(b), 255)
      in
        fprint_val<uchar> (outf, $UNSAFE.cast r);
        fprint_val<uchar> (outf, $UNSAFE.cast g);
        fprint_val<uchar> (outf, $UNSAFE.cast b);
      end

    val xscale = (xmax - xmin) / g0i2f width
    and yscale = (ymax - ymin) / g0i2f height

    fun
    loop_y {iy : nat | iy <= height}
           .<height - iy>.
           (iy : int iy) : void =
      if iy <> height then
        let
          fun
          loop_x {ix : nat | ix <= width}
                 .<width - ix>.
                 (ix : int ix) : void =
            if ix <> width then
              let
                (* We want to go from top to bottom, left to right. *)
                val x = xmin + (xscale * g0i2f ix)
                and y = ymin + (yscale * g0i2f (height - iy))
                val i = mandel_iter (x, y, max_iter)

                (* We can PROVE that "i" is no greater than
                  "max_iter". *)
                prval [i : int] EQINT () = eqint_make_gint i
                prval [max_iter : int] EQINT () = eqint_make_gint max_iter
                prval () = prop_verify {i <= max_iter} ()

                val c = (4.0 * log (g0i2f i)) / log (g0i2f max_iter)
              in
                if i = max_iter then
                  output (0, 0, 0)
                else if c < 1.0 then
                  output (0, 0, 255.0 * (c - 1.0))
                else if c < 2.0 then
                  output (0, 255.0 * (c - 1.0), 255)
                else
                  output (255.0 * (c - 2.0), 255, 255);
                loop_x (succ ix)
              end
        in
          loop_x 0;
          loop_y (succ iy)
        end
  in
    fprintln! (outf, "P6");
    fprintln! (outf, width, " ", height);
    fprintln! (outf, 255);
    loop_y 0
  end

implement
main0 () =
  let
    val outf = stdout_ref
    val width = 1024
    val height = 1024
    val xmin = ~2.25
    val xmax = 0.75
    val ymin = ~1.5
    val ymax = 1.5
    val max_iter = 1000
  in
    write_mandelbrot_ppm (outf, width, height, xmin, xmax,
                          ymin, ymax, max_iter)
  end
Output:
The Mandelbrot set, displayed in colors.

An interactive program that can write PAM images

Translation of: ObjectIcon
Translation of: Scheme
Library: SDL2
Library: ats2-xprelude
(*-*- ATS -*-*)

(* This program requires ats2-xprelude:
   https://sourceforge.net/p/chemoelectric/ats2-xprelude

   Also required is the SDL2 library for C. Not everything in the SDL
   interface below is used. The interface is meant to be relatively
   safe. For instance, you cannot create a window or renderer without
   later destroying it, and you cannot use one at all that was not
   properly created. Also you cannot accidentally use an
   SDL_WindowEvent as an SDL_TextInputEvent, etc.

   The program uses 32+32-bit fixed point to calculate escape times.
   One does not need so many bits left of the decimal point, but this
   is the fixed point format available from ats2-xprelude.

   There are some "FIXME" notes below that refer to a few of the ways
   the program could be improved. This is a demo version of something
   I am likely to expand into a better program.

   Compile the program with (for example)
   "myatscc mandelbrot_task_interactive.dats"

##myatsccdef=\
patscc -std=gnu2x -O3 \
  -DATS_MEMALLOC_GCBDW \
  `pkg-config --define-variable=PATSHOME="${PATSHOME}" \
              --cflags sdl2 ats2-xprelude bdw-gc` \
  `pkg-config --define-variable=PATSHOME="${PATSHOME}" \
              --variable=PATSCCFLAGS ats2-xprelude` \
  -o $fname($1) $1 \
  `pkg-config --define-variable=PATSHOME="${PATSHOME}" \
              --libs sdl2 ats2-xprelude bdw-gc`

*)

(* How to use the program:

     Left click          : re-center the image
     Double left-click   : zoom in
     Double right-click  : zoom out
     p or P              : save an image as a Portable Arbitrary Map
     q or Q              : quit the program

   The window is resizable.
   Closing the window quits the program, just as the Q key does. *)

(*------------------------------------------------------------------*)

#include "share/atspre_staload.hats"
staload UN = "prelude/SATS/unsafe.sats"

#include "xprelude/HATS/xprelude.hats"

(* To use 32+32-bit fixed point: *)
staload "xprelude/SATS/fixed32p32.sats"
staload _ = "xprelude/DATS/fixed32p32.dats"
stadef realknd = fix32p32knd
typedef real = fixed32p32
(* Actually, one could use different kinds of real number for
   different algorithms: fixed point, floating point,
   multiple-precision rational, interval arithmetic, ... even
   continued fractions. *)

(*------------------------------------------------------------------*)

(* This is a weak choice of ATS_EXTERN_PREFIX, but will spare us from
   having to do a lot of writing. *)
#define ATS_EXTERN_PREFIX ""

extern fn atexit : (() -> void) -> int = "mac#%"

%{^

#define SDL_MAIN_HANDLED 1
#include <SDL.h>

ATSinline() atstype_bool
SDL_bool2ATS (SDL_bool b)
{
  return (b == SDL_FALSE) ? atsbool_false : atsbool_true;
}

%}

typedef SDL_bool = $extype"SDL_bool"
extern fn SDL_bool2ATS (b : SDL_bool) :<> bool = "mac#%"

(* -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  - *)
(* Housekeeping. *)

extern fn SDL_SetMainReady () : void = "mac#%"
extern fn SDL_Init (flags : uint32) : void = "mac#%"
extern fn SDL_Quit () : void = "mac#%"

(* -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  - *)
(* Timers. *)

extern fn SDL_Delay (ms : uint32) : void = "mac#%"

(* -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  - *)
(* Video handling. *)

(* Screensavers are disabled by default, except in very early versions
   of SDL2. *)
extern fn SDL_DisableScreenSaver () : void = "mac#%"
extern fn SDL_EnableScreenSaver () : void = "mac#%"
extern fn SDL_IsScreenSaverEnabled () : SDL_bool = "mac#%"

absvtype SDL_Window_ptr (p : addr) = ptr p
vtypedef SDL_Window_ptr0 = [p : addr] SDL_Window_ptr p
vtypedef SDL_Window_ptr1 = [p : agz] SDL_Window_ptr p

absvtype SDL_Renderer_ptr (p : addr) = ptr p
vtypedef SDL_Renderer_ptr0 = [p : addr] SDL_Renderer_ptr p
vtypedef SDL_Renderer_ptr1 = [p : agz] SDL_Renderer_ptr p

extern castfn SDL_Window_ptr2ptr :
  {p : addr} (!SDL_Window_ptr p) -<> ptr p
extern castfn SDL_Renderer_ptr2ptr :
  {p : addr} (!SDL_Renderer_ptr p) -<> ptr p

macdef SDL_INIT_EVENTS = $extval (uint32, "SDL_INIT_EVENTS")
macdef SDL_INIT_TIMER = $extval (uint32, "SDL_INIT_TIMER")
macdef SDL_INIT_VIDEO = $extval (uint32, "SDL_INIT_VIDEO")

macdef SDL_WINDOWPOS_CENTERED = $extval (int, "SDL_WINDOWPOS_CENTERED")
macdef SDL_WINDOWPOS_UNDEFINED = $extval (int, "SDL_WINDOWPOS_UNDEFINED")

macdef SDL_WINDOW_OPENGL = $extval (uint32, "SDL_WINDOW_OPENGL")
macdef SDL_WINDOW_RESIZABLE = $extval (uint32, "SDL_WINDOW_RESIZABLE")

extern fn
SDL_CreateWindow (title : string,
                  x : int, y : int,
                  w : int, h : int,
                  flags : uint32) : SDL_Window_ptr0 = "mac#%"

extern fn
SDL_DestroyWindow : SDL_Window_ptr1 -> void = "mac#%"
fn {}
SDL_DestroyWindow_null
          (window : SDL_Window_ptr null) : void =
  $UN.castvwtp0{void} window

extern fn
SDL_CreateRenderer (window : !SDL_Window_ptr1,
                    index  : int,
                    flags  : uint32) : SDL_Renderer_ptr0 = "mac#%"

extern fn
SDL_DestroyRenderer : SDL_Renderer_ptr1 -> void = "mac#%"
fn {}
SDL_DestroyRenderer_null
          (renderer : SDL_Renderer_ptr null) : void =
  $UN.castvwtp0{void} renderer

extern fn
SDL_GetRendererOutputSize (renderer : !SDL_Renderer_ptr1,
                           w        : &int? >> int,
                           h        : &int? >> int) : int = "mac#%"

extern fn
SDL_SetRenderDrawColor (renderer : !SDL_Renderer_ptr1,
                        r        : uint8,
                        g        : uint8,
                        b        : uint8,
                        a        : uint8) : int = "mac#%"

extern fn
SDL_RenderClear (renderer : !SDL_Renderer_ptr1) : int = "mac#%"

extern fn
SDL_RenderDrawPoint (renderer : !SDL_Renderer_ptr1,
                     x        : int,
                     y        : int) : int = "mac#%"
extern fn
SDL_RenderPresent (renderer : !SDL_Renderer_ptr1) : void = "mac#%"

(* -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  - *)
(* Event handling. *)

typedef SDL_Event (t : int) =
  $extype_struct"SDL_Event" of
    {
      type = uint32 t,
      timestamp = uint32
    }
typedef SDL_Event = [t : int] SDL_Event t

extern fn
SDL_PollEvent (event : &SDL_Event? >> SDL_Event)
    : intBtwe (0, 1) = "mac#%"

extern fn
SDL_GetMouseState (x : &int? >> int,
                   y : &int? >> int) : uint32 = "mac#%"

macdef SDL_BUTTON_LMASK = $extval (uint32, "SDL_BUTTON_LMASK")
macdef SDL_BUTTON_MMASK = $extval (uint32, "SDL_BUTTON_MMASK")
macdef SDL_BUTTON_RMASK = $extval (uint32, "SDL_BUTTON_RMASK")
macdef SDL_BUTTON_X1MASK = $extval (uint32, "SDL_BUTTON_X1MASK")
macdef SDL_BUTTON_X2MASK = $extval (uint32, "SDL_BUTTON_X2MASK")

(*  -    -    -    -    -    -    -    -    -    -    -    -    -   *)

stacst SDL_QUIT : int
macdef SDL_QUIT = $extval (uint32 SDL_QUIT, "SDL_QUIT")

typedef SDL_QuitEvent =
  $extype_struct"SDL_QuitEvent" of
    {
      type = uint32 SDL_QUIT,
      timestamp = uint32
    }

extern praxi
SDL_Event2QuitEvent_v :
  {p : addr}
  SDL_Event SDL_QUIT @ p -<prf>
    @(SDL_QuitEvent @ p,
      SDL_QuitEvent @ p -<lin,prf> SDL_Event SDL_QUIT @ p)

(*  -    -    -    -    -    -    -    -    -    -    -    -    -   *)

stacst SDL_WINDOWEVENT : int
macdef SDL_WINDOWEVENT = $extval (uint32 SDL_WINDOWEVENT, "SDL_WINDOWEVENT")

typedef SDL_WindowEvent =
  $extype_struct"SDL_WindowEvent" of
    {
      type = uint32 SDL_WINDOWEVENT,
      timestamp = uint32,
      windowID = uint32,
      event = uint8,
      padding1 = uint8,
      padding2 = uint8,
      padding3 = uint8,
      data1 = int32,
      data2 = int32
    }

extern praxi
SDL_Event2WindowEvent_v :
  {p : addr}
  SDL_Event SDL_WINDOWEVENT @ p -<prf>
    @(SDL_WindowEvent @ p,
      SDL_WindowEvent @ p -<lin,prf> SDL_Event SDL_WINDOWEVENT @ p)

macdef SDL_WINDOWEVENT_NONE = $extval (uint8, "SDL_WINDOWEVENT_NONE")
macdef SDL_WINDOWEVENT_SHOWN = $extval (uint8, "SDL_WINDOWEVENT_SHOWN")
macdef SDL_WINDOWEVENT_HIDDEN = $extval (uint8, "SDL_WINDOWEVENT_HIDDEN")
macdef SDL_WINDOWEVENT_EXPOSED = $extval (uint8, "SDL_WINDOWEVENT_EXPOSED")
macdef SDL_WINDOWEVENT_MOVED = $extval (uint8, "SDL_WINDOWEVENT_MOVED")
macdef SDL_WINDOWEVENT_RESIZED = $extval (uint8, "SDL_WINDOWEVENT_RESIZED")
macdef SDL_WINDOWEVENT_SIZE_CHANGED = $extval (uint8, "SDL_WINDOWEVENT_SIZE_CHANGED")
macdef SDL_WINDOWEVENT_MINIMIZED = $extval (uint8, "SDL_WINDOWEVENT_MINIMIZED")
macdef SDL_WINDOWEVENT_MAXIMIZED = $extval (uint8, "SDL_WINDOWEVENT_MAXIMIZED")
macdef SDL_WINDOWEVENT_RESTORED = $extval (uint8, "SDL_WINDOWEVENT_RESTORED")
macdef SDL_WINDOWEVENT_ENTER = $extval (uint8, "SDL_WINDOWEVENT_ENTER")
macdef SDL_WINDOWEVENT_LEAVE = $extval (uint8, "SDL_WINDOWEVENT_LEAVE")
macdef SDL_WINDOWEVENT_FOCUS_GAINED = $extval (uint8, "SDL_WINDOWEVENT_FOCUS_GAINED")
macdef SDL_WINDOWEVENT_FOCUS_LOST = $extval (uint8, "SDL_WINDOWEVENT_FOCUS_LOST")
macdef SDL_WINDOWEVENT_CLOSE = $extval (uint8, "SDL_WINDOWEVENT_CLOSE")
macdef SDL_WINDOWEVENT_TAKE_FOCUS = $extval (uint8, "SDL_WINDOWEVENT_TAKE_FOCUS")
macdef SDL_WINDOWEVENT_HIT_TEST = $extval (uint8, "SDL_WINDOWEVENT_HIT_TEST")
macdef SDL_WINDOWEVENT_ICCPROF_CHANGED = $extval (uint8, "SDL_WINDOWEVENT_ICCPROF_CHANGED")
macdef SDL_WINDOWEVENT_DISPLAY_CHANGED = $extval (uint8, "SDL_WINDOWEVENT_DISPLAY_CHANGED")

(*  -    -    -    -    -    -    -    -    -    -    -    -    -   *)

stacst SDL_MOUSEMOTION : int
macdef SDL_MOUSEMOTION = $extval (uint32 SDL_MOUSEMOTION, "SDL_MOUSEMOTION")

typedef SDL_MouseMotionEvent =
  $extype_struct"SDL_MouseMotionEvent" of
    {
      type = uint32 SDL_MOUSEMOTION,
      timestamp = uint32,
      windowID = uint32,
      which = uint32,
      state = uint32,
      x = int32,
      y = int32,
      xrel = int32,
      yrel = int32
    }

extern praxi
SDL_Event2MouseMotionEvent_v :
  {p : addr}
  SDL_Event SDL_MOUSEMOTION @ p -<prf>
    @(SDL_MouseMotionEvent @ p,
      SDL_MouseMotionEvent @ p -<lin,prf> SDL_Event SDL_MOUSEMOTION @ p)

(*  -    -    -    -    -    -    -    -    -    -    -    -    -   *)

stacst SDL_MOUSEBUTTONDOWN : int
macdef SDL_MOUSEBUTTONDOWN = $extval (uint32 SDL_MOUSEBUTTONDOWN, "SDL_MOUSEBUTTONDOWN")

stacst SDL_MOUSEBUTTONUP : int
macdef SDL_MOUSEBUTTONUP = $extval (uint32 SDL_MOUSEBUTTONUP, "SDL_MOUSEBUTTONUP")

typedef SDL_MouseButtonEvent (t : int) =
  [t == SDL_MOUSEBUTTONDOWN || t == SDL_MOUSEBUTTONUP]
  $extype_struct"SDL_MouseButtonEvent" of
    {
      type = uint32 t,
      timestamp = uint32,
      windowID = uint32,
      which = uint32,
      button = uint8,
      state = uint8,
      clicks = uint8,
      padding1 = uint8,
      x = int32,
      y = int32
    }
typedef SDL_MouseButtonEvent = [t : int] SDL_MouseButtonEvent t

extern praxi
SDL_Event2MouseButtonEvent_v :
  {p : addr}
  {t : int | t == SDL_MOUSEBUTTONDOWN || t == SDL_MOUSEBUTTONUP}
  SDL_Event t @ p -<prf>
    @(SDL_MouseButtonEvent t @ p,
      SDL_MouseButtonEvent t @ p -<lin,prf> SDL_Event t @ p)

macdef SDL_BUTTON_LEFT = $extval (uint8, "SDL_BUTTON_LEFT")
macdef SDL_BUTTON_MIDDLE = $extval (uint8, "SDL_BUTTON_MIDDLE")
macdef SDL_BUTTON_RIGHT = $extval (uint8, "SDL_BUTTON_RIGHT")
macdef SDL_BUTTON_X1 = $extval (uint8, "SDL_BUTTON_X1")
macdef SDL_BUTTON_X2 = $extval (uint8, "SDL_BUTTON_X2")

macdef SDL_PRESSED = $extval (uint8, "SDL_PRESSED")
macdef SDL_RELEASED = $extval (uint8, "SDL_RELEASED")

(*  -    -    -    -    -    -    -    -    -    -    -    -    -   *)

stacst SDL_TEXTINPUT : int
macdef SDL_TEXTINPUT = $extval (uint32 SDL_TEXTINPUT, "SDL_TEXTINPUT")

#define SDL_TEXTINPUTEVENT_TEXT_SIZE 32

typedef SDL_TextInputEvent =
  $extype_struct"SDL_TextInputEvent" of
    {
      type = uint32 SDL_TEXTINPUT,
      timestamp = uint32,
      windowID = uint32,
      text = @[char][SDL_TEXTINPUTEVENT_TEXT_SIZE]
    }

extern praxi
SDL_Event2TextInputEvent_v :
  {p : addr}
  SDL_Event SDL_TEXTINPUT @ p -<prf>
    @(SDL_TextInputEvent @ p,
      SDL_TextInputEvent @ p -<lin,prf> SDL_Event SDL_TEXTINPUT @ p)

(*------------------------------------------------------------------*)

exception bailout of string

typedef rgba = @(uint8, uint8, uint8, uint8)

val empty_scene_color =
  @(g0i2u 200, g0i2u 200, g0i2u 200, g0i2u 255) : rgba

typedef rgba_array (w : int, h : int) =
  matrixref (rgba, w, h)

typedef scene_computer =
  {w, h : nat}
  (int w, int h, real, real, real) -<cloref1>
    rgba_array (w, h)

vtypedef situation (p : addr, q : addr,
                    w : int, h : int) =
  [null < p; null < q; 0 <= w; 0 <= h]
  @{window   = SDL_Window_ptr p,
    renderer = SDL_Renderer_ptr q,
    width    = int w,
    height   = int h,
    xcenter  = real,
    ycenter  = real,
    pixels_per_unit = real,
    compute_scene = scene_computer}
vtypedef situation (w : int, h : int) =
  [p, q : agz]
  situation (p, q, w, h)
vtypedef situation =
  [w, h : nat]
  situation (w, h)

fn
destroy_situation (situation : situation) : void =
  begin
    SDL_DestroyRenderer (situation.renderer);
    SDL_DestroyWindow (situation.window)
  end

fn
get_renderer_size (situation : &situation)
    : [renderer_width, renderer_height : nat]
      @(int renderer_width, int renderer_height) =
  let
    var w : int
    var h : int
    val status = SDL_GetRendererOutputSize (situation.renderer, w, h)
    val w = g1ofg0 w and h = g1ofg0 h
  in
    if (status < 0) + (w < 0) + (h < 0) then
      begin
        destroy_situation situation;
        $raise bailout "rendering error"
      end
    else
      @(w, h)
  end

fn
resize_needed (situation : &situation) : bool =
  let
    val @(w, h) = get_renderer_size situation
  in
    (w <> situation.width) + (h <> situation.height)
  end

(*------------------------------------------------------------------*)

fn
compute_escape_times
          {w, h : nat}
          {mxtm : nat}
          (width           : int w,
           height          : int h,
           xcenter         : real,
           ycenter         : real,
           pixels_per_unit : real,
           max_time        : uint16 mxtm)
    : matrixref ([tm : nat | tm <= mxtm] uint16 tm, w, h) =
  let
    typedef tm = [tm : nat | tm <= mxtm] uint16 tm

    val times = matrixref_make_elt<tm> (i2sz width, i2sz height,
                                        max_time)
    and ppu2 = pixels_per_unit + pixels_per_unit

    fun
    ij_loop {i, j : nat | i <= w; j <= h}
            .<w - i, h - j>.
            (i : int i,
             j : int j) :<!refwrt> void =
      if i = width then
        ()
      else if j = height then
        ij_loop (succ i, 0)
      else
        let
          val cx = xcenter + (g0i2f ((i + i) - width) / ppu2)
          and cy = ycenter + (g0i2f (height - (j + j)) / ppu2)

          fun
          tm_loop {tm : nat | tm <= mxtm}
                  .<mxtm - tm>.
                  (x     : real,
                   y     : real,
                   xx    : real,
                   yy    : real,
                   tm    : uint16 tm)
              :<> [tm1 : nat | tm1 <= mxtm] uint16 tm1 =
            if tm = max_time then
              tm
            else if g0i2f 4 < xx + yy then
              tm
            else
              let
                val x = xx - yy + cx and y = ((x + x) * y) + cy
                val xx = x * x and yy = y * y
              in
                tm_loop (x, y, xx, yy, succ tm)
              end

          val tm = tm_loop (g0i2f 0, g0i2f 0,
                            g0i2f 0, g0i2f 0,
                            g1i2u 0)
        in
          times[i, height, j] := tm;
          ij_loop (i, succ j)
        end
  in
    ij_loop (0, 0);
    times
  end

fn
the_durn_simplest_scene_computer
          {w, h            : nat}
          (width           : int w,
           height          : int h,
           xcenter         : real,
           ycenter         : real,
           pixels_per_unit : real)
    :<cloref1> rgba_array (w, h) =
  let
    val escape_times =
      compute_escape_times (width, height, xcenter, ycenter,
                            pixels_per_unit, g1i2u 255)
    and points = matrixref_make_elt<rgba> (i2sz width, i2sz height,
                                           empty_scene_color)

    fn {}
    time2rgba {tm : nat | tm <= 255}
              (tm : uint16 tm) : rgba =
      let
        val v = (g0u2u (g1i2u 255 - tm)) : uint8
      in
        @(v, v, v, g0i2u 255)
      end

    fun
    loop {i, j : nat | i <= w; j <= h}
         .<w - i, h - j>.
         (i : int i,
          j : int j) : void =
      if i = width then
        ()
      else if j = height then
        loop (succ i, 0)
      else
        begin
          points[i, height, j] :=
            time2rgba escape_times[i, height, j];
          loop (i, succ j)
        end
  in
    loop (0, 0);
    points
  end

(*------------------------------------------------------------------*)
(* Writing an image to a Portable Arbitrary Map. *)

fn
write_rgba_points_as_pam
           {w, h   : nat}
           (outf   : FILEref,
            width  : int w,
            height : int h,
            points : rgba_array (w, h)) : void =
  let
    fun
    loop {i, j : nat | i <= w; j <= h}
         .<h - j, w - i>.
         (i : int i,
          j : int j) : void =
      if j = height then
        ()
      else if i = width then
        loop (0, succ j)
      else
        let
          val @(r, g, b, a) = points[i, height, j]
        in
          fprint! (outf, int2uchar0 (g0u2i r));
          fprint! (outf, int2uchar0 (g0u2i g));
          fprint! (outf, int2uchar0 (g0u2i b));
          fprint! (outf, int2uchar0 (g0u2i a));
          loop (succ i, j)
        end
  in
    (* Portable Arbitrary Map:
       https://netpbm.sourceforge.net/doc/pam.html *)
    fprintln! (outf, "P7");
    fprintln! (outf, "WIDTH ", width);
    fprintln! (outf, "HEIGHT ", height);
    fprintln! (outf, "DEPTH 4");
    fprintln! (outf, "MAXVAL 255");
    fprintln! (outf, "TUPLTYPE RGB_ALPHA");
    fprintln! (outf, "ENDHDR");
    loop (0, 0)
  end

(* For this demo, simply number the images, starting at 1 on each run
   of the program. *)
val image_number : ref uint = ref 1U
fn
write_image {w, h     : nat}
            (width    : int w,
             height   : int h,
             points   : rgba_array (w, h)) : void =
  let
    val filename =
      strptr2string (string_append ("mandelbrot-image-",
                                    tostring_val<uint> !image_number,
                                    ".pam"))
  in
    case+ fileref_open_opt (filename, file_mode_w) of
    | ~ None_vt () =>
      println! ("ERROR: could not open ", filename, " for writing.")
    | ~ Some_vt outf =>
      begin
        write_rgba_points_as_pam (outf, width, height, points);
        fileref_close (outf);
        println! ("SUCCESS: wrote ", filename);
        !image_number := succ !image_number
      end
  end

(*------------------------------------------------------------------*)

val initial_width : intGte 0 = 400
val initial_height : intGte 0 = 400
val initial_xcenter : real = g0f2f ~0.75
val initial_ycenter : real = g0f2f 0.0
val initial_pixels_per_unit : real = g0f2f 150.0
val initial_scene_computer : scene_computer =
  the_durn_simplest_scene_computer

(* Zoom factor could be adjustable, but is not in this simple demo. *)
val zoom_factor : real = g0f2f 2.0
val min_pixels_per_unit : real = g0f2f 10.0

fn
set_render_rgba (renderer : !SDL_Renderer_ptr1,
                 rgba     : rgba) : int =
  let
    val @(r, g, b, a) = rgba
  in
    SDL_SetRenderDrawColor (renderer, r, g, b, a)
  end

fn
draw_scene {w, h : nat}
           (renderer : !SDL_Renderer_ptr1,
            width    : int w,
            height   : int h,
            points   : rgba_array (w, h)) : void =
  let
    prval () = mul_gte_gte_gte {w, h} ()

    fun
    loop {i, j : nat | i <= w; j <= h}
         .<w - i, h - j>.
         (renderer : !SDL_Renderer_ptr1,
          i        : int i,
          j        : int j) : void =
      if i = width then
        ()
      else if j = height then
        loop (renderer, succ i, 0)
      else
        let
          val rgba = points[i, height, j]
          val _ = set_render_rgba (renderer, rgba)
          val _ = SDL_RenderDrawPoint (renderer, i, j)
        in
          loop (renderer, i, succ j)
        end
  in
    ignoret (set_render_rgba (renderer, empty_scene_color));
    ignoret (SDL_RenderClear (renderer));
    loop (renderer, 0, 0);
  end

fnx
situation_changed
          {w, h : nat}
          (situation   : &situation (w, h) >> situation,
           event       : &SDL_Event? >> SDL_Event) : void =
  let
    val compute_scene = situation.compute_scene
    val points =
      compute_scene (situation.width, situation.height,
                     situation.xcenter, situation.ycenter,
                     situation.pixels_per_unit)
  in
    SDL_Delay (g0i2u 16);
    event_loop (situation, points, event)
  end
and
event_loop {w, h : nat}
           (situation   : &situation (w, h) >> situation,
            points      : rgba_array (w, h),
            event       : &SDL_Event? >> SDL_Event) : void =
  let
    macdef quit_the_event_loop =
      ()
    macdef present_the_scene =
      present_scene (situation, points, event)
    macdef deal_with_changed_situation =
      situation_changed (situation, event)
    macdef write_an_image =
      write_image (situation.width, situation.height, points);
  in
    if resize_needed situation then
      let
        val @(w, h) = get_renderer_size situation
      in
        situation.width := w;
        situation.height := h;
        deal_with_changed_situation
      end
    else
      let
      in
        draw_scene (situation.renderer,
                    situation.width, situation.height,
                    points);
        case+ SDL_PollEvent (event) of
        | 0 => present_the_scene
        | 1 =>
          if event.type = SDL_QUIT then
            quit_the_event_loop
          else if event.type = SDL_WINDOWEVENT then
            let
              prval @(pf, fpf) = SDL_Event2WindowEvent_v (view@ event)
              prval () = view@ event := pf
              val window_event = event
              prval () = view@ event := fpf (view@ event)
            in
              if window_event.event = SDL_WINDOWEVENT_SIZE_CHANGED then
                deal_with_changed_situation
              else if window_event.event = SDL_WINDOWEVENT_CLOSE then
                quit_the_event_loop
              else
                present_the_scene
            end
          else if event.type = SDL_MOUSEBUTTONDOWN then
            let
              prval @(pf, fpf) = SDL_Event2MouseButtonEvent_v (view@ event)
              prval () = view@ event := pf
              val button_event = event
              prval () = view@ event := fpf (view@ event)
            in
              if button_event.button = SDL_BUTTON_LEFT then
                begin
                  if button_event.clicks = g0i2u 1 then
                    let         (* Re-center. *)
                      val x = g0i2i button_event.x
                      and y = g0i2i button_event.y
                      and w = situation.width
                      and h = situation.height
                      and ppu = situation.pixels_per_unit
                      val ppu2 = ppu + ppu
                    in
                      situation.xcenter :=
                        situation.xcenter + (g0i2f (x + x - w) / ppu2);
                      situation.ycenter :=
                        situation.ycenter + (g0i2f (h - y - y) / ppu2);
                      deal_with_changed_situation
                    end
                  else
                    let         (* Zoom in. *)
                      val new_ppu = situation.pixels_per_unit * zoom_factor
                    in
                      situation.pixels_per_unit := new_ppu;
                      deal_with_changed_situation
                    end
                end
              else if button_event.button = SDL_BUTTON_RIGHT then
                begin
                  if button_event.clicks = g0i2u 1 then
                    present_the_scene
                  else
                    let         (* Zoom out *)
                      val new_ppu = situation.pixels_per_unit / zoom_factor
                    in
                      if min_pixels_per_unit <= new_ppu then
                        situation.pixels_per_unit := new_ppu;
                      deal_with_changed_situation
                    end
                end
              else
                present_the_scene
            end
          else if event.type = SDL_TEXTINPUT then
            let
              prval @(pf, fpf) = SDL_Event2TextInputEvent_v (view@ event)
              prval () = view@ event := pf
              var text_event = event
              prval () = view@ event := fpf (view@ event)
              macdef text = text_event.text
            in
              case+ @(text[0], text[1]) of
              | @('q', '\0') => quit_the_event_loop
              | @('Q', '\0') => quit_the_event_loop
              | @('p', '\0') =>
                begin
                  write_an_image;
                  present_the_scene
                end
              | @('P', '\0') =>
                begin
                  write_an_image;
                  present_the_scene
                end
              | _ => present_the_scene
            end
          else
            present_the_scene
      end
  end
and
present_scene {w, h : nat}
              (situation   : &situation (w, h) >> situation,
               points      : rgba_array (w, h),
               event       : &SDL_Event? >> SDL_Event) : void =
  begin
    SDL_RenderPresent (situation.renderer);
    SDL_Delay (g0i2u 16);
    event_loop (situation, points, event)
  end

fn
run_program () : void =
  let
    (* FIXME: For best form, we should also set up a signal handler
       that runs SDL_Quit, so the display does not get stuck in an
       undesired state even if the program crashes. For instance,
       there could be a signaled divide by zero or overflow event. And
       we are at least changing whether the screensaver is enabled. *)
    val _ = atexit SDL_Quit

    val () = SDL_Init (SDL_INIT_EVENTS
                        lor SDL_INIT_TIMER
                        lor SDL_INIT_VIDEO)

    (* FIXME: Find out whether the screensaver was enabled BEFORE we
       started SDL2, and set SDL2 to whichever setting it was. *)
    val () = SDL_EnableScreenSaver ()

    val window = SDL_CreateWindow ("mandelbrot_task_interactive",
                                   SDL_WINDOWPOS_CENTERED,
                                   SDL_WINDOWPOS_CENTERED,
                                   initial_width, initial_height,
                                   SDL_WINDOW_RESIZABLE)
    val p_window = SDL_Window_ptr2ptr window
    prval () = lemma_ptr_param p_window
  in
    if iseqz p_window then
      begin
        SDL_DestroyWindow_null window;
        $raise bailout "failed to initialize a window"
      end
    else
      let
        val renderer = SDL_CreateRenderer (window, ~1, g0i2u 0)
        val p_renderer = SDL_Renderer_ptr2ptr renderer
        prval () = lemma_ptr_param p_renderer
      in
        if iseqz p_renderer then
          begin
            SDL_DestroyRenderer_null renderer;
            SDL_DestroyWindow window;
            $raise bailout "failed to initialize a renderer"
          end
        else
          let
            var situation : situation =
              @{window = window,
                renderer = renderer,
                width = initial_width,
                height = initial_height,
                xcenter = initial_xcenter,
                ycenter = initial_ycenter,
                pixels_per_unit = initial_pixels_per_unit,
                compute_scene = initial_scene_computer}
            var event : SDL_Event?
          in
            situation_changed (situation, event);
            destroy_situation situation
          end
      end
  end

implement
main () =
  try
    begin
      SDL_SetMainReady ();
      run_program ();
      0
    end
  with
  | ~ bailout msg =>
    begin    
      println! ("Error: ", msg);
      1
    end

(*------------------------------------------------------------------*)
Output:

A snapshot image of part of the set:

A portion of the Mandelbrot set, in shades of gray and black.

AutoHotkey

Max_Iteration := 256
Width := Height := 400

File := "MandelBrot." Width ".bmp"
Progress, b2 w400 fs9, Creating Colours ...
Gosub, CreateColours
Gosub, CreateBitmap
Progress, Off
Gui, -Caption
Gui, Margin, 0, 0
Gui, Add, Picture,, %File%
Gui, Show,, MandelBrot
Return

GuiClose:
GuiEscape:
ExitApp



;---------------------------------------------------------------------------
CreateBitmap: ; create and save a 32bit bitmap file
;---------------------------------------------------------------------------
    ; define header details
    HeaderBMP  := 14
    HeaderDIB  := 40
    DataOffset := HeaderBMP + HeaderDIB
    ImageSize  := Width * Height * 4 ; 32bit
    FileSize   := DataOffset + ImageSize
    Resolution := 3780 ; from mspaint

    ; create bitmap header
    VarSetCapacity(IMAGE, FileSize, 0)
    NumPut(Asc("B")   , IMAGE, 0x00, "Char")
    NumPut(Asc("M")   , IMAGE, 0x01, "Char")
    NumPut(FileSize   , IMAGE, 0x02, "UInt")
    NumPut(DataOffset , IMAGE, 0x0A, "UInt")
    NumPut(HeaderDIB  , IMAGE, 0x0E, "UInt")
    NumPut(Width      , IMAGE, 0x12, "UInt")
    NumPut(Height     , IMAGE, 0x16, "UInt")
    NumPut(1          , IMAGE, 0x1A, "Short") ; Planes
    NumPut(32         , IMAGE, 0x1C, "Short") ; Bits per Pixel
    NumPut(ImageSize  , IMAGE, 0x22, "UInt")
    NumPut(Resolution , IMAGE, 0x26, "UInt")
    NumPut(Resolution , IMAGE, 0x2A, "UInt")

    ; fill in Data
    Gosub, CreatePixels

    ; save Bitmap to file
    FileDelete, %File%
    Handle := DllCall("CreateFile", "Str", File, "UInt", 0x40000000
            , "UInt", 0, "UInt", 0, "UInt", 2, "UInt", 0, "UInt", 0)
    DllCall("WriteFile", "UInt", Handle, "UInt", &IMAGE, "UInt"
            , FileSize, "UInt *", Bytes, "UInt", 0)
    DllCall("CloseHandle", "UInt", Handle)

Return



;---------------------------------------------------------------------------
CreatePixels: ; create pixels for [-2 < x < 1] [-1.5 < y < 1.5]
;---------------------------------------------------------------------------
    Loop, % Height // 2 + 1 {
        yi := A_Index - 1
        y0 := -1.5 + yi / Height * 3 ; range -1.5 .. +1.5
        Progress, % 200*yi // Height, % "Current line: " 2*yi " / " Height
        Loop, %Width% {
            xi := A_Index - 1
            x0 := -2 + xi / Width * 3 ; range -2 .. +1
            Gosub, Mandelbrot
            p1 := DataOffset + 4 * (Width * yi + xi)
            NumPut(Colour, IMAGE, p1, "UInt")
            p2 := DataOffset + 4 * (Width * (Height-yi) + xi)
            NumPut(Colour, IMAGE, p2, "UInt")
        }
    }
Return



;---------------------------------------------------------------------------
Mandelbrot: ; calculate a colour for each pixel
;---------------------------------------------------------------------------
    x := y := Iteration := 0
    While, (x*x + y*y <= 4) And (Iteration < Max_Iteration) {
        xtemp := x*x - y*y + x0
        y := 2*x*y + y0
        x := xtemp
        Iteration++
    }
    Colour := Iteration = Max_Iteration ? 0 : Colour_%Iteration%

Return



;---------------------------------------------------------------------------
CreateColours: ; borrowed from PureBasic example
;---------------------------------------------------------------------------
    Loop, 64 {
        i4 := (i3 := (i2 := (i1 := A_Index - 1) + 64) + 64) + 64
        Colour_%i1% := RGB(4*i1 + 128, 4*i1, 0)
        Colour_%i2% := RGB(64, 255, 4*i1)
        Colour_%i3% := RGB(64, 255 - 4*i1, 255)
        Colour_%i4% := RGB(64, 0, 255 - 4*i1)
    }
Return



;---------------------------------------------------------------------------
RGB(r, g, b) { ; return 24bit color value
;---------------------------------------------------------------------------
    Return, (r&0xFF)<<16 | g<<8 | b
}

AWK

BEGIN {
  XSize=59; YSize=21;
  MinIm=-1.0; MaxIm=1.0;MinRe=-2.0; MaxRe=1.0;
  StepX=(MaxRe-MinRe)/XSize; StepY=(MaxIm-MinIm)/YSize;
  for(y=0;y<YSize;y++)
  {
    Im=MinIm+StepY*y;
    for(x=0;x<XSize;x++)
        {
      Re=MinRe+StepX*x; Zr=Re; Zi=Im;
      for(n=0;n<30;n++)
          {
        a=Zr*Zr; b=Zi*Zi;
        if(a+b>4.0) break;
        Zi=2*Zr*Zi+Im; Zr=a-b+Re;
      }
      printf "%c",62-n;
    }
    print "";
  }
  exit;
}
Output:
>>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<==========
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<=======
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<======
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<====
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<===
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<==
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<=
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<
><;;;;;;::::9875&      .3                       *9;;;<<<<<<
>;;;;;;::997564'        '                       8:;;;<<<<<<
>::988897735/                                 &89:;;;<<<<<<
>::988897735/                                 &89:;;;<<<<<<
>;;;;;;::997564'        '                       8:;;;<<<<<<
><;;;;;;::::9875&      .3                       *9;;;<<<<<<
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<=
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<==
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<===
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<====
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<=======

B

This implements a 16bit fixed point arithmetic Mandelbrot set calculation.

Works with: The Amsterdam Compiler Kit - B version V6.1pre1
main() {
  auto cx,cy,x,y,x2,y2;
  auto iter;

  auto xmin,xmax,ymin,ymax,maxiter,dx,dy;

  xmin = -8601;
  xmax =  2867;
  ymin = -4915;
  ymax =  4915;

  maxiter = 32;

  dx = (xmax-xmin)/79;
  dy = (ymax-ymin)/24;

  cy=ymin;
  while( cy<=ymax ) {
    cx=xmin;
    while( cx<=xmax ) {
      x = 0;
      y = 0;
      x2 = 0;
      y2 = 0;
      iter=0;
      while( iter<maxiter ) {
        if( x2+y2>16384 ) break;
        y = ((x*y)>>11)+cy;
        x = x2-y2+cx;
        x2 = (x*x)>>12;
        y2 = (y*y)>>12;
        iter++;
      }
      putchar(' '+iter);
      cx =+ dx;
    }
    putchar(13);
    putchar(10);
    cy =+ dy;
  }

  return(0);
}
Output:
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'+)%%%$$$$$#####"""""""""""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(+,)++&%$$$$$$######""""""
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*5:/+('&%%$$$$$$#######"""
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),@@@@@@@,'&%%%%%$$$$########
!!!!!!!"""####################$$$$$$$$%%%&'())((())*,@@@@@@/+))('&&&&)'%$$######
!!!!!!""###################$$$$$%%%%%%&&&'+.@@=/<@@@@@@@@@@@@@@@/++@..93%%$#####
!!!!!"################$$$%%%%%%%%%%&&&&'),+2@@@@@@@@@@@@@@@@@@@@@@@@@1(&&%$$####
!!!!"##########$$$$$%%&(-(''''''''''''(*,5@@@@@@@@@@@@@@@@@@@@@@@@@@@@+)-&%$$###
!!!!####$$$$$$$$%%%%%&'(*-@1.+.@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4-(&%$$$##
!!!!#$$$$$$$$$%%%%%%'''++.6@@@@@@@@@8/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3(%%$$$$#
!!!#$$$$$$$%&&&&''()/-5.5@@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?'&%%$$$$#
!!!(**+/+<523/80/46@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+)'&&%%$$$$#
!!!#$$$$$$$%&&&&''().-2.@@@@@@@@@@@@@@?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$#
!!!!#$$$$$$$$$%%%%%&'''/,.7@@@@@@@@@;/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0'%%$$$$#
!!!!####$$$$$$$$%%%%%&'(*-:2.,/?-5+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+(&%$$$##
!!!!"##########$$$$$%%&(-(''''(''''''((*,4@@@@@@@@@@@@@@@@@@@@@@@@@@@4+).&%$$###
!!!!!"################$$$%%%%%%%%%%&&&&')<,4@@@@@@@@@@@@@@@@@@@@@@@@@/('&%%$####
!!!!!!""##################$$$$$$%%%%%%&&&'*.@@@0@@@@@@@@@@@@@@@@1,,@//9)%%$#####
!!!!!!!"""####################$$$$$$$$%%%&(())((()**-@@@@@@/+)))'&&&')'%$$######
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''(,@@@@@@@+'&&%%%%%$$$########
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*7@0+('&%%%$$$$$#######"""
!!!!!!!!!!!"""""""######################$$$$$$$$$%%%&&(+-).*&%$$$$$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$%%'3(%%%$$$$$######""""""""""
!!!!!!!!!!!!!!!""""""""""""#####################################""""""""""""""""

bc

File:Mandelbrot-bc.jpg

Producing a PGM image.

To work properly, this needs to run with the environment variable BC_LINE_LENGTH set to 0.

max_iter = 50
width = 400; height = 401
scale = 10 
xmin = -2; xmax = 1/2
ymin = -5/4; ymax = 5/4

define mandelbrot(c_re, c_im) {
  auto i

  # z = 0
  z_re  = 0;   z_im = 0
  z2_re = 0; z2_im = 0

  for (i=0; i<max_iter; i++) {
    # z *= z
    z_im = 2*z_re*z_im
    z_re = z2_re - z2_im
    # z += c
    z_re += c_re
    z_im += c_im
    # z2 = z.*z
    z2_re = z_re*z_re
    z2_im = z_im*z_im
    if (z2_re + z2_im > 4) return i
  }
  return 0
}

print "P2\n", width, " ", height, "\n255\n"

for (i = 0; i < height; i++) {
  y = ymin + (ymax - ymin) / height * i
  for (j = 0; j < width; j++) {
    x = xmin + (xmax - xmin) / width * j
    tmp_scale = scale
    scale = 0
    m = (255 * mandelbrot(x, y) + max_iter + 1) / max_iter
    print m
    if ( j < width - 1 ) print " "
    scale = tmp_scale

  }
  print "\n"
}

quit

BASIC

AmigaBASIC

Translation of: QBasic
SCREEN 1,320,200,5,1
WINDOW 2,"Mandelbrot",,0,1

maxIteration = 100
xmin = -2
xmax = 1
ymin = -1.5
ymax = 1.5
xs = 300
ys = 180
st = .01   ' use e.g. st = .05 for a coarser but faster picture
           '   and perhaps also lower maxIteration = 10 or so
xp = xs / (xmax - xmin) * st
yp = ys / (ymax - ymin) * st

FOR x0 = xmin TO xmax STEP st
    FOR y0 = ymin TO ymax STEP st
        x = 0
        y = 0
        iteration = 0
 
        WHILE (x * x + y * y <= (2 * 2) AND iteration < maxIteration)
            xtemp = x * x - y * y + x0
            y = 2 * x * y + y0
 
            x = xtemp
 
            iteration = iteration + 1
        WEND
 
        IF iteration <> maxIteration THEN
            c = iteration
        ELSE
            c = 0
        END IF
        COLOR c MOD 32
        AREA ((x0 - xmin) * xp / st, (y0 - ymin) * yp / st)
        AREA STEP (xp, 0)
        AREA STEP (0, yp)
        AREA STEP (-xp, 0)
        AREA STEP (0, -yp)
        AREAFILL
    NEXT
NEXT

' endless loop, use Run -> Stop from the menu to stop program
WHILE (1)
WEND

Applesoft BASIC

This version takes into account the Apple II's funky 280×192 6-color display, which has an effective resolution of only 140×192 in color.

10  HGR2
20  XC = -0.5           : REM CENTER COORD X
30  YC = 0              : REM   "      "   Y
40  S = 2               : REM SCALE
45  IT = 20             : REM ITERATIONS
50  XR = S * (280 / 192): REM TOTAL RANGE OF X
60  YR = S              : REM   "     "   "  Y
70  X0 = XC - (XR/2)    : REM MIN VALUE OF X
80  X1 = XC + (XR/2)    : REM MAX   "   "  X
90  Y0 = YC - (YR/2)    : REM MIN   "   "  Y
100 Y1 = YC + (YR/2)    : REM MAX   "   "  Y
110 XM = XR / 279       : REM SCALING FACTOR FOR X
120 YM = YR / 191       : REM    "      "     "  Y
130 FOR YI = 0 TO 3     : REM INTERLEAVE
140   FOR YS = 0+YI TO 188+YI STEP 4 : REM Y SCREEN COORDINATE
145   HCOLOR=3 : HPLOT 0,YS TO 279,YS
150     FOR XS = 0 TO 278 STEP 2     : REM X SCREEN COORDINATE
170       X = XS * XM + X0  : REM TRANSL SCREEN TO TRUE X
180       Y = YS * YM + Y0  : REM TRANSL SCREEN TO TRUE Y
190       ZX = 0
200       ZY = 0
210       XX = 0
220       YY = 0
230       FOR I = 0 TO IT
240         ZY = 2 * ZX * ZY + Y
250         ZX = XX - YY + X
260         XX = ZX * ZX
270         YY = ZY * ZY
280         C = IT-I
290         IF XX+YY >= 4 GOTO 301
300       NEXT I
301       IF C >= 8 THEN C = C - 8 : GOTO 301
310       HCOLOR = C : HPLOT XS, YS TO XS+1, YS
320     NEXT XS
330   NEXT YS
340 NEXT YI

By making the following modifications, the same code will render the Mandelbrot set in monochrome at full 280×192 resolution.

150 FOR XS = 0 TO 279
301 C = (C - INT(C/2)*2)*3
310 HCOLOR = C: HPLOT XS, YS


ARM BBC BASIC

The ARM development second processor for the BBC series of microcomputers came with ARM BBC Basic V. In version 1.0 this included a built-in MANDEL function that uses D% (depth) to update C% (colour) at given coordinates x and y. Presumably this was for benchmarking/demo purposes; it was removed from later versions. This can be run in BeebEm. Select BBC model as Master 128 with ARM Second Processor. Load disc armdisc3.adl and switch to ADFS. At the prompt load ARM Basic by running the AB command.

10MODE5:VDU5
20D%=100 : REM adjust for speed/precision
30FORX%=0 TO 1279 STEP8
40FORY%=0 TO 1023 STEP4
50MANDEL (Y%-512)/256, (X%-640)/256
51REM (not sure why X and Y need to be swapped to correct orientation)
60GCOL0,C%
70PLOT69,X%,Y%
80NEXT
90NEXT

File:Mandelbrot armbasic.png

BASIC256

fastgraphics

graphsize 384,384
refresh
kt = 319 : m = 4.0
xmin = -2.1 : xmax = 0.6 : ymin = -1.35 : ymax = 1.35
dx = (xmax - xmin) / graphwidth : dy = (ymax - ymin) / graphheight

for x = 0 to graphwidth
	jx = xmin + x * dx
	for y = 0 to graphheight
		jy = ymin + y * dy
		k = 0 : wx = 0.0 : wy = 0.0
		do
			tx = wx * wx - wy * wy + jx
			ty = 2.0 * wx * wy + jy
			wx = tx
			wy = ty
			r = wx * wx + wy * wy
			k = k + 1
		until r > m or k > kt
		
		if k > kt then
			color black
		else 
			if k < 16 then color k * 8, k * 8, 128 + k * 4
			if k >= 16 and k < 64 then color 128 + k - 16, 128 + k - 16, 192 + k - 16
			if k >= 64 then color kt - k, 128 + (kt - k) / 2, kt - k
		end if
		plot x, y
	next y
	refresh
next x
imgsave "Mandelbrot_BASIC-256.png", "PNG"
Image generated by the script:

BBC BASIC

      sizex% = 300 : sizey% = 300
      maxiter% = 128
      VDU 23,22,sizex%;sizey%;8,8,16,128
      ORIGIN 0,sizey%
      GCOL 1
      FOR X% = 0 TO 2*sizex%-2 STEP 2
        xi = X%/200 - 2
        FOR Y% = 0 TO sizey%-2 STEP 2
          yi = Y% / 200
          x = 0
          y = 0
          FOR I% = 1 TO maxiter%
            IF x*x+y*y > 4 EXIT FOR
            xt = xi + x*x-y*y
            y = yi + 2*x*y
            x = xt
          NEXT
          IF I%>maxiter% I%=0
          COLOUR 1,I%*15,I%*8,0
          PLOT X%,Y% : PLOT X%,-Y%
        NEXT
      NEXT X%

Commander X16 BASIC

10  CLS
20  SCREEN $80
30  FOR X=1 TO 199: 
40   FOR Y=1 TO 99:
50    LET I=0
60    LET CX=(X-100)/50
70    LET CY=(Y-100)/50
80    LET VX=0
90    LET VY=0
100   REM START OF THE CALCULATION LOOP
110   LET I=I+1
120   LET X2 = VX*VX
130   LET Y2 = VY*VY
140   LET VY = CY + (VX+VX)*VY
150   LET VX = CX + X2-Y2
160   IF I<32 AND (X2+Y2)<4 THEN GOTO 100
170  LET YR = 199-Y
180  PSET X,Y,I
190  PSET X,YR,I
200 :NEXT:NEXT

Commodore BASIC

The standard version 2.0 of BASIC that came with the VIC-20 and C-64 had no built-in support for graphics (though you could use POKE statements to put values in the VIC chip's registers and the RAM being used for video). However, Commodore sold add-on cartridges that provided such support, which was also included in later versions of BASIC (3.5 on the C-16 and Plus/4, 7.0 on the C-128). In all of these cases the programs are very slow; rendering the Mandelbrot set even with the escape threshold set to just 20 iterations takes hours. The fastest is the VIC-20, because it has only a 160x160-pixel bitmap display.

VIC-20 with Super Expander cartridge

Runs in about 90 minutes.

100 TH=20:REM ESCAPE THRESHOLD IN ITERATIONS 
110 COLOR 1,3,0,0:GRAPHIC 2:TH=20
120 FOR PY=0 TO 80
130 : SY=INT(PY*6.4)
140 : IM=1.12-PY/160*2.24
150 : FOR PX=0 TO 160
160 :  SX=INT(PX*6.4)
170 :  RE=PX/160*2.47-2
180 :  X=0:Y=0:IT=0
190 :  XT=X*X-Y*Y+RE
200 :  Y = 2*X*Y+IM
210 :  X=XT
220 :  IT=IT+1
230 :  IF(X*X+Y*Y<=4)AND(IT<TH) THEN 190
240 :  IF IT<TH THEN 270
250 :  DRAW 1,SX,SY TO SX,SY
260 :  DRAW 1,SX,1024-SY TO SX,1024-SY
270 : NEXT PX
280 NEXT PY
290 GET K$:IF K$="" THEN 290
300 GRAPHIC 4

C-64 with Super Expander 64

Runs in about 4.5 hours.

100 TH=20:REM ESCAPE THRESHOLD IN ITERATIONS 
110 COLOR 6,0,0,0,6:GRAPHIC 2,1
120 FOR PY=0 TO 100
140 : IM=1.12-PY/200*2.24
150 : FOR PX=0 TO 319
170 :  RE=PX/320*2.47-2
180 :  X=0:Y=0:IT=0
190 :  XT=X*X-Y*Y+RE
200 :  Y = 2*X*Y+IM
210 :  X=XT
220 :  IT=IT+1
230 :  IF(X*X+Y*Y<=4)AND(IT<TH) THEN 190
240 :  IF IT<TH THEN 270
250 :  DRAW 1,PX,PY
260 :  DRAW 1,PX,200-PY
270 : NEXT PX
280 NEXT PY
290 GET K$:IF K$="" THEN 290
300 GRAPHIC 0

Commodore-16 / 116 / Plus/4

Works with: Commodore BASIC version 3.5

Despite the faster clock on the TED systems compared to the C-64, this takes almost six hours to run.

100 TH=20:REM ESCAPE THRESHOLD IN ITERATIONS 
110 COLOR 0,2:COLOR 1,1:GRAPHIC 1,1
120 FOR PY=0 TO 100
130 : IM = 1.12-PY*2.24/200
140 : FOR PX=0 TO 319
150 :   RE=PX/320*2.47-2
160 :   X=0:Y=0:IT=0
170 :   DO WHILE (X*X+Y*Y<=4) AND (IT<TH)
180 :     XT = X*X-Y*Y+RE
190 :      Y = 2*X*Y+IM
200 :      X = XT
210 :     IT = IT +1
220 :   LOOP
230 :   IF IT=TH THEN DRAW 1,PX,PY:DRAW 1,PX,199-PY
240 : NEXT PX
250 NEXT PY
260 GETKEY K$
270 GRAPHIC 0

Commodore 128 (40-column display)

Works with: Commodore BASIC version 7.0

With the switch to FAST (2MHz) mode, this runs in about 2.5 hours, but you get to stare at a blank screen until it's done rendering. Without that switch it takes about 5.5 hours, splitting the difference between the Super Expander 64 and Plus/4 versions.

100 TH=20:REM ESCAPE THRESHOLD IN ITERATIONS 
110 COLOR 0,12:GRAPHIC 1,1:COLOR 1,1:GRAPHIC0:FAST
120 FOR PY=0 TO 100
130 : IM = 1.12-PY*2.24/200
140 : FOR PX=0 TO 319
150 :   RE=PX/320*2.47-2
160 :   X=0:Y=0:IT=0
170 :   DO WHILE (X*X+Y*Y<=4) AND (IT<TH)
180 :     XT = X*X-Y*Y+RE
190 :      Y = 2*X*Y+IM
200 :      X = XT
210 :     IT = IT +1
220 :   LOOP
230 :   IF IT=TH THEN DRAW 1,PX,PY:DRAW 1,PX,199-PY
240 : NEXT PX
250 NEXT PY
260 SLOW:GRAPHIC 1
270 GETKEY K$
280 GRAPHIC 0

Commodore 128 (80-column display)

Works with: Commodore BASIC version 8.0

This uses BASIC 8 to create a 640x200 render on the C-128's 80-column display. The doubled resolution comes with a commensurate increase in run time; this takes about 5h20m using FAST 2MHz mode.

100 TH=20:REM ESCAPE THRESHOLD IN ITERATIONS
110 @MODE,0:@COLOR,15,0,0:@SCREEN,0,0:@CLEAR,0:FAST
120 FOR PY=0 TO 100
130 : IM = 1.12-PY*2.24/200
140 : FOR PX=0 TO 639

150 :   RE=PX/640*2.47-2
160 :   X=0:Y=0:IT=0
170 :   DO WHILE (X*X+Y*Y<=4) AND (IT<20)
180 :     XT = X*X-Y*Y+RE
190 :      Y = 2*X*Y+IM
200 :      X = XT
210 :     IT = IT +1
220 :   LOOP
230 :   IF IT=20 THEN @DOT,PX,PY,0:@DOT,PX,199-PY,0
240 : NEXT PX
250 NEXT PY
260 GETKEY K$
270 @TEXT
Output:

Screen shots of all of the above running in the VICE emulator can be found here.

Commodore PET

Here's a version using mostly ASCII and some PETSCII (could probably improve the tile set for PETSCII) inspired by the Perl solution. Designed for a PET with an 80-column display.

100 TH=20:REM ESCAPE THRESHOLD IN ITERATIONS
110 CH$=" .:-=+*#@"+CHR$(255)
120 FOR Y=1 TO -1 STEP -0.08
130 : FOR X = -2 TO 0.5 STEP 0.0315
140 :   GOSUB 200:IF I=20 THEN PRINT CHR$(18);" ";CHR$(146);:GOTO 160
150 :   PRINT MID$(CH$,I/2+1,1);
160 : NEXT X:IF PEEK(198) THEN PRINT
170 NEXT Y
180 GET K$:IF K$=""THEN 180
190 END
200 CX=X:CY=Y:ZX=X:ZY=Y
210 FOR I=1 TO TH
220 : TX=ZX*ZX-ZY*ZY
230 : TY=ZX*ZY*2
240 : ZX = TX + CX
250 : ZY = TY + CY
260 : IF ZX*ZX+ZY*ZY > 4 THEN 280
270 NEXT I
280 IF I>TH THEN I=TH
290 RETURN
Output:
VICE screenshot here.

DEC BASIC-PLUS

Works under RSTS/E v7.0 on the simh PDP-11 emulator. For installation procedures for RSTS/E, see here.

10 X1=59\Y1=21
20 I1=-1.0\I2=1.0\R1=-2.0\R2=1.0
30 S1=(R2-R1)/X1\S2=(I2-I1)/Y1
40 FOR Y=0 TO Y1
50 I3=I1+S2*Y
60 FOR X=0 TO X1
70 R3=R1+S1*X\Z1=R3\Z2=I3
80 FOR N=0 TO 30
90 A=Z1*Z1\B=Z2*Z2
100 IF A+B>4.0 THEN GOTO 130
110 Z2=2*Z1*Z2+I3\Z1=A-B+R3
120 NEXT N
130 PRINT STRING$(1%,62%-N);
140 NEXT X
150 PRINT
160 NEXT Y
170 END
Output:
>>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<===========
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<========
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<=======
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<=====
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<====
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<===
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<==
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<=
><;;;;;;::::9875&      .3                       *9;;;<<<<<<=
>;;;;;;::997564'        '                       8:;;;<<<<<<=
>::988897735/                                 &89:;;;<<<<<<=
>::988897735/                                 &89:;;;<<<<<<=
>;;;;;;::997564'        '                       8:;;;<<<<<<=
><;;;;;;::::9875&      .3                       *9;;;<<<<<<=
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<=
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<==
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<===
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<====
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<=====
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<=======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<========
>>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<===========

FreeBASIC

#define pix 1./120
#define zero_x 320
#define zero_y 240
#define maxiter 250

screen 12

type complex
    r as double
    i as double
end type

operator + (x as complex, y as complex) as complex
    dim as complex ret
    ret.r = x.r + y.r
    ret.i = x.i + y.i
    return ret
end operator

operator * (x as complex, y as complex) as complex
    dim as complex ret
    ret.r = x.r*y.r - x.i*y.i
    ret.i = x.r*y.i + x.i*y.r
    return ret
end operator

operator abs ( x as complex ) as double
    return sqr(x.r*x.r + x.i*x.i)
end operator

dim as complex c, z
dim as integer x, y, iter

for x=0 to 639
   for y=0 to 240
      c.r = (x-zero_x)*pix
      c.i = (y-zero_y)*pix
      z.r = 0.0
      z.i = 0.0
      for iter=0 to maxiter
          z = z*z + c
          if abs(z)>2 then
              pset(x,y),iter mod 16
              pset(x,480-y),iter mod 16
              goto cont
          end if
       next iter
       pset(x,y),1
       pset(x,480-y),1
       cont:
    next y
next x

while inkey=""
wend
end

GW-BASIC

10 SCALE# = 1/60 : ZEROX = 160
20 ZEROY = 100 : MAXIT = 32
30 SCREEN 1
40 FOR X = 0 TO 2*ZEROX - 1
50 CR# = (X-ZEROX)*SCALE#
60 FOR Y = 0 TO ZEROY
70 CI# = (ZEROY-Y)*SCALE#
80 ZR# = 0
90 ZI# = 0
100 FOR I = 1 TO MAXIT
110 BR# = CR# + ZR#*ZR# - ZI#*ZI#
120 ZI# = CI# + 2*ZR#*ZI#
130 ZR# = BR#
140 IF ZR#*ZR# + ZI#*ZI# > 4 THEN GOTO 170
150 NEXT I
160 GOTO 190
170 PSET (X, Y), 1 + (I MOD 3)
180 PSET (X, 2*ZEROY-Y), 1+(I MOD 3)
190 NEXT Y
200 NEXT X

Liberty BASIC

Any words of description go outside of lang tags.

nomainwin

WindowWidth  =440
WindowHeight =460

open "Mandelbrot Set" for graphics_nsb_nf as #w

#w "trapclose [quit]"
#w "down"

for x0 = -2 to 1 step .0033
    for y0 = -1.5 to 1.5 step .0075
        x = 0
        y = 0

        iteration    =   0
        maxIteration = 255

        while ( ( x *x +y *y) <=4) and ( iteration <maxIteration)
            xtemp      =x *x -y *y +x0
            y          =2 *x *y +y0
            x          = xtemp
            iteration  = iteration + 1
        wend

        if iteration <>maxIteration then
            c =iteration
        else
            c =0
        end if

        call pSet x0, y0, c
        scan
    next
next

#w "flush"

wait

sub pSet x, y, c
    xScreen = 10 +( x +2)   /3 *400
    yScreen = 10 +( y +1.5) /3 *400
    if c =0 then
        col$ ="red"
    else
        if c mod 2 =1 then col$ ="lightgray" else col$ ="white"
    end if
    #w "color "; col$
    #w "set "; xScreen; " "; yScreen
end sub

[quit]
close #w
end

Locomotive Basic

Translation of: QBasic

This program is meant for use in CPCBasic specifically, where it draws a 16-color 640x400 image in less than a minute. (Real CPC hardware would take far longer than that and has lower resolution.)

1 MODE 3    ' Note the CPCBasic-only screen mode!
2 FOR xp = 0 TO 639
3 FOR yp = 0 TO 399
4 x = 0 : y = 0
5 x0 = xp / 213 - 2 : y0 = yp / 200 - 1
6 iteration = 0
7 maxIteration = 100
8 WHILE (x * x + y * y <= (2 * 2) AND iteration < maxIteration)
9 xtemp = x * x - y * y + x0
10 y = 2 * x * y + y0
11 x = xtemp
12 iteration = iteration + 1
13 WEND
14 IF iteration <> maxIteration THEN c = iteration ELSE c = 0
15 PLOT xp, yp, c MOD 16
16 NEXT
17 NEXT

Microsoft Small Basic

GraphicsWindow.Show()
size = 500
half = 250
GraphicsWindow.Width = size * 1.5
GraphicsWindow.Height = size
GraphicsWindow.Title = "Mandelbrot"
For px = 1 To size * 1.5
  x_0 = px/half - 2
  For py = 1 To size
    y_0 = py/half - 1
    x = x_0
    y = y_0
    i = 0
    While(c <= 2 AND i<100)
      x_1 = Math.Power(x, 2) - Math.Power(y, 2) + x_0
      y_1 = 2 * x * y + y_0
      c = Math.Power(Math.Power(x_1, 2) + Math.Power(y_1, 2), 0.5)
      x = x_1
      y = y_1
      i = i + 1
    EndWhile
    If i < 99 Then
      GraphicsWindow.SetPixel(px, py, GraphicsWindow.GetColorFromRGB((255/25)*i, (255/25)*i, (255/5)*i))
    Else 
      GraphicsWindow.SetPixel(px, py, "black")
    EndIf
    c=0
 EndFor
EndFor

Microsoft Super Extended Color BASIC (Tandy Color Computer 3)

1 REM MANDELBROT SET - TANDY COCO 3
2 POKE 65497,1
10 HSCREEN 2
20 HCLS
30 X1=319:Y1=191
40 I1=-1.0:I2=1.0:R1=-2:R2=1.0
50 S1=(R2-R1)/X1:S2=(I2-I1)/Y1
60 FOR Y=0 TO Y1
70 I3=I1+S2*Y
80 FOR X=0 TO X1
90 R3=R1+S1*X:Z1=R3:Z2=I3
100 FOR N=0 TO 30
110 A=Z1*Z1:B=Z2*Z2
120 IF A+B>4.0 GOTO 150
130 Z2=2*Z1*Z2+I3:Z1=A-B+R3
140 NEXT N
150 HSET(X,Y,N-16*INT(N/16))
160 NEXT X
170 NEXT Y
180 GOTO 180

MSX Basic

Works with: MSX BASIC version any
100 SCREEN 2
110 CLS
120 x1 = 256 : y1 = 192
130 i1 = -1 : i2 = 1
140 r1 = -2 : r2 = 1
150 s1 = (r2-r1)/x1 : s2 = (i2-i1)/y1
160 FOR y = 0 TO y1
170   i3 = i1+s2*y
180   FOR x = 0 TO x1
190     r3 = r1+s1*x
200     z1 = r3 : z2 = i3
210     FOR n = 0 TO 30
220       a = z1*z1 : b = z2*z2
230       IF a+b > 4 GOTO 270
240       z2 = 2*z1*z2+i3
250       z1 = a-b+r3
260     NEXT n
270   PSET (x,y),n-16*INT(n/16)
280   NEXT x
290 NEXT y
300 GOTO 300
Output:

Nascom BASIC

Translation of: Sinclair ZX81 BASIC

In fact, it is based on the ZX81 version, but some optimizations are done to shorten the execution time (though they lengthen the code):

  • The variables X2 and Y2 for XA*XA and YA*YA respectively are introduced in order to calculate the squares only once.
  • The value of X does not depend on J, so it is calculated before the FOR J loop.
  • The symmetry of the shape is taken into account in order to calculate symmetric values only once. It is the most significant optimization. The case X=0 (corresponding to the line 22 on the screen grid) is treated separately.

Only a fragment of the shape is drawn because of low resolution of block graphics. Like in the ZX81 version, you can adjust the constants in lines 40 and 70 to zoom in on a particular area, if you like.

Works with: Nascom ROM BASIC version 4.7
10 REM Mandelbrot set
20 CLS
30 FOR I=0 TO 95
40 LET X=(I-78)/48
50 REM ** When X<>0
60 FOR J=1 TO 22
70 LET Y=(22-J)/30
80 LET XA=0:X2=0
90 LET YA=0:Y2=0
100 LET ITER=0
110 LET XTEMP=X2-Y2+X
120 LET YA=2*XA*YA+Y:Y2=YA*YA
130 LET XA=XTEMP:X2=XA*XA
140 LET ITER=ITER+1
150 IF X2+Y2<=4 AND ITER<200 THEN 110
160 IF ITER=200 THEN SET(I,J):SET(I,44-J)
170 NEXT J
180 REM ** When X=0
190 LET XA=0:X2=0
200 LET ITER=0
210 LET XA=X2+X:X2=XA*XA
220 LET ITER=ITER+1
230 IF X2<=4 AND ITER<200 THEN 210
240 IF ITER=200 THEN SET(I,22)
250 NEXT I
290 REM ** Set up machine code INKEY$ command
300 IF PEEK(1)<>0 THEN RESTORE 510
310 DOKE 4100,3328:FOR A=3328 TO 3342 STEP 2
320 READ B:DOKE A,B:NEXT A
400 SCREEN 1,15
410 PRINT "Hit any key to exit.";
420 A=USR(0):IF A<0 THEN 420
430 CLS
440 END
490 REM ** Data for machine code INKEY$
500 DATA 25055,1080,-53,536,-20665,3370,-5664,0
510 DATA 27085,14336,-13564,6399,18178,10927
520 DATA -8179,233

OS/8 BASIC

Works under BASIC on a PDP-8 running OS/8. Various emulators exist including simh's PDP-8 emulator and the PDP-8/E Simulator for Classic Macintosh and OS X.

10 X1=59\Y1=21
20 I1=-1.0\I2=1.0\R1=-2.0\R2=1.0
30 S1=(R2-R1)/X1\S2=(I2-I1)/Y1
40 FOR Y=0 TO Y1
50 I3=I1+S2*Y
60 FOR X=0 TO X1
70 R3=R1+S1*X\Z1=R3\Z2=I3
80 FOR N=0 TO 30
90 A=Z1*Z1\B=Z2*Z2
100 IF A+B>4.0 GOTO 130
110 Z2=2*Z1*Z2+I3\Z1=A-B+R3
120 NEXT N
130 PRINT CHR$(62-N);
140 NEXT X
150 PRINT
160 NEXT Y
170 END
Output:
>>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<===========
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<========
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<=======
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<=====
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<====
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<===
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<==
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<=
><;;;;;;::::9875&      .3                       *9;;;<<<<<<=
>;;;;;;::997564'        '                       8:;;;<<<<<<=
>::988897735/                                 &89:;;;<<<<<<=
>::988897735/                                 &89:;;;<<<<<<=
>;;;;;;::997564'        '                       8:;;;<<<<<<=
><;;;;;;::::9875&      .3                       *9;;;<<<<<<=
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<=
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<==
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<===
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<====
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<=====
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<=======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<========
>>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<===========

PureBasic

PureBasic forum: discussion

EnableExplicit

#Window1   = 0
#Image1    = 0
#ImgGadget = 0

#max_iteration =  64
#width         = 800
#height        = 600
Define.d x0 ,y0 ,xtemp ,cr, ci
Define.i i, n, x, y ,Event ,color

Dim Color.l (255)
For n = 0 To 63
  Color(   0 + n ) = RGB(  n*4+128, 4 * n, 0 )
  Color(  64 + n ) = RGB(  64, 255, 4 * n )
  Color( 128 + n ) = RGB(  64, 255 - 4 * n , 255 )
  Color( 192 + n ) = RGB(  64, 0, 255 - 4 * n )
Next

If OpenWindow(#Window1, 0, 0, #width, #height, "'Mandelbrot set' PureBasic Example", #PB_Window_SystemMenu )
    If CreateImage(#Image1, #width, #height)
       ImageGadget(#ImgGadget, 0, 0, #width, #height, ImageID(#Image1))
       For y.i = 1 To #height -1
         StartDrawing(ImageOutput(#Image1))
         For x.i = 1 To  #width -1
           x0 = 0
           y0 = 0;
           cr = (x / #width)*2.5 -2
           ci = (y / #height)*2.5 -1.25
           i = 0
           While  (x0*x0 + y0*y0 <= 4.0) And i < #max_iteration
             i +1
             xtemp = x0*x0 - y0*y0 + cr
             y0    = 2*x0*y0 + ci
             x0    = xtemp
           Wend
           If i >= #max_iteration
              Plot(x, y,  0 )
           Else
              Plot(x, y,  Color(i & 255))
           EndIf
           
         Next
         StopDrawing()
         SetGadgetState(#ImgGadget, ImageID(#Image1))
         Repeat
           Event = WindowEvent()
           If Event = #PB_Event_CloseWindow
             End
           EndIf
         Until Event = 0 
       Next
    EndIf
    Repeat
      Event = WaitWindowEvent()
    Until Event = #PB_Event_CloseWindow
  EndIf
Example:

QBasic

This is almost exactly the same as the pseudocode from the Wikipedia entry's "For programmers" section (which it's closely based on, of course). The image generated is very blocky ("low-res") due to the selected video mode, but it's fairly accurate.

SCREEN 13
WINDOW (-2, 1.5)-(2, -1.5)
FOR x0 = -2 TO 2 STEP .01
    FOR y0 = -1.5 TO 1.5 STEP .01
        x = 0
        y = 0

        iteration = 0
        maxIteration = 223

        WHILE (x * x + y * y <= (2 * 2) AND iteration < maxIteration)
            xtemp = x * x - y * y + x0
            y = 2 * x * y + y0

            x = xtemp

            iteration = iteration + 1
        WEND

        IF iteration <> maxIteration THEN
            c = iteration
        ELSE
            c = 0
        END IF

        PSET (x0, y0), c + 32
    NEXT
NEXT

Quite BASIC

      
1000 REM Mandelbrot Set Project
1010 REM Quite BASIC Math Project
1015 REM 'http://www.quitebasic.com/prj/math/mandelbrot/
1020 REM ------------------------ 
1030 CLS
1040 PRINT "This program plots a graphical representation of the famous Mandelbrot set.  It takes a while to finish so have patience and don't have too high expectations;  the graphics resolution is not very high on our canvas."
2000 REM Initialize the color palette
2010 GOSUB 3000
2020 REM L is the maximum iterations to try
2030 LET L = 100
2040 FOR I = 0 TO 100
2050 FOR J = 0 TO 100
2060 REM Map from pixel coordinates (I,J) to math (U,V)
2060 LET U = I / 50 - 1.5
2070 LET V = J / 50 - 1
2080 LET X = U
2090 LET Y = V
2100 LET N = 0
2110 REM Inner iteration loop starts here 
2120 LET R = X * X
2130 LET Q = Y * Y
2140 IF R + Q > 4 OR N >= L THEN GOTO 2190
2150 LET Y = 2 * X * Y + V
2160 LET X = R - Q + U
2170 LET N = N + 1
2180 GOTO 2120
2190 REM Compute the color to plot
2200 IF N < 10 THEN LET C = "black" ELSE LET C = P[ROUND(8 * (N-10) / (L-10))]
2210 PLOT I, J, C 
2220 NEXT J
2230 NEXT I
2240 END
3000 REM Subroutine -- Set up Palette
3010 ARRAY P
3020 LET P[0] = "black"
3030 LET P[1] = "magenta"
3040 LET P[2] = "blue"
3050 LET P[3] = "green"
3060 LET P[4] = "cyan"
3070 LET P[5] = "red"
3080 LET P[6] = "orange"
3090 LET P[7] = "yellow"
3090 LET P[8] = "white"
3100 RETURN

Run BASIC

'Mandelbrot V4 for RunBasic
'Based on LibertyBasic solution
'copy the code and go to runbasic.com
'http://rosettacode.org/wiki/Mandelbrot_set#Liberty_BASIC
'May 2015 (updated 29 Apr 2018)
'
'Note - we only get so much processing time on the server, so the
'graph is computed in three or four pieces
'
WindowWidth  = 320  'RunBasic max size 800 x 600
WindowHeight = 320
'print zone -2 to 1 (X)
'print zone -1.5 to 1.5 (Y)  
a = -1.5  'graph -1.5 to -0.75, first "loop" 
b = -0.75  'adjust for max processor time (y0 for loop below)

'open "Mandelbrot Set" for graphics_nsb_nf as #w  not used in RunBasic
 
graphic #w, WindowWidth, WindowHeight
'#w "trapclose [quit]"       not used in RunBasic
'#w "down"                   not used in RunBasic
 
cls 
'#w flush() 
#w cls("black")
render #w
 '#w flush()
input "OK, hit enter to continue"; guess
cls
 
[man_calc]
'3/screen size 3/800 = 0.00375  ** 3/790 = 0.0037974
'3/screen size (y) 3/600 = .005 ** 3/590 = 0.0050847
'3/215 = .0139 .0068 = 3/440
cc = 3/299
'
    for x0 = -2 to 1 step cc    
    for y0 = a to b step  cc 
        x = 0
        y = 0
 
        iteration    =   0
        maxIteration = 255 
 
        while ( ( x *x +y *y) <=4) and ( iteration <maxIteration)
            xtemp      =x *x -y *y +x0
            y          =2 *x *y +y0
            x          = xtemp
            iteration  = iteration + 1
        wend
 
        if iteration <>maxIteration then
            c =iteration
        else
            c =0
        end if
 
        call pSet x0, y0, c
        'scan why scan? (wait for user input) with RunBasic ?
    next
next
 
'#w flush()  'what is flush? RunBasic uses the render command.
render #w
 
input "OK, hit enter to continue"; guess
cls
a = a + 0.75
b = b + 0.75
if b > 1.6 then goto[quit] else goto[man_calc]
 
sub pSet x, y, c
    xScreen = 5+(x +2)   /3 * 300 'need positive screen number
    yScreen = 5+(y +1.5) /3 * 300 'and 5x5 boarder
    if c =0 then
        col$ ="red"
    else
        if c mod 2 =1 then col$ ="lightgray" else col$ ="white"
    end if
    #w "color "; col$
    #w "set "; xScreen; " "; yScreen
end sub
 
[quit]
'cls
print
print "This is a Mandelbrot Graph output from www.runbasic.com" 
render #w
print "All done, good bye."
end

Sinclair ZX81 BASIC

Translation of: QBasic

Requires at least 2k of RAM.

Glacially slow, but does eventually produce a tolerable low-resolution image (screenshot here). You can adjust the constants in lines 30 and 40 to zoom in on a particular area, if you like.

 10 FOR I=0 TO 63
 20 FOR J=43 TO 0 STEP -1
 30 LET X=(I-52)/31
 40 LET Y=(J-22)/31
 50 LET XA=0
 60 LET YA=0
 70 LET ITER=0
 80 LET XTEMP=XA*XA-YA*YA+X
 90 LET YA=2*XA*YA+Y
100 LET XA=XTEMP
110 LET ITER=ITER+1
120 IF XA*XA+YA*YA<=4 AND ITER<200 THEN GOTO 80
130 IF ITER=200 THEN PLOT I, J
140 NEXT J
150 NEXT I

SmileBASIC

Generates the points at random, gradually building up the image.

X = RNDF()*4-2
Y = RNDF()*4-2@N
N = N+16
I = X+S*S-T*T
T = Y+S*T*2
S = I
IF N < #L&&S*S+T*T < 4 GOTO @N
GPSET X*50+99, Y*50+99, RGB(99 XOR N,N,N)
EXEC.

Alternative, based on the QBasic and other BASIC samples.
The 3DS screen is 400 x 240 pixels. SmileBASIC doesn't have +=, -=, etc. but there are INC and DEC statements.

OPTION STRICT
VAR XP, YP, X, Y, X0, Y0, X2, Y2
VAR NEXT_X, IT, C
FOR XP = -200 TO 199
  FOR YP = -120 TO 119
    X = 0: Y = 0
    X0 = XP / 100: Y0 = YP / 100
    IT = 0
    X2 = X * X: Y2 = Y * Y
    WHILE X2 + Y2 <= 4 AND IT < 100
      NEXT_X = X2 - Y2 + X0
      Y = 2 * X * Y + Y0
      X = NEXT_X
      X2 = X * X: Y2 = Y * Y
      INC IT
    WEND
    IF IT == 100 THEN C = 0 ELSE C = IT
    GPSET XP + 200, YP + 120, RGB((C * 3) MOD 200 + 50, FLOOR(C * 1.2) + 20, C)
  NEXT
NEXT

TI-Basic Color

ClrDraw
~2->Xmin:1->Xmax:~1->Ymin:1->Ymax
AxesOff
FnOff 
For(A,~2,1,.034
	For(B,~1,1,.036
		A+B[i]->C
		DelVar Z9->N
		While abs(Z)<=2 and N<24
			Z^^2+C->Z
			N+1->N
		End
		Pt-On(real(C),imag(C),N
	End
End

True BASIC

SET WINDOW 0, 256, 0, 192

LET x1 = 256/2
LET y1 = 192/2
LET i1 = -1
LET i2 = 1
LET r1 = -2
LET r2 = 1
LET s1 = (r2-r1) / x1
LET s2 = (i2-i1) / y1

FOR y = 0 TO y1 STEP .05
    LET i3 = i1 + s2 * y
    FOR x = 0 TO x1 STEP .05
        LET r3 = r1 + s1 * x
        LET z1 = r3
        LET z2 = i3
        FOR n = 0 TO 30
            LET a = z1 * z1
            LET b = z2 * z2
            IF a+b > 4 THEN EXIT FOR
            LET z2 = 2 * z1 * z2 + i3
            LET z1 = a - b + r3
        NEXT n
        SET COLOR n - 16*INT(n/16)
        PLOT POINTS: x,y
    NEXT x
NEXT y
END

Visual BASIC for Applications on Excel

Works with: Excel 2013

Based on the BBC BASIC version. Create a spreadsheet with -2 to 2 in row 1 and -2 to 2 in the A column (in steps of your choosing). In the cell B2, call the function with =mandel(B$1,$A2) and copy the cell to all others in the range. Conditionally format the cells to make the colours pleasing (eg based on values, 3-color scale, min value 2 [colour red], midpoint number 10 [green] and highest value black. Then format the cells with the custom type "";"";"" to remove the numbers.

Function mandel(xi As Double, yi As Double)

maxiter = 256
x = 0
y = 0

For i = 1 To maxiter
    If ((x * x) + (y * y)) > 4 Then Exit For
    xt = xi + ((x * x) - (y * y))
    y = yi + (2 * x * y)
    x = xt
    Next
    
mandel = i
End Function

File:Vbamandel.png Edit: I don't seem to be able to upload the screenshot, so I've shared it here: https://goo.gl/photos/LkezpuQziJPAtdnd9

Yabasic

open window 640, 320
wid = 4
xcenter = -1: ycenter = 0
ms = 0
for xcoord = 0 to 639
   for ycoord = 0 to 160
       ms = 0
       ca =(xcoord-320)/640*wid+xcenter
       cb =(ycoord-160)/640*wid+ycenter
       x = 0: y=0

       for t = 1 to 20
           xnew = x*x-y*y+ca
           ynew = 2*x*y+cb
           x=xnew:y=ynew
           magnitudesquared=x*x+y*y
           ms = magnitudesquared
           if (magnitudesquared > 100) break
           //if(magnitudesquared < 100) then : color 0,0,0 : dot xcoord, ycoord : end if
       next t
       ms = ms+1
       if(ms > 250) then
       	    color 32,64,mod(ms,255)
            dot xcoord, ycoord
            dot xcoord, 320- ycoord
        elseif (ms > 150) then
            color mod(ms,255),64,32
            dot xcoord, ycoord
            dot xcoord, 320-ycoord
        else
            color 0,0,0
            dot xcoord, ycoord
            dot xcoord, 320-ycoord
        end if
    next ycoord
next xcoord

Befunge

Using 14-bit fixed point arithmetic for simplicity and portability. It should work in most interpreters, but the exact output is implementation dependent, and some will be unbearably slow.

X scale is (-2.0, 0.5); Y scale is (-1, 1); Max iterations 94 with the ASCII character set as the "palette".

0>:00p58*`#@_0>:01p78vv$$<
@^+1g00,+55_v# !`\+*9<>4v$
@v30p20"?~^"< ^+1g10,+*8<$
@>p0\>\::*::882**02g*0v >^
`*:*" d":+*:-*"[Z"+g3 < |<
v-*"[Z"+g30*g20**288\--\<#
>2**5#>8*:*/00g"P"*58*:*v^
v*288 p20/**288:+*"[Z"+-<:
>*%03 p58*:*/01g"3"* v>::^
   \_^#!:-1\+-*2*:*85<^
Output:
}}}}}}}}}|||||||{{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzyyyyxwusjuthwyzzzzzzz{{{{{{{
}}}}}}}}|||||||{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzyyyyxwwvtqptvwxyyzzzzzzz{{{{{
}}}}}}}||||||{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzzyyyyxwvuqaZlnvwxyyyzzzzzzz{{{{
}}}}}}|||||{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzzyyyyxxvqXp^g Ynslvxyyyyyzzzzz{{{
}}}}}}||||{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzzyyyxxxxwvtp      6puwxyyyyyyzzzz{{
}}}}}||||{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzyyyxxxxxwwvvqc      &8uvwxxxyyyyyzzz{
}}}}|||{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzyyyywwvtvvvvuutsp      Hrtuuvwxxxxwqxyzz
}}}}||{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzyyyyyxwvqemrttj m id+    PRUiPp_rvvvvudwxyz
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}}}||{{{{{{{{{{{{{{{{{{{zzzzyyyyyyyyyyxxxwvusg                        N  Uquxyy
}}||{{{{{{{{{{{{{{{{{zzzzyyyyyyyyyyyxxxxwvrrrkC                          grwxxy
}}|{{{{{{{{{{{{{{{zzzzyxxxxxyyyyyxxxxxwwukM!f                            ptvwxy
}}|{{{{{{{{{{zzzzzzyyxwsuwwwwwwwwwwwwwvvurn[                              ptuox
}|{{{{{{{zzzzzzzzyyyxxvptuuvvumsuvvvvvvu`                                   hjx
}|{{{{zzzzzzzzzyyyyyxxwusogoqsqg]pptuuttlc                                 ntwx
}{{{zzzzzzzzzyyyyyyxxwwuto  -    O jpssrO                                  nsvx
}{{zzzzzzzzzyyyyyyxwwwvrrT4          TonR                                  Ufwy
}{zzzzzzzzyyyyyxxwttuutqe             Dj                                   $uxy
}zzzzzzzzyxxxxxwwvuppnpn               `                                   twxy
}yyyxxwvwwwxwvvvrtppc  Y                                                 auwxxy
                                                                       dqtvwxyy
}yyyxxwvwwwxwvvvrtppc  Y                                                 auwxxy
}zzzzzzzzyxxxxxwwvuppnpn               `                                   twxy
}{zzzzzzzzyyyyyxxwttuutqe             Dj                                   $uxy
}{{zzzzzzzzzyyyyyyxwwwvrrT4          TonR                                  Ufwy
}{{{zzzzzzzzzyyyyyyxxwwuto  -    O jpssrO                                  nsvx
}|{{{{zzzzzzzzzyyyyyxxwusogoqsqg]pptuuttlc                                 ntwx
}|{{{{{{{zzzzzzzzyyyxxvptuuvvumsuvvvvvvu`                                   hjx
}}|{{{{{{{{{{zzzzzzyyxwsuwwwwwwwwwwwwwvvurn[                              ptuox
}}|{{{{{{{{{{{{{{{zzzzyxxxxxyyyyyxxxxxwwukM!f                            ptvwxy
}}||{{{{{{{{{{{{{{{{{zzzzyyyyyyyyyyyxxxxwvrrrkC                          grwxxy
}}}||{{{{{{{{{{{{{{{{{{{zzzzyyyyyyyyyyxxxwvusg                        N  Uquxyy
}}}||{{{{{{{{{{{{{{{{{{{{{zzzzzzyyyyyyyxxxwurf  ZnW                4nrslnobgwyy
}}}}||{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzyyyyyxwvqemrttj m id+    PRUiPp_rvvvvudwxyz
}}}}|||{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzyyyywwvtvvvvuutsp      Hrtuuvwxxxxwqxyzz
}}}}}||||{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzyyyxxxxxwwvvqc      &8uvwxxxyyyyyzzz{
}}}}}}||||{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzzyyyxxxxwvtp      6puwxyyyyyyzzzz{{
}}}}}}|||||{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzzyyyyxxvqXp^g Ynslvxyyyyyzzzzz{{{
}}}}}}}||||||{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzzyyyyxwvuqaZlnvwxyyyzzzzzzz{{{{
}}}}}}}}|||||||{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzyyyyxwwvtqptvwxyyzzzzzzz{{{{{
}}}}}}}}}|||||||{{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzyyyyxwusjuthwyzzzzzzz{{{{{{{

Brace

This is a simple Mandelbrot plotter. A longer version based on this smooths colors, and avoids calculating the time-consuming black pixels: http://sam.ai.ki/brace/examples/mandelbrot.d/1

#!/usr/bin/env bx
use b

Main():
	num outside = 16, ox = -0.5, oy = 0, r = 1.5
	long i, max_i = 100, rb_i = 30
	space()
	uint32_t *px = pixel()
	num d = 2*r/h, x0 = ox-d*w_2, y0 = oy+d*h_2
	for(y, 0, h):
		cmplx c = x0 + (y0-d*y)*I
		repeat(w):
			cmplx w = 0
			for i=0; i < max_i && cabs(w) < outside; ++i
				w = w*w + c
			*px++ = i < max_i ? rainbow(i*359 / rb_i % 360) : black
			c += d

An example plot from the longer version:

Brainf***

     A mandelbrot set fractal viewer in brainf*ck written by Erik Bosman
+++++++++++++[->++>>>+++++>++>+<<<<<<]>>>>>++++++>--->>>>>>>>>>+++++++++++++++[[
>>>>>>>>>]+[<<<<<<<<<]>>>>>>>>>-]+[>>>>>>>>[-]>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>[-]+
<<<<<<<+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>>>+>>>>>>>>>>>>>>>>>>>>>>>>>>
>+<<<<<<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+[>>>>>>[>>>>>>>[-]>>]<<<<<<<<<[<<<<<<<<<]>>
>>>>>[-]+<<<<<<++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>>+<<<<<<+++++++[-[->>>
>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>>+<<<<<<<<<<<<<<<<[<<<<<<<<<]>>>[[-]>>>>>>[>>>>>
>>[-<<<<<<+>>>>>>]<<<<<<[->>>>>>+<<+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>
[>>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<+<<]>>>>>>>>]<<<<<<<<<[<<<<<<<
<<]>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<<<]>>>>>>>>>+++++++++++++++[[
>>>>>>>>>]+>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[
>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>[-<<<<+>>>>]<<<<[->>>>+<<<<<[->>[
-<<+>>]<<[->>+>>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<
<<[>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<
[>[-]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+<<<<<<<<<]>>>>>
>>>>[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+
<<<<<<[->>>[-<<<+>>>]<<<[->>>+>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>
>>>>>>>]<<<<<<<<<[>>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<<]>>[->>>>>>>>>+<<<<<<<<<]<<
+>>>>>>>>]<<<<<<<<<[>[-]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<
<]<+<<<<<<<<<]>>>>>>>>>[>>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>
>>>>>]<<<<<<<<<-<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+>>>>>>>>>>>>>>>>>>>>>+<<<[<<<<<<
<<<]>>>>>>>>>[>>>[-<<<->>>]+<<<[->>>->[-<<<<+>>>>]<<<<[->>>>+<<<<<<<<<<<<<[<<<<<
<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>[-<<<<->>>>]+<<<<[->>>>-<[-<<<+>>>]<<<[->
>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<
<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]<<<<<<<[->+>>>-<<<<]>>>>>>>>>+++++++++++++++++++
+++++++>>[-<<<<+>>>>]<<<<[->>>>+<<[-]<<]>>[<<<<<<<+<[-<+>>>>+<<[-]]>[-<<[->+>>>-
<<<<]>>>]>>>>>>>>>>>>>[>>[-]>[-]>[-]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-]>>>>>>[>>>>>
[-<<<<+>>>>]<<<<[->>>>+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>[-<<<<<<<<
<+>>>>>>>>>]>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>>>>>>]+>[-
]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[>+>>>>>>>>]<<<
<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<<<[->>[-<<+>>]<
<[->>+>+<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>[->>>>
>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[>[-]<->>>
[-<<<+>[<->-<<<<<<<+>>>>>>>]<[->+<]>>>]<<[->>+<<]<+<<<<<<<<<]>>>>>>>>>[>>>>>>[-<
<<<<+>>>>>]<<<<<[->>>>>+<<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>+>>>>>>>>
]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<<<[->>[-<<+
>>]<<[->>+>>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>
[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[>[-
]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+<<<<<<<<<]>>>>>>>>>
[>>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>]>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>++++++++
+++++++[[>>>>>>>>>]<<<<<<<<<-<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[>>>>>>>>[-<<<<<<<+
>>>>>>>]<<<<<<<[->>>>>>>+<<<<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>>[
-]>>>]<<<<<<<<<[<<<<<<<<<]>>>>+>[-<-<<<<+>>>>>]>[-<<<<<<[->>>>>+<++<<<<]>>>>>[-<
<<<<+>>>>>]<->+>]<[->+<]<<<<<[->>>>>+<<<<<]>>>>>>[-]<<<<<<+>>>>[-<<<<->>>>]+<<<<
[->>>>->>>>>[>>[-<<->>]+<<[->>->[-<<<+>>>]<<<[->>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]
+>>>>>>[>>>>>>>>>]>+<]]+>>>[-<<<->>>]+<<<[->>>-<[-<<+>>]<<[->>+<<<<<<<<<<<[<<<<<
<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<<<
[<<<<<<<<<]>>>>[-<<<<+>>>>]<<<<[->>>>+>>>>>[>+>>[-<<->>]<<[->>+<<]>>>>>>>>]<<<<<
<<<+<[>[->>>>>+<<<<[->>>>-<<<<<<<<<<<<<<+>>>>>>>>>>>[->>>+<<<]<]>[->>>-<<<<<<<<<
<<<<<+>>>>>>>>>>>]<<]>[->>>>+<<<[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>>+<<<]<<
<<<<<<<<<<]>>>>[-]<<<<]>>>[-<<<+>>>]<<<[->>>+>>>>>>[>+>[-<->]<[->+<]>>>>>>>>]<<<
<<<<<+<[>[->>>>>+<<<[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>[->>>>+<<<<]>]<[->>>>-<<<<<<<
<<<<<<<+>>>>>>>>>>]<]>>[->>>+<<<<[->>>>-<<<<<<<<<<<<<<+>>>>>>>>>>]>]<[->>>>+<<<<
]<<<<<<<<<<<]>>>>>>+<<<<<<]]>>>>[-<<<<+>>>>]<<<<[->>>>+>>>>>[>>>>>>>>>]<<<<<<<<<
[>[->>>>>+<<<<[->>>>-<<<<<<<<<<<<<<+>>>>>>>>>>>[->>>+<<<]<]>[->>>-<<<<<<<<<<<<<<
+>>>>>>>>>>>]<<]>[->>>>+<<<[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>>+<<<]<<<<<<<
<<<<<]]>[-]>>[-]>[-]>>>>>[>>[-]>[-]>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>[-<
<<<+>>>>]<<<<[->>>>+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[
[>>>>>>>>>]+>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+
[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>[-<<<<+>>>>]<<<<[->>>>+<<<<<[->>
[-<<+>>]<<[->>+>+<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<
<[>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[
>[-]<->>>[-<<<+>[<->-<<<<<<<+>>>>>>>]<[->+<]>>>]<<[->>+<<]<+<<<<<<<<<]>>>>>>>>>[
>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>]>
>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>[-]>>>>+++++++++++++++[[>>>>>>>>>]<<<<<<<<<-<<<<<
<<<<[<<<<<<<<<]>>>>>>>>>-]+[>>>[-<<<->>>]+<<<[->>>->[-<<<<+>>>>]<<<<[->>>>+<<<<<
<<<<<<<<[<<<<<<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>[-<<<<->>>>]+<<<<[->>>>-<[-
<<<+>>>]<<<[->>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>
>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-<<<+>>>]<<<[->>>+>>>>>>[>+>>>
[-<<<->>>]<<<[->>>+<<<]>>>>>>>>]<<<<<<<<+<[>[->+>[-<-<<<<<<<<<<+>>>>>>>>>>>>[-<<
+>>]<]>[-<<-<<<<<<<<<<+>>>>>>>>>>>>]<<<]>>[-<+>>[-<<-<<<<<<<<<<+>>>>>>>>>>>>]<]>
[-<<+>>]<<<<<<<<<<<<<]]>>>>[-<<<<+>>>>]<<<<[->>>>+>>>>>[>+>>[-<<->>]<<[->>+<<]>>
>>>>>>]<<<<<<<<+<[>[->+>>[-<<-<<<<<<<<<<+>>>>>>>>>>>[-<+>]>]<[-<-<<<<<<<<<<+>>>>
>>>>>>>]<<]>>>[-<<+>[-<-<<<<<<<<<<+>>>>>>>>>>>]>]<[-<+>]<<<<<<<<<<<<]>>>>>+<<<<<
]>>>>>>>>>[>>>[-]>[-]>[-]>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-]>[-]>>>>>[>>>>>>>[-<<<<<
<+>>>>>>]<<<<<<[->>>>>>+<<<<+<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>+>[-<-<<<<+>>>>
>]>>[-<<<<<<<[->>>>>+<++<<<<]>>>>>[-<<<<<+>>>>>]<->+>>]<<[->>+<<]<<<<<[->>>>>+<<
<<<]+>>>>[-<<<<->>>>]+<<<<[->>>>->>>>>[>>>[-<<<->>>]+<<<[->>>-<[-<<+>>]<<[->>+<<
<<<<<<<<<[<<<<<<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>[-<<->>]+<<[->>->[-<<<+>>>]<
<<[->>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<
<<<<<<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-<<<+>>>]<<<[->>>+>>>>>>[>+>[-<->]<[->+
<]>>>>>>>>]<<<<<<<<+<[>[->>>>+<<[->>-<<<<<<<<<<<<<+>>>>>>>>>>[->>>+<<<]>]<[->>>-
<<<<<<<<<<<<<+>>>>>>>>>>]<]>>[->>+<<<[->>>-<<<<<<<<<<<<<+>>>>>>>>>>]>]<[->>>+<<<
]<<<<<<<<<<<]>>>>>[-]>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<<<]]>>>>[-<<<<+>
>>>]<<<<[->>>>+>>>>>[>+>>[-<<->>]<<[->>+<<]>>>>>>>>]<<<<<<<<+<[>[->>>>+<<<[->>>-
<<<<<<<<<<<<<+>>>>>>>>>>>[->>+<<]<]>[->>-<<<<<<<<<<<<<+>>>>>>>>>>>]<<]>[->>>+<<[
->>-<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>+<<]<<<<<<<<<<<<]]>>>>[-]<<<<]>>>>[-<<<<+>>
>>]<<<<[->>>>+>[-]>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<<<]>>>>>>>>>[>>>>>>
>>>]<<<<<<<<<[>[->>>>+<<<[->>>-<<<<<<<<<<<<<+>>>>>>>>>>>[->>+<<]<]>[->>-<<<<<<<<
<<<<<+>>>>>>>>>>>]<<]>[->>>+<<[->>-<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>+<<]<<<<<<<<
<<<<]]>>>>>>>>>[>>[-]>[-]>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-]>[-]>>>>>[>>>>>[-<<<<+
>>>>]<<<<[->>>>+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>>[-<<<<<+>>>>>
]<<<<<[->>>>>+<<<+<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>
>>>>>]+>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[>+>>
>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>[-<<<<+>>>>]<<<<[->>>>+<<<<<[->>[-<<+
>>]<<[->>+>>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>
[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[>[-
]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+<<<<<<<<<]>>>>>>>>>
[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<
<<[->>>[-<<<+>>>]<<<[->>>+>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>
>>>]<<<<<<<<<[>>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<<]>>[->>>>>>>>>+<<<<<<<<<]<<+>>>
>>>>>]<<<<<<<<<[>[-]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+
<<<<<<<<<]>>>>>>>>>[>>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>>>>>
>]<<<<<<<<<-<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+>>>>>>>>>>>>>>>>>>>>>+<<<[<<<<<<<<<]
>>>>>>>>>[>>>[-<<<->>>]+<<<[->>>->[-<<<<+>>>>]<<<<[->>>>+<<<<<<<<<<<<<[<<<<<<<<<
]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>[-<<<<->>>>]+<<<<[->>>>-<[-<<<+>>>]<<<[->>>+<
<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>
>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>->>[-<<<<+>>>>]<<<<[->>>>+<<[-]<<]>>]<<+>>>>[-<<<<
->>>>]+<<<<[->>>>-<<<<<<.>>]>>>>[-<<<<<<<.>>>>>>>]<<<[-]>[-]>[-]>[-]>[-]>[-]>>>[
>[-]>[-]>[-]>[-]>[-]>[-]>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>[-]>>>>]<<<<<<<<<
[<<<<<<<<<]>+++++++++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>+>>>>>>>>>+<<<<<<<<
<<<<<<[<<<<<<<<<]>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+[-]>>[>>>>>>>>>]<<<<<
<<<<[>>>>>>>[-<<<<<<+>>>>>>]<<<<<<[->>>>>>+<<<<<<<[<<<<<<<<<]>>>>>>>[-]+>>>]<<<<
<<<<<<]]>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+>>[>+>>>>[-<<<<->>>>]<<<<[->>>
>+<<<<]>>>>>>>>]<<+<<<<<<<[>>>>>[->>+<<]<<<<<<<<<<<<<<]>>>>>>>>>[>>>>>>>>>]<<<<<
<<<<[>[-]<->>>>>>>[-<<<<<<<+>[<->-<<<+>>>]<[->+<]>>>>>>>]<<<<<<[->>>>>>+<<<<<<]<
+<<<<<<<<<]>>>>>>>-<<<<[-]+<<<]+>>>>>>>[-<<<<<<<->>>>>>>]+<<<<<<<[->>>>>>>->>[>>
>>>[->>+<<]>>>>]<<<<<<<<<[>[-]<->>>>>>>[-<<<<<<<+>[<->-<<<+>>>]<[->+<]>>>>>>>]<<
<<<<[->>>>>>+<<<<<<]<+<<<<<<<<<]>+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>+<<<
<<[<<<<<<<<<]>>>>>>>>>[>>>>>[-<<<<<->>>>>]+<<<<<[->>>>>->>[-<<<<<<<+>>>>>>>]<<<<
<<<[->>>>>>>+<<<<<<<<<<<<<<<<[<<<<<<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>>>>[-<
<<<<<<->>>>>>>]+<<<<<<<[->>>>>>>-<<[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<<<<<<<<<<<[<<<
<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<
<<[<<<<<<<<<]>>>>[-]<<<+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>-<<<<<[<<<<<<<
<<]]>>>]<<<<.>>>>>>>>>>[>>>>>>[-]>>>]<<<<<<<<<[<<<<<<<<<]>++++++++++[-[->>>>>>>>
>+<<<<<<<<<]>>>>>>>>>]>>>>>+>>>>>>>>>+<<<<<<<<<<<<<<<[<<<<<<<<<]>>>>>>>>[-<<<<<<
<<+>>>>>>>>]<<<<<<<<[->>>>>>>>+[-]>[>>>>>>>>>]<<<<<<<<<[>>>>>>>>[-<<<<<<<+>>>>>>
>]<<<<<<<[->>>>>>>+<<<<<<<<[<<<<<<<<<]>>>>>>>>[-]+>>]<<<<<<<<<<]]>>>>>>>>[-<<<<<
<<<+>>>>>>>>]<<<<<<<<[->>>>>>>>+>[>+>>>>>[-<<<<<->>>>>]<<<<<[->>>>>+<<<<<]>>>>>>
>>]<+<<<<<<<<[>>>>>>[->>+<<]<<<<<<<<<<<<<<<]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>[-]<-
>>>>>>>>[-<<<<<<<<+>[<->-<<+>>]<[->+<]>>>>>>>>]<<<<<<<[->>>>>>>+<<<<<<<]<+<<<<<<
<<<]>>>>>>>>-<<<<<[-]+<<<]+>>>>>>>>[-<<<<<<<<->>>>>>>>]+<<<<<<<<[->>>>>>>>->[>>>
>>>[->>+<<]>>>]<<<<<<<<<[>[-]<->>>>>>>>[-<<<<<<<<+>[<->-<<+>>]<[->+<]>>>>>>>>]<<
<<<<<[->>>>>>>+<<<<<<<]<+<<<<<<<<<]>+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>
+>>>>>>>>>>>>>>>>>>>>>>>>>>>+<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>>[-<<<<<<->>>>>>]+<
<<<<<[->>>>>>->>[-<<<<<<<<+>>>>>>>>]<<<<<<<<[->>>>>>>>+<<<<<<<<<<<<<<<<<[<<<<<<<
<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>>>>>[-<<<<<<<<->>>>>>>>]+<<<<<<<<[->>>>>>>>
-<<[-<<<<<<+>>>>>>]<<<<<<[->>>>>>+<<<<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>
>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>[-]<<<++++
+[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>->>>>>>>>>>>>>>>>>>>>>>>>>>>-<<<<<<[<<<<
<<<<<]]>>>]
Output:
AAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDEGFFEEEEDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAAAAABBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDEEEFGIIGFFEEEDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEEEFFFI KHGGGHGEDDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAABBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEEFFGHIMTKLZOGFEEDDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAABBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEEEFGGHHIKPPKIHGFFEEEDDDDDDDDDCCCCCCCCCCBBBBBBBBBBBBBBBBBB
AAAAAAAAAABBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEEFFGHIJKS  X KHHGFEEEEEDDDDDDDDDCCCCCCCCCCBBBBBBBBBBBBBBBB
AAAAAAAAABBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEEFFGQPUVOTY   ZQL[MHFEEEEEEEDDDDDDDCCCCCCCCCCCBBBBBBBBBBBBBB
AAAAAAAABBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEFFFFFGGHJLZ         UKHGFFEEEEEEEEDDDDDCCCCCCCCCCCCBBBBBBBBBBBB
AAAAAAABBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEFFFFFFGGGGHIKP           KHHGGFFFFEEEEEEDDDDDCCCCCCCCCCCBBBBBBBBBBB
AAAAAAABBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEEEEFGGHIIHHHHHIIIJKMR        VMKJIHHHGFFFFFFGSGEDDDDCCCCCCCCCCCCBBBBBBBBB
AAAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDEEEEEEFFGHK   MKJIJO  N R  X      YUSR PLV LHHHGGHIOJGFEDDDCCCCCCCCCCCCBBBBBBBB
AAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDEEEEEEEEEFFFFGH O    TN S                       NKJKR LLQMNHEEDDDCCCCCCCCCCCCBBBBBBB
AAAAABBCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDEEEEEEEEEEEEFFFFFGHHIN                                 Q     UMWGEEEDDDCCCCCCCCCCCCBBBBBB
AAAABBCCCCCCCCCCCCCCCCCCCCCCCCCDDDDEEEEEEEEEEEEEEEFFFFFFGHIJKLOT                                     [JGFFEEEDDCCCCCCCCCCCCCBBBBB
AAAABCCCCCCCCCCCCCCCCCCCCCCDDDDEEEEEEEEEEEEEEEEFFFFFFGGHYV RQU                                     QMJHGGFEEEDDDCCCCCCCCCCCCCBBBB
AAABCCCCCCCCCCCCCCCCCDDDDDDDEEFJIHFFFFFFFFFFFFFFGGGGGGHIJN                                            JHHGFEEDDDDCCCCCCCCCCCCCBBB
AAABCCCCCCCCCCCDDDDDDDDDDEEEEFFHLKHHGGGGHHMJHGGGGGGHHHIKRR                                           UQ L HFEDDDDCCCCCCCCCCCCCCBB
AABCCCCCCCCDDDDDDDDDDDEEEEEEFFFHKQMRKNJIJLVS JJKIIIIIIJLR                                               YNHFEDDDDDCCCCCCCCCCCCCBB
AABCCCCCDDDDDDDDDDDDEEEEEEEFFGGHIJKOU  O O   PR LLJJJKL                                                OIHFFEDDDDDCCCCCCCCCCCCCCB
AACCCDDDDDDDDDDDDDEEEEEEEEEFGGGHIJMR              RMLMN                                                 NTFEEDDDDDDCCCCCCCCCCCCCB
AACCDDDDDDDDDDDDEEEEEEEEEFGGGHHKONSZ                QPR                                                NJGFEEDDDDDDCCCCCCCCCCCCCC
ABCDDDDDDDDDDDEEEEEFFFFFGIPJIIJKMQ                   VX                                                 HFFEEDDDDDDCCCCCCCCCCCCCC
ACDDDDDDDDDDEFFFFFFFGGGGHIKZOOPPS                                                                      HGFEEEDDDDDDCCCCCCCCCCCCCC
ADEEEEFFFGHIGGGGGGHHHHIJJLNY                                                                        TJHGFFEEEDDDDDDDCCCCCCCCCCCCC
A                                                                                                 PLJHGGFFEEEDDDDDDDCCCCCCCCCCCCC
ADEEEEFFFGHIGGGGGGHHHHIJJLNY                                                                        TJHGFFEEEDDDDDDDCCCCCCCCCCCCC
ACDDDDDDDDDDEFFFFFFFGGGGHIKZOOPPS                                                                      HGFEEEDDDDDDCCCCCCCCCCCCCC
ABCDDDDDDDDDDDEEEEEFFFFFGIPJIIJKMQ                   VX                                                 HFFEEDDDDDDCCCCCCCCCCCCCC
AACCDDDDDDDDDDDDEEEEEEEEEFGGGHHKONSZ                QPR                                                NJGFEEDDDDDDCCCCCCCCCCCCCC
AACCCDDDDDDDDDDDDDEEEEEEEEEFGGGHIJMR              RMLMN                                                 NTFEEDDDDDDCCCCCCCCCCCCCB
AABCCCCCDDDDDDDDDDDDEEEEEEEFFGGHIJKOU  O O   PR LLJJJKL                                                OIHFFEDDDDDCCCCCCCCCCCCCCB
AABCCCCCCCCDDDDDDDDDDDEEEEEEFFFHKQMRKNJIJLVS JJKIIIIIIJLR                                               YNHFEDDDDDCCCCCCCCCCCCCBB
AAABCCCCCCCCCCCDDDDDDDDDDEEEEFFHLKHHGGGGHHMJHGGGGGGHHHIKRR                                           UQ L HFEDDDDCCCCCCCCCCCCCCBB
AAABCCCCCCCCCCCCCCCCCDDDDDDDEEFJIHFFFFFFFFFFFFFFGGGGGGHIJN                                            JHHGFEEDDDDCCCCCCCCCCCCCBBB
AAAABCCCCCCCCCCCCCCCCCCCCCCDDDDEEEEEEEEEEEEEEEEFFFFFFGGHYV RQU                                     QMJHGGFEEEDDDCCCCCCCCCCCCCBBBB
AAAABBCCCCCCCCCCCCCCCCCCCCCCCCCDDDDEEEEEEEEEEEEEEEFFFFFFGHIJKLOT                                     [JGFFEEEDDCCCCCCCCCCCCCBBBBB
AAAAABBCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDEEEEEEEEEEEEFFFFFGHHIN                                 Q     UMWGEEEDDDCCCCCCCCCCCCBBBBBB
AAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDEEEEEEEEEFFFFGH O    TN S                       NKJKR LLQMNHEEDDDCCCCCCCCCCCCBBBBBBB
AAAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDEEEEEEFFGHK   MKJIJO  N R  X      YUSR PLV LHHHGGHIOJGFEDDDCCCCCCCCCCCCBBBBBBBB
AAAAAAABBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEEEEFGGHIIHHHHHIIIJKMR        VMKJIHHHGFFFFFFGSGEDDDDCCCCCCCCCCCCBBBBBBBBB
AAAAAAABBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEFFFFFFGGGGHIKP           KHHGGFFFFEEEEEEDDDDDCCCCCCCCCCCBBBBBBBBBBB
AAAAAAAABBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEFFFFFGGHJLZ         UKHGFFEEEEEEEEDDDDDCCCCCCCCCCCCBBBBBBBBBBBB
AAAAAAAAABBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEEFFGQPUVOTY   ZQL[MHFEEEEEEEDDDDDDDCCCCCCCCCCCBBBBBBBBBBBBBB
AAAAAAAAAABBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEEFFGHIJKS  X KHHGFEEEEEDDDDDDDDDCCCCCCCCCCBBBBBBBBBBBBBBBB
AAAAAAAAAAABBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEEEFGGHHIKPPKIHGFFEEEDDDDDDDDDCCCCCCCCCCBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAABBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEEFFGHIMTKLZOGFEEDDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEEEFFFI KHGGGHGEDDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAAAAABBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDEEEFGIIGFFEEEDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBB

C

PPM non interactive

Here is one file program. It directly creates ppm file.

 /* 
 c program:
 --------------------------------
  1. draws Mandelbrot set for Fc(z)=z*z +c
  using Mandelbrot algorithm ( boolean escape time )
 -------------------------------         
 2. technique of creating ppm file is  based on the code of Claudio Rocchini
 http://en.wikipedia.org/wiki/Image:Color_complex_plot.jpg
 create 24 bit color graphic file ,  portable pixmap file = PPM 
 see http://en.wikipedia.org/wiki/Portable_pixmap
 to see the file use external application ( graphic viewer)
  */
 #include <stdio.h>
 #include <math.h>
 int main()
 {
          /* screen ( integer) coordinate */
        int iX,iY;
        const int iXmax = 800; 
        const int iYmax = 800;
        /* world ( double) coordinate = parameter plane*/
        double Cx,Cy;
        const double CxMin=-2.5;
        const double CxMax=1.5;
        const double CyMin=-2.0;
        const double CyMax=2.0;
        /* */
        double PixelWidth=(CxMax-CxMin)/iXmax;
        double PixelHeight=(CyMax-CyMin)/iYmax;
        /* color component ( R or G or B) is coded from 0 to 255 */
        /* it is 24 bit color RGB file */
        const int MaxColorComponentValue=255; 
        FILE * fp;
        char *filename="new1.ppm";
        char *comment="# ";/* comment should start with # */
        static unsigned char color[3];
        /* Z=Zx+Zy*i  ;   Z0 = 0 */
        double Zx, Zy;
        double Zx2, Zy2; /* Zx2=Zx*Zx;  Zy2=Zy*Zy  */
        /*  */
        int Iteration;
        const int IterationMax=200;
        /* bail-out value , radius of circle ;  */
        const double EscapeRadius=2;
        double ER2=EscapeRadius*EscapeRadius;
        /*create new file,give it a name and open it in binary mode  */
        fp= fopen(filename,"wb"); /* b -  binary mode */
        /*write ASCII header to the file*/
        fprintf(fp,"P6\n %s\n %d\n %d\n %d\n",comment,iXmax,iYmax,MaxColorComponentValue);
        /* compute and write image data bytes to the file*/
        for(iY=0;iY<iYmax;iY++)
        {
             Cy=CyMin + iY*PixelHeight;
             if (fabs(Cy)< PixelHeight/2) Cy=0.0; /* Main antenna */
             for(iX=0;iX<iXmax;iX++)
             {         
                        Cx=CxMin + iX*PixelWidth;
                        /* initial value of orbit = critical point Z= 0 */
                        Zx=0.0;
                        Zy=0.0;
                        Zx2=Zx*Zx;
                        Zy2=Zy*Zy;
                        /* */
                        for (Iteration=0;Iteration<IterationMax && ((Zx2+Zy2)<ER2);Iteration++)
                        {
                            Zy=2*Zx*Zy + Cy;
                            Zx=Zx2-Zy2 +Cx;
                            Zx2=Zx*Zx;
                            Zy2=Zy*Zy;
                        };
                        /* compute  pixel color (24 bit = 3 bytes) */
                        if (Iteration==IterationMax)
                        { /*  interior of Mandelbrot set = black */
                           color[0]=0;
                           color[1]=0;
                           color[2]=0;                           
                        }
                     else 
                        { /* exterior of Mandelbrot set = white */
                             color[0]=255; /* Red*/
                             color[1]=255;  /* Green */ 
                             color[2]=255;/* Blue */
                        };
                        /*write color to the file*/
                        fwrite(color,1,3,fp);
                }
        }
        fclose(fp);
        return 0;
 }

PPM Interactive

Infinitely zoomable OpenGL program. Adjustable colors, max iteration, black and white, screen dump, etc. Compile with gcc mandelbrot.c -lglut -lGLU -lGL -lm

  • OpenBSD users, install freeglut package, and compile with make mandelbrot CPPFLAGS='-I/usr/local/include `pkg-config glu --cflags`' LDLIBS='-L/usr/local/lib -lglut `pkg-config glu --libs` -lm'
Library: GLUT

The following version should work on architectures (such as x86/x86-64) that allow unaligned pointers.

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <GL/glut.h>
#include <GL/gl.h>
#include <GL/glu.h>
 
void set_texture();
 
typedef struct {unsigned char r, g, b;} rgb_t;
rgb_t **tex = 0;
int gwin;
GLuint texture;
int width, height;
int tex_w, tex_h;
double scale = 1./256;
double cx = -.6, cy = 0;
int color_rotate = 0;
int saturation = 1;
int invert = 0;
int max_iter = 256;
 
void render()
{
	double	x = (double)width /tex_w,
		y = (double)height/tex_h;
 
	glClear(GL_COLOR_BUFFER_BIT);
	glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_REPLACE);
 
	glBindTexture(GL_TEXTURE_2D, texture);
 
	glBegin(GL_QUADS);
 
	glTexCoord2f(0, 0); glVertex2i(0, 0);
	glTexCoord2f(x, 0); glVertex2i(width, 0);
	glTexCoord2f(x, y); glVertex2i(width, height);
	glTexCoord2f(0, y); glVertex2i(0, height);
 
	glEnd();
 
	glFlush();
	glFinish();
}
 
int dump = 1;
void screen_dump()
{
	char fn[100];
	int i;
	sprintf(fn, "screen%03d.ppm", dump++);
	FILE *fp = fopen(fn, "w");
	fprintf(fp, "P6\n%d %d\n255\n", width, height);
	for (i = height - 1; i >= 0; i--)
		fwrite(tex[i], 1, width * 3, fp);
	fclose(fp);
	printf("%s written\n", fn);
}
 
void keypress(unsigned char key, int x, int y)
{
	switch(key) {
	case 'q':	glFinish();
			glutDestroyWindow(gwin);
			return;
	case 27:	scale = 1./256; cx = -.6; cy = 0; break;
 
	case 'r':	color_rotate = (color_rotate + 1) % 6;
			break;
 
	case '>': case '.':
			max_iter += 128;
			if (max_iter > 1 << 15) max_iter = 1 << 15;
			printf("max iter: %d\n", max_iter);
			break;
 
	case '<': case ',':
			max_iter -= 128;
			if (max_iter < 128) max_iter = 128;
			printf("max iter: %d\n", max_iter);
			break;
 
	case 'c':	saturation = 1 - saturation;
			break;
 
	case 's':	screen_dump(); return;
	case 'z':	max_iter = 4096; break;
	case 'x':	max_iter = 128; break;
	case ' ':	invert = !invert;
	}
	set_texture();
}
 
void hsv_to_rgb(int hue, int min, int max, rgb_t *p)
{
	if (min == max) max = min + 1;
	if (invert) hue = max - (hue - min);
	if (!saturation) {
		p->r = p->g = p->b = 255 * (max - hue) / (max - min);
		return;
	}
	double h = fmod(color_rotate + 1e-4 + 4.0 * (hue - min) / (max - min), 6);
#	define VAL 255
	double c = VAL * saturation;
	double X = c * (1 - fabs(fmod(h, 2) - 1));
 
	p->r = p->g = p->b = 0;
 
	switch((int)h) {
	case 0: p->r = c; p->g = X; return;
	case 1:	p->r = X; p->g = c; return;
	case 2: p->g = c; p->b = X; return;
	case 3: p->g = X; p->b = c; return;
	case 4: p->r = X; p->b = c; return;
	default:p->r = c; p->b = X;
	}
}
 
void calc_mandel()
{
	int i, j, iter, min, max;
	rgb_t *px;
	double x, y, zx, zy, zx2, zy2;
	min = max_iter; max = 0;
	for (i = 0; i < height; i++) {
		px = tex[i];
		y = (i - height/2) * scale + cy;
		for (j = 0; j  < width; j++, px++) {
			x = (j - width/2) * scale + cx;
			iter = 0;
 
			zx = hypot(x - .25, y);
			if (x < zx - 2 * zx * zx + .25) iter = max_iter;
			if ((x + 1)*(x + 1) + y * y < 1/16) iter = max_iter;
 
			zx = zy = zx2 = zy2 = 0;
			for (; iter < max_iter && zx2 + zy2 < 4; iter++) {
				zy = 2 * zx * zy + y;
				zx = zx2 - zy2 + x;
				zx2 = zx * zx;
				zy2 = zy * zy;
			}
			if (iter < min) min = iter;
			if (iter > max) max = iter;
			*(unsigned short *)px = iter;
		}
	}
 
	for (i = 0; i < height; i++)
		for (j = 0, px = tex[i]; j  < width; j++, px++)
			hsv_to_rgb(*(unsigned short*)px, min, max, px);
}
 
void alloc_tex()
{
	int i, ow = tex_w, oh = tex_h;
 
	for (tex_w = 1; tex_w < width;  tex_w <<= 1);
	for (tex_h = 1; tex_h < height; tex_h <<= 1);
 
	if (tex_h != oh || tex_w != ow)
		tex = realloc(tex, tex_h * tex_w * 3 + tex_h * sizeof(rgb_t*));
 
	for (tex[0] = (rgb_t *)(tex + tex_h), i = 1; i < tex_h; i++)
		tex[i] = tex[i - 1] + tex_w;
}
 
void set_texture()
{
	alloc_tex();
	calc_mandel();
 
	glEnable(GL_TEXTURE_2D);
	glBindTexture(GL_TEXTURE_2D, texture);
	glTexImage2D(GL_TEXTURE_2D, 0, 3, tex_w, tex_h,
		0, GL_RGB, GL_UNSIGNED_BYTE, tex[0]);
 
	glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
	glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
	render();
}
 
void mouseclick(int button, int state, int x, int y)
{
	if (state != GLUT_UP) return;
 
	cx += (x - width / 2) * scale;
	cy -= (y - height/ 2) * scale;
 
	switch(button) {
	case GLUT_LEFT_BUTTON: /* zoom in */
		if (scale > fabs(x) * 1e-16 && scale > fabs(y) * 1e-16)
			scale /= 2;
		break;
	case GLUT_RIGHT_BUTTON: /* zoom out */
		scale *= 2;
		break;
	/* any other button recenters */
	}
	set_texture();
}
 
 
void resize(int w, int h)
{
	printf("resize %d %d\n", w, h);
	width = w;
	height = h;
 
	glViewport(0, 0, w, h);
	glOrtho(0, w, 0, h, -1, 1);
 
	set_texture();
}
 
void init_gfx(int *c, char **v)
{
	glutInit(c, v);
	glutInitDisplayMode(GLUT_RGB);
	glutInitWindowSize(640, 480);
	
	gwin = glutCreateWindow("Mandelbrot");
	glutDisplayFunc(render);
 
	glutKeyboardFunc(keypress);
	glutMouseFunc(mouseclick);
	glutReshapeFunc(resize);
	glGenTextures(1, &texture);
	set_texture();
}
 
int main(int c, char **v)
{
	init_gfx(&c, v);
	printf("keys:\n\tr: color rotation\n\tc: monochrome\n\ts: screen dump\n\t"
		"<, >: decrease/increase max iteration\n\tq: quit\n\tmouse buttons to zoom\n");
 
	glutMainLoop();
	return 0;
}

Here is a variant that hopefully will work on a broader range of architectures, although it has been tested only on x86-64.

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <GL/glut.h>
#include <GL/gl.h>
#include <GL/glu.h>

void set_texture();

unsigned char *tex;
int gwin;
GLuint texture;
int width, height;
int old_width, old_height;
double scale = 1. / 256;
double cx = -.6, cy = 0;
int color_rotate = 0;
int saturation = 1;
int invert = 0;
int max_iter = 256;

void render()
{
    glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_REPLACE);

    glBindTexture(GL_TEXTURE_2D, texture);

    glBegin(GL_QUADS);

    glTexCoord2d(0, 0);
    glVertex2i(0, 0);
    glTexCoord2d(1, 0);
    glVertex2i(width, 0);
    glTexCoord2d(1, 1);
    glVertex2i(width, height);
    glTexCoord2d(0, 1);
    glVertex2i(0, height);

    glEnd();

    glFlush();
    glFinish();
}

int dump = 1;
void screen_dump()
{
    char fn[100];
    sprintf(fn, "screen%03d.ppm", dump++);
    FILE *fp = fopen(fn, "w");
    fprintf(fp, "P6\n%d %d\n255\n", width, height);
    for (int i = height - 1; i >= 0; i -= 1) {
        for (int j = 0; j < width; j += 1) {
            fwrite(&tex[((i * width) + j) * 4], 1, 3, fp);
        }
    }
    fclose(fp);
    printf("%s written\n", fn);
}

void keypress(unsigned char key,[[maybe_unused]]
              int x,[[maybe_unused]]
              int y)
{
    switch (key) {
    case 'q':
        glFinish();
        glutDestroyWindow(gwin);
        break;

    case 27:
        scale = 1. / 256;
        cx = -.6;
        cy = 0;
        set_texture();
        break;

    case 'r':
        color_rotate = (color_rotate + 1) % 6;
        set_texture();
        break;

    case '>':
    case '.':
        max_iter += 128;
        if (max_iter > 1 << 15)
            max_iter = 1 << 15;
        printf("max iter: %d\n", max_iter);
        set_texture();
        break;

    case '<':
    case ',':
        max_iter -= 128;
        if (max_iter < 128)
            max_iter = 128;
        printf("max iter: %d\n", max_iter);
        set_texture();
        break;

    case 'c':
        saturation = 1 - saturation;
        set_texture();
        break;

    case 's':
        screen_dump();
        break;

    case 'z':
        max_iter = 4096;
        set_texture();
        break;

    case 'x':
        max_iter = 128;
        set_texture();
        break;

    case ' ':
        invert = !invert;
        set_texture();
        break;

    default:
        set_texture();
        break;
    }
}

#define VAL 255

void hsv_to_rgba(int hue, int min, int max, unsigned char *px)
{
    unsigned char r;
    unsigned char g;
    unsigned char b;

    if (min == max)
        max = min + 1;
    if (invert)
        hue = max - (hue - min);
    if (!saturation) {
        r = 255 * (max - hue) / (max - min);
        g = r;
        b = r;
    } else {
        double h =
            fmod(color_rotate + 1e-4 + 4.0 * (hue - min) / (max - min), 6);
        double c = VAL * saturation;
        double X = c * (1 - fabs(fmod(h, 2) - 1));

        r = 0;
        g = 0;
        b = 0;

        switch ((int) h) {
        case 0:
            r = c;
            g = X;
            break;
        case 1:
            r = X;
            g = c;
            break;
        case 2:
            g = c;
            b = X;
            break;
        case 3:
            g = X;
            b = c;
            break;
        case 4:
            r = X;
            b = c;
            break;
        default:
            r = c;
            b = X;
            break;
        }
    }

    /* Using an alpha channel neatly solves the problem of aligning
     * rows on 4-byte boundaries (at the expense of memory, of
     * course). */
    px[0] = r;
    px[1] = g;
    px[2] = b;
    px[3] = 255;                /* Alpha channel. */
}

void calc_mandel()
{
    int i, j, iter, min, max;
    double x, y, zx, zy, zx2, zy2;
    unsigned short *hsv = malloc(width * height * sizeof(unsigned short));

    min = max_iter;
    max = 0;
    for (i = 0; i < height; i++) {
        y = (i - height / 2) * scale + cy;
        for (j = 0; j < width; j++) {
            x = (j - width / 2) * scale + cx;
            iter = 0;

            zx = hypot(x - .25, y);
            if (x < zx - 2 * zx * zx + .25)
                iter = max_iter;
            if ((x + 1) * (x + 1) + y * y < 1 / 16)
                iter = max_iter;

            zx = 0;
            zy = 0;
            zx2 = 0;
            zy2 = 0;
            while (iter < max_iter && zx2 + zy2 < 4) {
                zy = 2 * zx * zy + y;
                zx = zx2 - zy2 + x;
                zx2 = zx * zx;
                zy2 = zy * zy;
                iter += 1;
            }
            if (iter < min)
                min = iter;
            if (iter > max)
                max = iter;
            hsv[(i * width) + j] = iter;
        }
    }

    for (i = 0; i < height; i += 1) {
        for (j = 0; j < width; j += 1) {
            unsigned char *px = tex + (((i * width) + j) * 4);
            hsv_to_rgba(hsv[(i * width) + j], min, max, px);
        }
    }

    free(hsv);
}

void alloc_tex()
{
    if (tex == NULL || width != old_width || height != old_height) {
        free(tex);
        tex = malloc(height * width * 4 * sizeof(unsigned char));
        memset(tex, 0, height * width * 4 * sizeof(unsigned char));
        old_width = width;
        old_height = height;
    }
}

void set_texture()
{
    alloc_tex();
    calc_mandel();

    glEnable(GL_TEXTURE_2D);
    glBindTexture(GL_TEXTURE_2D, texture);
    glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, width, height,
                 0, GL_RGBA, GL_UNSIGNED_BYTE, tex);

    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);

    render();
}

void mouseclick(int button, int state, int x, int y)
{
    if (state != GLUT_UP)
        return;

    cx += (x - width / 2) * scale;
    cy -= (y - height / 2) * scale;

    switch (button) {
    case GLUT_LEFT_BUTTON:     /* zoom in */
        if (scale > fabs((double) x) * 1e-16
            && scale > fabs((double) y) * 1e-16)
            scale /= 2;
        break;
    case GLUT_RIGHT_BUTTON:    /* zoom out */
        scale *= 2;
        break;
        /* any other button recenters */
    }
    set_texture();
}


void resize(int w, int h)
{
    printf("resize %d %d\n", w, h);

    width = w;
    height = h;

    glViewport(0, 0, w, h);
    glOrtho(0, w, 0, h, -1, 1);

    set_texture();
}

void init_gfx(int *c, char **v)
{
    glutInit(c, v);
    glutInitDisplayMode(GLUT_RGBA);
    glutInitWindowSize(640, 480);

    gwin = glutCreateWindow("Mandelbrot");
    glutDisplayFunc(render);

    glutKeyboardFunc(keypress);
    glutMouseFunc(mouseclick);
    glutReshapeFunc(resize);
    glGenTextures(1, &texture);
    set_texture();
}

int main(int c, char **v)
{
    tex = NULL;

    init_gfx(&c, v);
    printf
        ("keys:\n\tr: color rotation\n\tc: monochrome\n\ts: screen dump\n\t"
         "<, >: decrease/increase max iteration\n\tq: quit\n\tmouse buttons to zoom\n");

    glutMainLoop();
    return 0;
}

// local variables:
// mode: C
// c-file-style: "k&r"
// c-basic-offset: 4
// end:

(PLEASE FIXME: Does resizing work correctly, in either version?)

ASCII

Not mine, found it on Ken Perlin's homepage, this deserves a place here to illustrate how awesome C can be:

main(k){float i,j,r,x,y=-16;while(puts(""),y++<15)for(x
=0;x++<84;putchar(" .:-;!/>)|&IH%*#"[k&15]))for(i=k=r=0;
j=r*r-i*i-2+x/25,i=2*r*i+y/10,j*j+i*i<11&&k++<111;r=j);}

There may be warnings on compiling but disregard them, the output will be produced nevertheless. Such programs are called obfuscated and C excels when it comes to writing such cryptic programs. Google IOCCC for more.

.............::::::::::::::::::::::::::::::::::::::::::::::::.......................
.........::::::::::::::::::::::::::::::::::::::::::::::::::::::::...................
.....::::::::::::::::::::::::::::::::::-----------:::::::::::::::::::...............
...:::::::::::::::::::::::::::::------------------------:::::::::::::::.............
:::::::::::::::::::::::::::-------------;;;!:H!!;;;--------:::::::::::::::..........
::::::::::::::::::::::::-------------;;;;!!/>&*|I !;;;--------::::::::::::::........
::::::::::::::::::::-------------;;;;;;!!/>)|.*#|>/!!;;;;-------::::::::::::::......
::::::::::::::::-------------;;;;;;!!!!//>|:    !:|//!!!;;;;-----::::::::::::::.....
::::::::::::------------;;;;;;;!!/>)I>>)||I#     H&))>////*!;;-----:::::::::::::....
::::::::----------;;;;;;;;;;!!!//)H:  #|              IH&*I#/;;-----:::::::::::::...
:::::---------;;;;!!!!!!!!!!!//>|.H:                     #I>/!;;-----:::::::::::::..
:----------;;;;!/||>//>>>>//>>)|%                         %|&/!;;----::::::::::::::.
--------;;;;;!!//)& .;I*-H#&||&/                           *)/!;;-----::::::::::::::
-----;;;;;!!!//>)IH:-        ##                            #&!!;;-----::::::::::::::
;;;;!!!!!///>)H%.**           *                            )/!;;;------:::::::::::::
                                                         &)/!!;;;------:::::::::::::
;;;;!!!!!///>)H%.**           *                            )/!;;;------:::::::::::::
-----;;;;;!!!//>)IH:-        ##                            #&!!;;-----::::::::::::::
--------;;;;;!!//)& .;I*-H#&||&/                           *)/!;;-----::::::::::::::
:----------;;;;!/||>//>>>>//>>)|%                         %|&/!;;----::::::::::::::.
:::::---------;;;;!!!!!!!!!!!//>|.H:                     #I>/!;;-----:::::::::::::..
::::::::----------;;;;;;;;;;!!!//)H:  #|              IH&*I#/;;-----:::::::::::::...
::::::::::::------------;;;;;;;!!/>)I>>)||I#     H&))>////*!;;-----:::::::::::::....
::::::::::::::::-------------;;;;;;!!!!//>|:    !:|//!!!;;;;-----::::::::::::::.....
::::::::::::::::::::-------------;;;;;;!!/>)|.*#|>/!!;;;;-------::::::::::::::......
::::::::::::::::::::::::-------------;;;;!!/>&*|I !;;;--------::::::::::::::........
:::::::::::::::::::::::::::-------------;;;!:H!!;;;--------:::::::::::::::..........
...:::::::::::::::::::::::::::::------------------------:::::::::::::::.............
.....::::::::::::::::::::::::::::::::::-----------:::::::::::::::::::...............
.........::::::::::::::::::::::::::::::::::::::::::::::::::::::::...................
.............::::::::::::::::::::::::::::::::::::::::::::::::.......................

Fixed point 16 bit arithmetic

/**
  ascii Mandelbrot using 16 bits of fixed point integer maths with a selectable fractional precision in bits.

  This is still only 16 bits mathc and allocating more than 6 bits of fractional precision leads to an overflow that adds noise to the plot..

  This code frequently casts to short to ensure we're not accidentally benefitting from GCC promotion from short 16 bits to int.

  gcc fixedPoint.c  -lm

 */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <stdint.h>
#include <string.h>

short s(short i);
short toPrec(double f, int bitsPrecision);

int main(int argc, char* argv[])
{
  // chosen to match https://www.youtube.com/watch?v=DC5wi6iv9io
  int width = 32; // basic width of a zx81
  int height = 22; // basic width of a zx81
  int zoom=3;  // bigger with finer detail ie a smaller step size - leave at 1 for 32x22

  // params
  short bitsPrecision = 6;
  printf("PRECISION=%d\n", bitsPrecision);

  short X1 = toPrec(3.5,bitsPrecision) / zoom;
  short X2 = toPrec(2.25,bitsPrecision) ;
  short Y1 = toPrec(3,bitsPrecision)/zoom ;   // horiz pos
  short Y2 = toPrec(1.5,bitsPrecision) ; // vert pos
  short LIMIT = toPrec(4,bitsPrecision);


  // fractal
  //char * chr = ".:-=X$#@.";
  char * chr = "abcdefghijklmnopqr ";
  //char * chr = ".,'~=+:;[/<&?oxOX#.";
  short maxIters = strlen(chr);

  short py=0;
  while (py < height*zoom) {
    short px=0;
    while (px < width*zoom) {

      short x0 = s(s(px*X1) / width) - X2;
      short y0 = s(s(py*Y1) / height) - Y2;

      short x=0;
      short y=0;

      short i=0;

      short xSqr;
      short ySqr;
      while (i < maxIters) {
        xSqr = s(x * x) >> bitsPrecision;
        ySqr = s(y * y) >> bitsPrecision;

        // Breakout if sum is > the limit OR breakout also if sum is negative which indicates overflow of the addition has occurred
        // The overflow check is only needed for precisions of over 6 bits because for 7 and above the sums come out overflowed and negative therefore we always run to maxIters and we see nothing.
        // By including the overflow break out we can see the fractal again though with noise.
        if ((xSqr + ySqr) >= LIMIT || (xSqr+ySqr) < 0) {
          break;
        }

        short xt = xSqr - ySqr + x0;
        y = s(s(s(x * y) >> bitsPrecision) * 2) + y0;
        x=xt;

        i = i + 1;
      }
      i = i - 1;

      printf("%c", chr[i]);

      px = px + 1;
    }

    printf("\n");
    py = py + 1;
  }
}

// convert decimal value to a fixed point value in the given precision
short toPrec(double f, int bitsPrecision) {
  short whole = ((short)floor(f) << (bitsPrecision));
  short part = (f-floor(f))*(pow(2,bitsPrecision));
  short ret = whole + part;
  return ret;
}

// convenient casting
short s(short i) {
  return i;
}
$ gcc fixedPoint.c  -lm && ./a.out

PRECISION=6
aaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcdcccbbbbbb
aaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccddcbbbbb
aaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbegfcdbbb
aaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdccedbb
aaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdcccb
aaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbcfdddcccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdded
aaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbcccccddfcccccccccccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccc
aaaaaaaaaaaaaaaaaabbbbbbbbbbbbbcccccdeccccccccccccccccccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbcc
aaaaaaaaaaaaaaaaabbbbbbbbbbfcccccddeccccccccccccccccdddddeeeddddccccccbbbbbbbbbbbbbbbbbbbbbbbbbe
aaaaaaaaaaaaaaaabbbbbbbbbbcccccdddccccccccccccccdeddddeefigeeeddddecccccbbbbbbbbbbbbbbbbbbbbbbbb
aaaaaaaaaaaaaaaabbbbbbbecccccdddcccccccccccccdddddddddeefhmgfffddddedcccccbbbbbbbbbbbbbbbbbbbbbb
aaaaaaaaaaaaaaabbbbbbbcccccccdcccccccccccccccdgddddddfeefgjpijjfdddddedccccccbbbbbbbbbbbbbbbbbbb
aaaaaaaaaaaaaaabbbbbccccccdedccccccccccccccdddddddddeeefgkj ojgfedddddeccccccbbbbbbbbbbbbbbbbbbb
aaaaaaaaaaaaaabbbbbcccccegeccccccccccccccdeedddddddeeeeghhkp hgheefddddecccccccbbbbbbbbbbbbbbbbb
aaaaaaaaaaaaabbbbccccceddcccccccccccccccfddddddddeeeeefmlkr  ihheeeedddddgccccccbbbbbbbbbbbbbbbb
aaaaaaaaaaaaabbbccccddfcccccccccccccccedddddddddeeegffhnp    rpjffeeeiddddcccccccbbbbbbbbbbbbbbb
aaaaaaaaaaaabbbcccddecccccccccccccccddddddddddeeffffgghm       jgffeeeegdddccccccccbbbbbbbbbbbbb
aaaaaaaaaaabbbccdedccccccccccccccccdddddddddeefffffgghil       khggffffeeeddccccccccbbbbbbbbbbbb
aaaaaaaaaaabbccdeccccccccccccccccddddddddeeef ijjhhhkijlo     qkihjhgffgngeddcccccccbbbbbbbbbbbb
aaaaaaaaaabbcddccccccccccccccccdddddddfeeeefgjq  lkk p           n khhhiqifedcccccccdbbbbbbbbbbb
aaaaaaaaaabbccccccccccccccccccddddddefeeeeffgilq                   plk rrqgeddcccccccdbbbbbbbbbb
aaaaaaaaaabdccccccccccccccccdddhegeeeeeefffghiq                          mfeeddcccccccdbbbbbbbbb
aaaaaaaaaaccccccccccccccccdddeeeeeeeeeeffffhjklp                        phfeeddcccccccdcbbbbbbbb
aaaaaaaaabcccccccccccccddddegeeeeeeeeeffffhppp                          jgggedddccccccccbbbbbbbb
aaaaaaaaabccccccccccddddeefpifffffffffggggik                             hgfedddcccccccdcbbbbbbb
aaaaaaaaaccccccceddddddeeifl hgggjrhggggghj p                            qjnfdddcccccccdcbbbbbbb
aaaaaaaabccccddedddddefeefghqnokkloqiqhhhik                                ifdddcccccccdcbbbbbbb
aaaaaaaaccceddddddddgfeeffghir o n  qmjiijo                               igfedddcccccccccbbbbbb
aaaaaaaaccddedddddeeeeeefgghkq         lll                                lgfddddcccccccdcbbbbbb
aaaaaaaacddddddddeeeeeefhgjol           rn                                 geddddcccccccdcbbbbbb
aaaaaaaaedddddddeeeffggojjll                                              hfeddddeccccccdcbbbbbb
aaaaaaaaddddddefffffggmkopmop                                            ngfefdddfccccccdcbbbbbb
aaaaaaaaeeffgihggiihikk                                                  hfeefdddeccccccddbbbbbb
aaaaaaaa                                                               kigfgefdddecccccceebbbbbb
aaaaaaaaeeffhgjggghhhklqm                                              ligfhefdddeccccccddbbbbbb
aaaaaaaaddddddefffffgggirq                                               hffefdddeccccccdebbbbbb
aaaaaaaahdddddddeefgfggilkjk                                              hfeedddeccccccddbbbbbb
aaaaaaaacddddddddeeeeeefhhhkl                                             lfefdddeccccccdcbbbbbb
aaaaaaaaccddedddddefeeeeffgijo           on                                qfedddcccccccdcbbbbbb
aaaaaaaabcceddddddddegeeefggik       r  kko                               jhfedddcccccccdcbbbbbb
aaaaaaaabccccddddddddefeeefijmk jkp  kmiijlq                              qhfedddcccccccccbbbbbb
aaaaaaaaacccccccdddddddeeefh hhghi kjggghil                               r geddcccccccdcbbbbbbb
aaaaaaaaabccccccccccdddddefgnfgffghggggggghjm                            lj feddcccccccdcbbbbbbb
aaaaaaaaabccccccccccccccdddeffggeeeefffffggm                             igfefddcccccccdbbbbbbbb
aaaaaaaaaaccccccccccccccccdddeeeeeeeeeeffffhjm                           kgfeddcccccccdcbbbbbbbb
aaaaaaaaaabdccccccccccccccccdddfeeeeeeeegffgiikq                          feeddcccccccebbbbbbbbb
aaaaaaaaaabbccccccccccccccccccdddddegeeeegffgho                     p    nheeddcccccchfbbbbbbbbb
aaaaaaaaaabbbddcccccccccccccccccdddddeeeeeefhm     l                ki jlnjeddcccccccdbbbbbbbbbb
aaaaaaaaaaabbccecccccccccccccccccdddddddfeeefir  jii npm         k ohgggineedcccccccdbbbbbbbbbbb
aaaaaaaaaaabbbccdddccccccccccccccccddddddddeeefggggggiik       mjhhgfffffedddcccccccbbbbbbbbbbbb
aaaaaaaaaaaabbbcccedfcccccccccccccccdddddddddeegffffgghp        hgffgeeeedddccccccccbbbbbbbbbbbb
aaaaaaaaaaaabbbbccccdddcccccccccccccccgdddddddddeegffgil        ggfeeeeddddcccccccbbbbbbbbbbbbbb
aaaaaaaaaaaaabbbbbccccdddccccccccccccccfeddddddddeeeefgi l   nkqgeeegeddddcccccccbbbbbbbbbbbbbbb
aaaaaaaaaaaaabbbbbbcccccdedccccccccccccccdedddddddeeeeeghik  khhfeefdddddeccccccbbbbbbbbbbbbbbbb
aaaaaaaaaaaaaabbbbbbccccccdddcccccccccccccddedddddddeeefigil jggfedddddddcccccbbbbbbbbbbbbbbbbbb
aaaaaaaaaaaaaaabbbbbbbcccccccdccccccccccccccdefdddddeeeffhlliimfdddddedccccccbbbbbbbbbbbbbbbbbbb
aaaaaaaaaaaaaaaabbbbbbbccccccdddccccccccccccccdddddddeeefg jggheddddedccccccbbbbbbbbbbbbbbbbbbbb
aaaaaaaaaaaaaaaabbbbbbbbbccccccdddccccccccccccccdedddddefgiffeeddddeccccccbbbbbbbbbbbbbbbbbbbbbb
aaaaaaaaaaaaaaaaabbbbbbbbbbecccccdeeccccccccccccccceddddeffegddddgcccccbbbbbbbbbbbbbbbbbbbbbbbbb
aaaaaaaaaaaaaaaaaabbbbbbbbbbbbcccccdddcccccccccccccccccddddddddccccccbbbbbbbbbbbbbbbbbbbbbbbbbbc
aaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbccccddeccccccccccccccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbed
aaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbccceddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccd
aaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbdcccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbecccc
aaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccdebb
aaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdfccbbb
aaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcgdccbbbb

C#

using System;
using System.Drawing;
using System.Drawing.Imaging;
using System.Threading;
using System.Windows.Forms;

/// <summary>
/// Generates bitmap of Mandelbrot Set and display it on the form.
/// </summary>
public class MandelbrotSetForm : Form
{
    const double MaxValueExtent = 2.0;
    Thread thread;

    static double CalcMandelbrotSetColor(ComplexNumber c)
    {
        // from http://en.wikipedia.org/w/index.php?title=Mandelbrot_set
        const int MaxIterations = 1000;
        const double MaxNorm = MaxValueExtent * MaxValueExtent;

        int iteration = 0;
        ComplexNumber z = new ComplexNumber();
        do
        {
            z = z * z + c;
            iteration++;
        } while (z.Norm() < MaxNorm && iteration < MaxIterations);
        if (iteration < MaxIterations)
            return (double)iteration / MaxIterations;
        else
            return 0; // black
    }

    static void GenerateBitmap(Bitmap bitmap)
    {
        double scale = 2 * MaxValueExtent / Math.Min(bitmap.Width, bitmap.Height);
        for (int i = 0; i < bitmap.Height; i++)
        {
            double y = (bitmap.Height / 2 - i) * scale;
            for (int j = 0; j < bitmap.Width; j++)
            {
                double x = (j - bitmap.Width / 2) * scale;
                double color = CalcMandelbrotSetColor(new ComplexNumber(x, y));
                bitmap.SetPixel(j, i, GetColor(color));
            }
        }
    }

    static Color GetColor(double value)
    {
        const double MaxColor = 256;
        const double ContrastValue = 0.2;
        return Color.FromArgb(0, 0,
            (int)(MaxColor * Math.Pow(value, ContrastValue)));
    }
    
    public MandelbrotSetForm()
    {
        // form creation
        this.Text = "Mandelbrot Set Drawing";
        this.BackColor = System.Drawing.Color.Black;
        this.BackgroundImageLayout = System.Windows.Forms.ImageLayout.Stretch;
        this.MaximizeBox = false;
        this.StartPosition = FormStartPosition.CenterScreen;
        this.FormBorderStyle = FormBorderStyle.FixedDialog;
        this.ClientSize = new Size(640, 640);
        this.Load += new System.EventHandler(this.MainForm_Load);
    }

    void MainForm_Load(object sender, EventArgs e)
    {
        thread = new Thread(thread_Proc);
        thread.IsBackground = true;
        thread.Start(this.ClientSize);
    }

    void thread_Proc(object args)
    {
        // start from small image to provide instant display for user
        Size size = (Size)args;
        int width = 16;
        while (width * 2 < size.Width)
        {
            int height = width * size.Height / size.Width;
            Bitmap bitmap = new Bitmap(width, height, PixelFormat.Format24bppRgb);
            GenerateBitmap(bitmap);
            this.BeginInvoke(new SetNewBitmapDelegate(SetNewBitmap), bitmap);
            width *= 2;
            Thread.Sleep(200);
        }
        // then generate final image
        Bitmap finalBitmap = new Bitmap(size.Width, size.Height, PixelFormat.Format24bppRgb);
        GenerateBitmap(finalBitmap);
        this.BeginInvoke(new SetNewBitmapDelegate(SetNewBitmap), finalBitmap);
    }

    void SetNewBitmap(Bitmap image)
    {
        if (this.BackgroundImage != null)
            this.BackgroundImage.Dispose();
        this.BackgroundImage = image;
    }

    delegate void SetNewBitmapDelegate(Bitmap image);

    static void Main()
    {
        Application.Run(new MandelbrotSetForm());
    }
}

struct ComplexNumber
{
    public double Re;
    public double Im;

    public ComplexNumber(double re, double im)
    {
        this.Re = re;
        this.Im = im;
    }

    public static ComplexNumber operator +(ComplexNumber x, ComplexNumber y)
    {
        return new ComplexNumber(x.Re + y.Re, x.Im + y.Im);
    }

    public static ComplexNumber operator *(ComplexNumber x, ComplexNumber y)
    {
        return new ComplexNumber(x.Re * y.Re - x.Im * y.Im,
            x.Re * y.Im + x.Im * y.Re);
    }

    public double Norm()
    {
        return Re * Re + Im * Im;
    }
}

C++

This generic function assumes that the image can be accessed like a two-dimensional array of colors. It may be passed a true array (in which case the Mandelbrot set will simply be drawn into that array, which then might be saved as image file), or a class which maps the subscript operator to the pixel drawing routine of some graphics library. In the latter case, there must be functions get_first_dimension and get_second_dimension defined for that type, to be found by argument dependent lookup. The code provides those functions for built-in arrays.

#include <cstdlib>
#include <complex>

// get dimensions for arrays
template<typename ElementType, std::size_t dim1, std::size_t dim2>
 std::size_t get_first_dimension(ElementType (&a)[dim1][dim2])
{
  return dim1;
}

template<typename ElementType, std::size_t dim1, std::size_t dim2>
 std::size_t get_second_dimension(ElementType (&a)[dim1][dim2])
{
  return dim2;
}


template<typename ColorType, typename ImageType>
 void draw_Mandelbrot(ImageType& image,                                   //where to draw the image
                      ColorType set_color, ColorType non_set_color,       //which colors to use for set/non-set points
                      double cxmin, double cxmax, double cymin, double cymax,//the rect to draw in the complex plane
                      unsigned int max_iterations)                          //the maximum number of iterations
{
  std::size_t const ixsize = get_first_dimension(image);
  std::size_t const iysize = get_first_dimension(image);
  for (std::size_t ix = 0; ix < ixsize; ++ix)
    for (std::size_t iy = 0; iy < iysize; ++iy)
    {
      std::complex<double> c(cxmin + ix/(ixsize-1.0)*(cxmax-cxmin), cymin + iy/(iysize-1.0)*(cymax-cymin));
      std::complex<double> z = 0;
      unsigned int iterations;

      for (iterations = 0; iterations < max_iterations && std::abs(z) < 2.0; ++iterations) 
        z = z*z + c;

      image[ix][iy] = (iterations == max_iterations) ? set_color : non_set_color;

    }
}

Note this code has not been executed.



A Simple version in CPP. Definitely not as crazy good as the ASCII one in C above.

#include <stdio.h>

int f(float X, float Y, float x, float y, int n){
return (x*x+y*y<4 && n<100)?1+f(X, Y, x*x-y*y+X, 2*x*y+Y, n+1):0;
}

main(){
for(float j=1; j>=-1; j-=.015)
for(float i=-2, x; i<=.5; i+=.015, x=f(i, j, 0, 0, 0))
printf("%c%s", x<10?' ':x<20?'.':x<50?':':x<80?'*':'#', i>-2?" ":"\n");
}

C3

This program produces a BMP as output.

module mandelbrot;

extern fn int atoi(char *s);
extern fn int printf(char *s, ...);
extern fn void putchar(int c);

fn void main(int argc, char **argv)
{
  int w = atoi(argv[1]);
  int h = w;

  const LIMIT = 2.0;
  const SQUARE_LIMIT = LIMIT * LIMIT;

  printf("P4\n%d %d\n", w, h);
 
  int iter = 50;
  int bit_num = 0;
  char byte_acc = 0;
  for (double y = 0; y < h; y++)
  {
    for (double x = 0; x < w; x++)
    {
      double zr;
      double zi;
      double ti;
      double tr;
      double cr = (2.0 * x / w - 1.5);
      double ci = (2.0 * y / h - 1.0);
      for (int i = 0; i < iter && (tr + ti <= SQUARE_LIMIT); i++)
      {
        zi = 2.0 * zr * zi + ci;
        zr = tr - ti + cr;
        tr = zr * zr;
        ti = zi * zi;
      }

      byte_acc <<= 1;
      if (tr + ti <= SQUARE_LIMIT) byte_acc |= 0x01;

      ++bit_num;

      if (bit_num == 8)
      {
        putchar(byte_acc);
        byte_acc = 0;
        bit_num = 0;
      }
      else if (x == w - 1)
      {
        byte_acc <<= (8 - w % 8);
        putchar(byte_acc);
        byte_acc = 0;
        bit_num = 0;
      }
    }
  }
}

Cixl

Displays a zooming Mandelbrot using ANSI graphics.

use: cx;

define: max 4.0;
define: max-iter 570;

let: (max-x max-y) screen-size;
let: max-cx $max-x 2.0 /;
let: max-cy $max-y 2.0 /;
let: rows Stack<Str> new;
let: buf Buf new;
let: zoom 0 ref;

func: render()()
  $rows clear
  
  $max-y 2 / {
    let: y;
    $buf 0 seek

    $max-x {
      let: x;
      let: (zx zy) 0.0 ref %%;
      let: cx $x $max-cx - $zoom deref /;
      let: cy $y $max-cy - $zoom deref /;
      let: i #max-iter ref;

      {
        let: nzx $zx deref ** $zy deref ** - $cx +;
	$zy $zx deref *2 $zy deref * $cy + set
	$zx $nzx set
        $i &-- set-call	
        $nzx ** $zy deref ** + #max < $i deref and
      } while

      let: c $i deref % -7 bsh bor 256 mod;
      $c {$x 256 mod $y 256 mod} {0 0} if-else $c new-rgb $buf set-bg
      @@s $buf print
    } for

    $rows $buf str push   
  } for

  1 1 #out move-to
  $rows {#out print} for
  $rows riter {#out print} for;

#out hide-cursor
raw-mode

let: poll Poll new;
let: is-done #f ref;

$poll #in {
  #in read-char _
  $is-done #t set
} on-read

{
  $zoom &++ set-call
  render
  $poll 0 wait _
  $is-done deref !
} while

#out reset-style
#out clear-screen
1 1 #out move-to
#out show-cursor
normal-mode

Clojure

Inspired by the Ruby and Perl below

(defn complex-add
  [[a0 b0] [a1 b1]]
  [(+ a0 a1) (+ b0 b1)])

(defn complex-square
  [[a b]]
  [(- (* a a) (* b b)) (* 2 a b)])

(defn complex-abs
  [[a b]]
  (Math/sqrt (+ (* a a) (* b b))))

(defn f
  [z c]
  (complex-add z (complex-square c)))

(defn mandelbrot?
  [z]
  (> 2 (complex-abs (nth (iterate (partial f z) [0 0]) 20))))

(doseq [y (range 1 -1 -0.05)]
  (doseq [x (range -2 0.5 0.0315)]
    (print (if (mandelbrot? [(double x) (double y)]) "*" " ")))
  (println ""))
Output:
harold@freeside:~/src/mandelbrot$ clj -M mandelbrot.clj 
                                                                                
                                                                                
                                                            *                   
                                                        *  ***  *               
                                                        ********                
                                                       *********                
                                                         ******                 
                                             **    ** ************  *           
                                              *** *******************   *  *    
                                              *****************************     
                                              ****************************      
                                          ********************************      
                                           ********************************     
                                         ************************************ * 
                          *     *        ***********************************    
                          ***********    ***********************************    
                          ************  **************************************  
                         ************** ************************************    
                        ****************************************************    
                    *******************************************************     
 ************************************************************************       
                    *******************************************************     
                        ****************************************************    
                         ************** ************************************    
                          ************  **************************************  
                          ***********    ***********************************    
                          *     *        ***********************************    
                                         ************************************ * 
                                           ********************************     
                                          ********************************      
                                              ****************************      
                                              *****************************     
                                              *** *******************   *  *    
                                             **    ** ************  *           
                                                         ******                 
                                                       *********                
                                                        ********                
                                                        *  ***  *               
                                                            *

COBOL

EBCDIC art.

IDENTIFICATION DIVISION.
PROGRAM-ID. MANDELBROT-SET-PROGRAM.
DATA DIVISION.
WORKING-STORAGE SECTION.
01  COMPLEX-ARITHMETIC.
    05 X               PIC S9V9(9).
    05 Y               PIC S9V9(9).
    05 X-A             PIC S9V9(6).
    05 X-B             PIC S9V9(6).
    05 Y-A             PIC S9V9(6).
    05 X-A-SQUARED     PIC S9V9(6).
    05 Y-A-SQUARED     PIC S9V9(6).
    05 SUM-OF-SQUARES  PIC S9V9(6).
    05 ROOT            PIC S9V9(6).
01  LOOP-COUNTERS.
    05 I               PIC 99.
    05 J               PIC 99.
    05 K               PIC 999.
77  PLOT-CHARACTER     PIC X.
PROCEDURE DIVISION.
CONTROL-PARAGRAPH.
    PERFORM OUTER-LOOP-PARAGRAPH
    VARYING I FROM 1 BY 1 UNTIL I IS GREATER THAN 24.
    STOP RUN.
OUTER-LOOP-PARAGRAPH.
    PERFORM INNER-LOOP-PARAGRAPH
    VARYING J FROM 1 BY 1 UNTIL J IS GREATER THAN 64.
    DISPLAY ''.
INNER-LOOP-PARAGRAPH.
    MOVE SPACE TO PLOT-CHARACTER.
    MOVE ZERO  TO X-A.
    MOVE ZERO  TO Y-A.
    MULTIPLY J   BY   0.0390625   GIVING X.
    SUBTRACT 1.5 FROM X.
    MULTIPLY I   BY   0.083333333 GIVING Y.
    SUBTRACT 1 FROM Y.
    PERFORM ITERATION-PARAGRAPH VARYING K FROM 1 BY 1
    UNTIL K IS GREATER THAN 100 OR PLOT-CHARACTER IS EQUAL TO '#'.
    DISPLAY PLOT-CHARACTER WITH NO ADVANCING.
ITERATION-PARAGRAPH.
    MULTIPLY X-A BY X-A GIVING X-A-SQUARED.
    MULTIPLY Y-A BY Y-A GIVING Y-A-SQUARED.
    SUBTRACT Y-A-SQUARED FROM X-A-SQUARED GIVING X-B.
    ADD      X   TO X-B.
    MULTIPLY X-A BY Y-A GIVING Y-A.
    MULTIPLY Y-A BY 2   GIVING Y-A.
    SUBTRACT Y   FROM Y-A.
    MOVE     X-B TO   X-A.
    ADD X-A-SQUARED TO Y-A-SQUARED GIVING SUM-OF-SQUARES.
    MOVE FUNCTION SQRT (SUM-OF-SQUARES) TO ROOT.
    IF ROOT IS GREATER THAN 2 THEN MOVE '#' TO PLOT-CHARACTER.
Output:
################################################################
#################################   ############################
################################     ###########################
############################## ##   ############################
########################  #               ######################
########################                      ##################
#####################                          #################
####################                             ###############
######## ##    #####                            ################
#######           #                             ################
######            #                            #################
                                            ####################
######            #                            #################
#######           #                             ################
######## ##    #####                            ################
####################                             ###############
#####################                          #################
########################                      ##################
########################  #               ######################
############################## ##   ############################
################################     ###########################
#################################   ############################
################################################################
################################################################

Common Lisp

(defpackage #:mandelbrot
  (:use #:cl))

(in-package #:mandelbrot)

(deftype pixel () '(unsigned-byte 8))
(deftype image () '(array pixel))

(defun write-pgm (image filespec)
  (declare (image image))
  (with-open-file (s filespec :direction :output :element-type 'pixel :if-exists :supersede)
    (let* ((width  (array-dimension image 1))
           (height (array-dimension image 0))
           (header (format nil "P5~A~D ~D~A255~A" #\Newline width height #\Newline #\Newline)))
      (loop for c across header
            do (write-byte (char-code c) s))
      (dotimes (row height)
        (dotimes (col width)
          (write-byte (aref image row col) s))))))

(defparameter *x-max* 800)
(defparameter *y-max* 800)
(defparameter *cx-min* -2.5)
(defparameter *cx-max* 1.5)
(defparameter *cy-min* -2.0)
(defparameter *cy-max* 2.0)
(defparameter *escape-radius* 2)
(defparameter *iteration-max* 40)

(defun mandelbrot (filespec)
  (let ((pixel-width  (/ (- *cx-max* *cx-min*) *x-max*))
        (pixel-height (/ (- *cy-max* *cy-min*) *y-max*))
        (image (make-array (list *y-max* *x-max*) :element-type 'pixel :initial-element 0)))
    (loop for y from 0 below *y-max*
          for cy from *cy-min* by pixel-height
          do (loop for x from 0 below *x-max*
                   for cx from *cx-min* by pixel-width
                   for iteration = (loop with c = (complex cx cy)
                                         for iteration from 0 below *iteration-max*
                                         for z = c then (+ (* z z) c)
                                         while (< (abs z) *escape-radius*)
                                         finally (return iteration))
                   for pixel = (round (* 255 (/ (- *iteration-max* iteration) *iteration-max*)))
                   do (setf (aref image y x) pixel)))
    (write-pgm image filespec)))

Cowgol

Translation of: B
include "cowgol.coh";

const xmin := -8601;
const xmax := 2867;
const ymin := -4915;
const ymax := 4915;
const maxiter := 32;

const dx := (xmax-xmin)/79;
const dy := (ymax-ymin)/24;

var cy: int16 := ymin;
while cy <= ymax loop
    var cx: int16 := xmin;
    while cx <= xmax loop
        var x: int32 := 0;
        var y: int32 := 0;
        var x2: int32 := 0;
        var y2: int32 := 0;
        var iter: uint8 := 0;
        
        while iter < maxiter and x2 + y2 <= 16384 loop
            y := ((x*y)>>11)+cy as int32;
            x := x2-y2+cx as int32;
            x2 := (x*x)>>12;
            y2 := (y*y)>>12;
            iter := iter + 1;
        end loop;
        
        print_char(' ' + iter);
        cx := cx + dx;
    end loop;
    print_nl();
    cy := cy + dy;
end loop;
Output:
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'+)%%%$$$$$#####"""""""""""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(+,)++&%$$$$$$######""""""
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*5:/+('&%%$$$$$$#######"""
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),@@@@@@@,'&%%%%%$$$$########
!!!!!!!"""####################$$$$$$$$%%%&'())((())*,@@@@@@/+))('&&&&)'%$$######
!!!!!!""###################$$$$$%%%%%%&&&'+.@@=/<@@@@@@@@@@@@@@@/++@..93%%$#####
!!!!!"################$$$%%%%%%%%%%&&&&'),+2@@@@@@@@@@@@@@@@@@@@@@@@@1(&&%$$####
!!!!"##########$$$$$%%&(-(''''''''''''(*,5@@@@@@@@@@@@@@@@@@@@@@@@@@@@+)-&%$$###
!!!!####$$$$$$$$%%%%%&'(*-@1.+.@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4-(&%$$$##
!!!!#$$$$$$$$$%%%%%%'''++.6@@@@@@@@@8/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3(%%$$$$#
!!!#$$$$$$$%&&&&''()/-5.5@@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?'&%%$$$$#
!!!(**+/+<523/80/46@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+)'&&%%$$$$#
!!!#$$$$$$$%&&&&''().-2.@@@@@@@@@@@@@@?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$#
!!!!#$$$$$$$$$%%%%%&'''/,.7@@@@@@@@@;/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0'%%$$$$#
!!!!####$$$$$$$$%%%%%&'(*-:2.,/?-5+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+(&%$$$##
!!!!"##########$$$$$%%&(-(''''(''''''((*,4@@@@@@@@@@@@@@@@@@@@@@@@@@@4+).&%$$###
!!!!!"################$$$%%%%%%%%%%&&&&')<,4@@@@@@@@@@@@@@@@@@@@@@@@@/('&%%$####
!!!!!!""##################$$$$$$%%%%%%&&&'*.@@@0@@@@@@@@@@@@@@@@1,,@//9)%%$#####
!!!!!!!"""####################$$$$$$$$%%%&(())((()**-@@@@@@/+)))'&&&')'%$$######
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''(,@@@@@@@+'&&%%%%%$$$########
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*7@0+('&%%%$$$$$#######"""
!!!!!!!!!!!"""""""######################$$$$$$$$$%%%&&(+-).*&%$$$$$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$%%'3(%%%$$$$$######""""""""""
!!!!!!!!!!!!!!!""""""""""""#####################################""""""""""""""""

Craft Basic

define max = 15, w = 640, h = 480
define py = 0, px = 0, sx = 0, sy = 0
define xx = 0, xy = 0

bgcolor 0, 0, 0
cls graphics
fill on

do

	let px = 0

	do

		let sy = (py - h / 2) / 150 
		let sx = (px - w / 2) / 150
     
		let i = 0
		let x = 0
		let y = 0

		let xy = x * x + y * y

		do

			let xx = x * x - y * y + sx + .1
			let y = 2 * x * y + sy
			let x = xx

			let i = i + 1 

		loop i < max and xy < 4

		wait

		fgcolor 220 + i * x, 220 + i * y, 230 + i * xy
		rect px, py, 4, 4

		let px = px + 4

	loop px < w

	let py = py + 4

loop py < h

D

Textual Version

This uses std.complex because D built-in complex numbers are deprecated.

void main() {
    import std.stdio, std.complex;

    for (real y = -1.2; y < 1.2; y += 0.05) {
        for (real x = -2.05; x < 0.55; x += 0.03) {
            auto z = 0.complex;
            foreach (_; 0 .. 100)
                z = z ^^ 2 + complex(x, y);
            write(z.abs < 2 ? '#' : '.');
        }
        writeln;
    }
}
Output:
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
................................................................##.....................
.............................................................######....................
.............................................................#######...................
..............................................................######...................
..........................................................#.#.###..#.#.................
...................................................##....################..............
..................................................###.######################.###.......
...................................................############################........
................................................###############################........
................................................################################.......
.............................................#####################################.....
..............................................###################################......
..............................##.####.#......####################################......
..............................###########....####################################......
............................###############.######################################.....
............................###############.#####################################......
........................##.#####################################################.......
......#.#####################################################################..........
........................##.#####################################################.......
............................###############.#####################################......
............................###############.######################################.....
..............................###########....####################################......
..............................##.####.#......####################################......
..............................................###################################......
.............................................#####################################.....
................................................################################.......
................................................###############################........
...................................................############################........
..................................................###.######################.###.......
...................................................##....################..............
..........................................................#.#.###..#.#.................
..............................................................######...................
.............................................................#######...................
.............................................................######....................
................................................................##.....................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................

More Functional Textual Version

The output is similar.

void main() {
    import std.stdio, std.complex, std.range, std.algorithm;

    foreach (immutable y; iota(-1.2, 1.2, 0.05))
        iota(-2.05, 0.55, 0.03).map!(x => 0.complex
            .recurrence!((a, n) => a[n - 1] ^^ 2 + complex(x, y))
            .drop(100).front.abs < 2 ? '#' : '.').writeln;
}

Graphical Version

Library: QD
Library: SDL
Library: Phobos
import qd;

double lensqr(cdouble c) { return c.re * c.re + c.im * c.im; }

const Limit = 150;

void main() {
  screen(640, 480);
  for (int y = 0; y < screen.h; ++y) {
    flip; events;
    for (int x = 0; x < screen.w; ++x) {
      auto
        c_x = x * 1.0 / screen.w - 0.5,
        c_y = y * 1.0 / screen.h - 0.5,
        c = c_y * 2.0i + c_x * 3.0 - 1.0,
        z = 0.0i + 0.0,
        i = 0;
      for (; i < Limit; ++i) {
        z = z * z + c;
        if (lensqr(z) > 4) break;
      }
      auto value = cast(ubyte) (i * 255.0 / Limit);
      pset(x, y, rgb(value, value, value));
    }
  }
  while (true) { flip; events; }
}

Dart

Implementation in Google Dart works on http://try.dartlang.org/ (as of 10/18/2011) since the language is very new, it may break in the future. The implementation uses a incomplete Complex class supporting operator overloading.

class Complex {
  double _r,_i;

  Complex(this._r,this._i);
  double get r => _r;
  double get i => _i;
  String toString() => "($r,$i)";

  Complex operator +(Complex other) => new Complex(r+other.r,i+other.i);
  Complex operator *(Complex other) =>
      new Complex(r*other.r-i*other.i,r*other.i+other.r*i);
  double abs() => r*r+i*i;
}

void main() {
  double start_x=-1.5;
  double start_y=-1.0;
  double step_x=0.03;
  double step_y=0.1;

  for(int y=0;y<20;y++) {
    String line="";
    for(int x=0;x<70;x++) {
      Complex c=new Complex(start_x+step_x*x,start_y+step_y*y);
      Complex z=new Complex(0.0, 0.0);
      for(int i=0;i<100;i++) {
        z=z*(z)+c;
        if(z.abs()>2) {
          break;
        }
      }
      line+=z.abs()>2 ? " " : "*";
    }
    print(line);
  }
}

Dc

ASCII output

Works with: GNU dc
Works with: OpenBSD dc

This can be done in a more Dc-ish way, e.g. by moving the loop macros' definitions to the initialisations in the top instead of saving the macro definition of inner loops over and over again in outer loops.

 _2.1 sx # xmin = -2.1
  0.7 sX # xmax =  0.7

 _1.2 sy # ymin = -1.2
  1.2 sY # ymax =  1.2

   32 sM # maxiter = 32

   80 sW # image width
   25 sH # image height

    8 k  # precision

[ q ] sq # quitter helper macro

# for h from 0 to H-1
0 sh
[
  lh lH =q # quit if H reached

  # for w from 0 to W-1
  0 sw
  [
    lw lW =q # quit if W reached

    # (w,h) -> (R,I)
    #           | |
    #           | ymin + h*(ymax-ymin)/(height-1)
    #           xmin + w*(xmax-xmin)/(width-1)

    lX lx - lW 1 - / lw * lx + sR
    lY ly - lH 1 - / lh * ly + sI

    # iterate for (R,I)

    0 sr #     r:=0
    0 si #     i:=0
    0 sa #     a:=0 (r squared)
    0 sb #     b:=0 (i squared)
    0 sm #     m:=0

    # do while m!=M and a+b=<4
    [
      lm lM =q # exit if m==M
      la lb + 4<q # exit if >4

      2 lr * li * lI + si # i:=2*r*i+I
      la lb - lR + sr     # r:=a-b+R
      lm 1 + sm           # m+=1
      lr 2 ^ sa           # a:=r*r
      li 2 ^ sb           # b:=i*i

      l0 x                # loop
    ] s0
    l0 x

    lm 32 + P             # print "pixel"

    lw 1 + sw             # w+=1
    l1 x                  # loop
  ] s1
  l1 x

  A P                     # linefeed

  lh 1 + sh               # h+=1
  l2 x                    # loop
] s2
l2 x
Output:
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'0(%%%$$$$$#####"""""""""""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(++)++&$$$$$$$######""""""
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*@;/*('&%%$$$$$$#######"""
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),@@@@@@@+'&%%%%%$$$$########
!!!!!!!"""####################$$$$$$$$%%%&'())((())*-@@@@@@.+))('&&&&+&%$$######
!!!!!!""###################$$$$$%%%%%%&&&'+.@@@08@@@@@@@@@@@@@@@/+,@//@)%%$#####
!!!!!"################$$$%%%%%%%%%%&&&&')-+7@@@@@@@@@@@@@@@@@@@@@@@@@4(&&%$$####
!!!!"##########$$$$$%%&(,('''''''''''((*-5@@@@@@@@@@@@@@@@@@@@@@@@@@@3+)4&%$$###
!!!!####$$$$$$$$%%%%%&'(*-@1.+/@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3+'&%$$$##
!!!!#$$$$$$$$$%%%%%%'''++.7@@@@@@@@@9/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@<6'%%$$$$#
!!!#$$$$$$$%&&&&''().-2.6@@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$#
!!!@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@2+)'&&%%$$$$#
!!!#$$$$$$$%&&&&''().-2.6@@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$#
!!!!#$$$$$$$$$%%%%%%'''++.7@@@@@@@@@9/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@<6'%%$$$$#
!!!!####$$$$$$$$%%%%%&'(*-@1.+/@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3+'&%$$$##
!!!!"##########$$$$$%%&(,('''''''''''((*-5@@@@@@@@@@@@@@@@@@@@@@@@@@@3+)4&%$$###
!!!!!"################$$$%%%%%%%%%%&&&&')-+7@@@@@@@@@@@@@@@@@@@@@@@@@4(&&%$$####
!!!!!!""###################$$$$$%%%%%%&&&'+.@@@08@@@@@@@@@@@@@@@/+,@//@)%%$#####
!!!!!!!"""####################$$$$$$$$%%%&'())((())*-@@@@@@.+))('&&&&+&%$$######
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),@@@@@@@+'&%%%%%$$$$########
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*@;/*('&%%$$$$$$#######"""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(++)++&$$$$$$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'0(%%%$$$$$#####"""""""""""
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""

PGM (P5) output

This is a condensed version of the ASCII output variant modified to generate a PGM (P5) image.

_2.1 sx   0.7 sX  _1.2 sy   1.2 sY
32 sM
640 sW 480 sH
8 k
[P5] P A P
lW n 32 P lH n A P
lM 1 - n A P
[ q ] sq
0 sh
[
  lh lH =q
  0 sw
  [
    lw lW =q
    lX lx - lW 1 - / lw * lx + sR
    lY ly - lH 1 - / lh * ly + sI
    0 sr 0 si 0 sa 0 sb 0 sm
    [
      lm lM =q
      la lb + 4<q
      2 lr * li * lI + si
      la lb - lR + sr
      lm 1 + sm
      lr 2 ^ sa
      li 2 ^ sb
      l0 x
    ] s0
    l0 x
    lm 1 - P
    lw 1 + sw
    l1 x
  ] s1
  l1 x
  lh 1 + sh
  l2 x
] s2
l2 x


Delphi

See Pascal.

DWScript

Translation of: D
const maxIter = 256;

var x, y, i : Integer;
for y:=-39 to 39 do begin
   for x:=-39 to 39 do begin
      var c := Complex(y/40-0.5, x/40);
      var z := Complex(0, 0);
      for i:=1 to maxIter do begin
         z := z*z + c;
         if Abs(z)>=4 then Break;
      end;
      if i>=maxIter then
         Print('#')
      else Print('.');
    end;
    PrintLn('');
end;

EasyLang

Run it

# Mandelbrot
#  
res = 4
maxiter = 200
# 
# better but slower:
# res = 8
# maxiter = 300
# 
#  
mid = res * 50
center_x = 3 * mid / 2
center_y = mid
scale = mid
# 
background 000
textsize 2
# 
fastfunc iter cx cy maxiter .
   while xx + yy < 4 and it < maxiter
      y = 2 * x * y + cy
      x = xx - yy + cx
      xx = x * x
      yy = y * y
      it += 1
   .
   return it
.
proc draw . .
   clear
   for scr_y = 0 to 2 * mid - 1
      cy = (scr_y - center_y) / scale
      for scr_x = 0 to 2 * mid - 1
         cx = (scr_x - center_x) / scale
         it = iter cx cy maxiter
         if it < maxiter
            color3 it / 20 it / 100 it / 150
            move scr_x / res scr_y / res
            rect 1 / res 1 / res
         .
      .
   .
   color 990
   move 1 1
   text "Short press to zoom in, long to zoom out"
.
on mouse_down
   time0 = systime
.
on mouse_up
   center_x += mid - mouse_x * res
   center_y += mid - mouse_y * res
   if systime - time0 < 0.3
      center_x -= mid - center_x
      center_y -= mid - center_y
      scale *= 2
   else
      center_x += (mid - center_x) * 3 / 4
      center_y += (mid - center_y) * 3 / 4
      scale /= 4
   .
   draw
.
draw

eC

(Try it in a WebApp)

Drawing code:

void drawMandelbrot(Bitmap bmp, float range, Complex center, ColorAlpha * palette, int nPalEntries, int nIterations, float scale)
{
   int x, y;
   int w = bmp.width, h = bmp.height;
   ColorAlpha * picture = (ColorAlpha *)bmp.picture;
   double logOf2 = log(2);
   Complex d
   {
      w > h ? range : range * w / h,
      h > w ? range : range * h / w
   };
   Complex C0 { center.a - d.a/2, center.b - d.b/2 };
   Complex C = C0;
   double delta = d.a / w;

   for(y = 0; y < h; y++, C.a = C0.a, C.b += delta)
   {
      for(x = 0; x < w; x++, picture++, C.a += delta)
      {
         Complex Z { };
         int i;
         double ii = 0;
         bool out = false;
         double Za2 = Z.a * Z.a, Zb2 = Z.b * Z.b;
         for(i = 0; i < nIterations; i++)
         {
            double z2;
            Z = { Za2 - Zb2, 2*Z.a*Z.b };
            Z.a += C.a;
            Z.b += C.b;
            Za2 = Z.a * Z.a, Zb2 = Z.b * Z.b;
            z2 = Za2 + Zb2;

            if(z2 >= 2*2)
            {
               ii = (double)(i + 1 - log(0.5 * log(z2)) / logOf2);
               out = true;
               break;
            }
         }
         if(out)
         {
            float si = (float)(ii * scale);
            int i0 = ((int)si) % nPalEntries;
            *picture = palette[i0];
         }
         else
            *picture = black;
      }
   }
}

Interactive class with Rubberband Zoom:

class Mandelbrot : Window
{
   caption = $"Mandelbrot";
   borderStyle = sizable;
   hasMaximize = true;
   hasMinimize = true;
   hasClose = true;
   clientSize = { 600, 600 };

   Point mouseStart, mouseEnd;
   bool dragging;
   bool needUpdate;

   float scale;
   int nIterations; nIterations = 256;
   ColorAlpha * palette;
   int nPalEntries;
   Complex center { -0.75, 0 };

   float range; range = 4;
   Bitmap bmp { };

   Mandelbrot()
   {
      static ColorKey keys[] =
      {
         { navy, 0.0f },
         { Color { 146, 213, 237 }, 0.198606268f },
         { white, 0.3f },
         { Color { 255, 255, 124 }, 0.444250882f },
         { Color { 255, 100, 0 }, 0.634146333f },
         { navy, 1 }
      };

      nPalEntries = 30000;
      palette = new ColorAlpha[nPalEntries];
      scale = nPalEntries / 175.0f;
      PaletteGradient(palette, nPalEntries, keys, sizeof(keys)/sizeof(keys[0]), 1.0);
      needUpdate = true;
   }

   ~Mandelbrot() { delete palette; }

   void OnRedraw(Surface surface)
   {
      if(needUpdate)
      {
         drawMandelbrot(bmp, range, center, palette, nPalEntries, nIterations, scale);
         needUpdate = false;
      }
      surface.Blit(bmp, 0,0, 0,0, bmp.width, bmp.height);

      if(dragging)
      {
         surface.foreground = lime;
         surface.Rectangle(mouseStart.x, mouseStart.y, mouseEnd.x, mouseEnd.y);
      }
   }

   bool OnLeftButtonDown(int x, int y, Modifiers mods)
   {
      mouseEnd = mouseStart = { x, y };
      Capture();
      dragging = true;
      Update(null);
      return true;
   }

   bool OnLeftButtonUp(int x, int y, Modifiers mods)
   {
      if(dragging)
      {
         int dx = Abs(mouseEnd.x - mouseStart.x), dy = Abs(mouseEnd.y - mouseStart.y);
         if(dx > 4 && dy > 4)
         {
            int w = clientSize.w, h = clientSize.h;
            float rangeX = w > h ? range : range * w / h;
            float rangeY = h > w ? range : range * h / w;

            center.a += ((mouseStart.x + mouseEnd.x) - w) / 2.0f * rangeX / w;
            center.b += ((mouseStart.y + mouseEnd.y) - h) / 2.0f * rangeY / h;

            range = dy > dx ? dy * range / h : dx * range / w;

            needUpdate = true;
            Update(null);
         }
         ReleaseCapture();
         dragging = false;
      }
      return true;
   }

   bool OnMouseMove(int x, int y, Modifiers mods)
   {
      if(dragging)
      {
         mouseEnd = { x, y };
         Update(null);
      }
      return true;
   }

   bool OnRightButtonDown(int x, int y, Modifiers mods)
   {
      range = 4;
      nIterations = 256;
      center = { -0.75, 0 };
      needUpdate = true;
      Update(null);
      return true;
   }

   void OnResize(int width, int height)
   {
      bmp.Allocate(null, width, height, 0, pixelFormat888, false);
      needUpdate = true;
      Update(null);
   }

   bool OnKeyHit(Key key, unichar ch)
   {
      switch(key)
      {
         case space: case keyPadPlus: case plus:
            nIterations += 256;
            needUpdate = true;
            Update(null);
            break;
      }
      return true;
   }
}

Mandelbrot mandelbrotForm {};

EchoLisp

(lib 'math) ;; fractal function
(lib 'plot)

;; (fractal z zc n) iterates z := z^2 + c, n times
;; 100 iterations
(define (mset z) (if (= Infinity (fractal 0 z 100)) Infinity z))

;; plot function argument inside square (-2 -2), (2,2)
(plot-z-arg mset -2 -2)

;; result here [http://www.echolalie.org/echolisp/help.html#fractal]

Elixir

defmodule Mandelbrot do
  def set do
    xsize = 59
    ysize = 21
    minIm = -1.0
    maxIm = 1.0
    minRe = -2.0
    maxRe = 1.0
    stepX = (maxRe - minRe) / xsize
    stepY = (maxIm - minIm) / ysize
    Enum.each(0..ysize, fn y ->
      im = minIm + stepY * y
      Enum.map(0..xsize, fn x ->
        re = minRe + stepX * x
        62 - loop(0, re, im, re, im, re*re+im*im)
      end) |> IO.puts
    end)
  end
  
  defp loop(n, _, _, _, _, _) when n>=30, do: n
  defp loop(n, _, _, _, _, v) when v>4.0, do: n-1
  defp loop(n, re, im, zr, zi, _) do
    a = zr * zr
    b = zi * zi
    loop(n+1, re, im, a-b+re, 2*zr*zi+im, a+b)
  end
end

Mandelbrot.set
Output:
??????=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<===========
?????===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<========
????===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<=======
???==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<=====
??==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<====
??=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<===
?=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<==
?<<<<;;;;;:::972456-567763                      +9;;<<<<<<<=
?<;;;;;;::::9875&      .3                       *9;;;<<<<<<=
?;;;;;;::997564'        '                       8:;;;<<<<<<=
?::988897735/                                 &89:;;;<<<<<<=
?::988897735/                                 &89:;;;<<<<<<=
?;;;;;;::997564'        '                       8:;;;<<<<<<=
?<;;;;;;::::9875&      .3                       *9;;;<<<<<<=
?<<<<;;;;;:::972456-567763                      +9;;<<<<<<<=
?=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<==
??=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<===
??==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<====
???==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<=====
????===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<=======
?????===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<========
??????=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<===========

Emacs Lisp

Text mode

; === Mandelbrot ============================================

(setq mandel-size (cons 76 34))
(setq xmin -2)
(setq xmax .5)
(setq ymin -1.2)
(setq ymax 1.2)
(setq max-iter 20)

(defun mandel-iter-point (x y)
  "Run the actual iteration for each point."
  (let ((xp 0)
        (yp 0)
        (it 0)
        (xt 0))
    (while (and (< (+ (* xp xp) (* yp yp)) 4) (< it max-iter))
      (setq xt (+ (* xp xp) (* -1 yp yp) x))
      (setq yp (+ (* 2 xp yp) y))
      (setq xp xt)
      (setq it (1+ it)))
    it))

(defun mandel-iter (p)
  "Return string for point based on whether inside/outside the set."
  (let ((it (mandel-iter-point (car p) (cdr p))))
    (if (= it max-iter) "*" "-")))

(defun mandel-pos (x y)
  "Convert screen coordinates to input coordinates."
  (let ((xp (+ xmin (* (- xmax xmin) (/ (float x) (car mandel-size)))))
        (yp (+ ymin (* (- ymax ymin) (/ (float y) (cdr mandel-size))))))
       (cons xp yp)))

(defun mandel ()
  "Plot the Mandelbrot set."
  (dotimes (y (cdr mandel-size))
    (dotimes (x (car mandel-size))
      (if (= x 0)
        (insert(format "\n%s" (mandel-iter (mandel-pos x y))))
        (insert(format "%s" (mandel-iter (mandel-pos x y))))))))

(mandel)
Output:
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
---------------------------------------------------------*------------------
----------------------------------------------------------------------------
----------------------------------------------------**--***--*--------------
-----------------------------------------------------********---------------
------------------------------------------------------*******---------------
--------------------------------------------*-*--******************---------
--------------------------------------------****************************----
-----------------------------------------*-****************************-----
-----------------------------------------*******************************----
---------------------------------------************************************-
--------------------------**--**-*-----**********************************---
-------------------------***********---************************************-
------------------*-----**************************************************--
-------------------*****************************************************----
-*********************************************************************------
-------------------*****************************************************----
------------------*-----**************************************************--
-------------------------***********---************************************-
--------------------------**--**-*-----**********************************---
---------------------------------------************************************-
-----------------------------------------*******************************----
-----------------------------------------*-****************************-----
--------------------------------------------****************************----
--------------------------------------------*-*--******************---------
------------------------------------------------------*******---------------
-----------------------------------------------------********---------------
----------------------------------------------------**--***--*--------------
----------------------------------------------------------------------------
---------------------------------------------------------*------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------

Graphical version

With a few modifications (mandel-size, mandel-iter, string-to-image, mandel-pic), the code above can also render the Mandelbrot fractal to an XPM image and display it directly in the buffer. (You might have to scroll up in Emacs after the function has run to see its output.)

; === Graphical Mandelbrot ============================================

(setq mandel-size (cons 320 300))
(setq xmin -2)
(setq xmax .5)
(setq ymin -1.2)
(setq ymax 1.2)
(setq max-iter 20)

(defun mandel-iter-point (x y)
  "Run the actual iteration for each point."
  (let ((xp 0)
        (yp 0)
        (it 0)
        (xt 0))
    (while (and (< (+ (* xp xp) (* yp yp)) 4) (< it max-iter))
      (setq xt (+ (* xp xp) (* -1 yp yp) x))
      (setq yp (+ (* 2 xp yp) y))
      (setq xp xt)
      (setq it (1+ it)))
    it))

(defun mandel-iter (p)
  "Return string for point based on whether inside/outside the set."
  (let ((it (mandel-iter-point (car p) (cdr p))))
    (if (= it max-iter) "*" (if (cl-oddp it) "+" "-"))))

(defun mandel-pos (x y)
  "Convert screen coordinates to input coordinates."
  (let ((xp (+ xmin (* (- xmax xmin) (/ (float x) (car mandel-size)))))
        (yp (+ ymin (* (- ymax ymin) (/ (float y) (cdr mandel-size))))))
       (cons xp yp)))

(defun string-to-image (str)
  "Convert image data string to XPM image."
  (create-image (concat (format "/* XPM */
static char * mandel[] = {
\"%i %i 3 1\",
\"+      c #ff0000\",
\"-      c #0000ff\",
\"*      c #000000\"," (car mandel-size) (cdr mandel-size))
    str "};") 'xpm t))

(defun mandel-pic ()
  "Plot the Mandelbrot set."
  (setq all "")
  (dotimes (y (cdr mandel-size))
    (setq line "")
    (dotimes (x (car mandel-size))
      (setq line (concat line (mandel-iter (mandel-pos x y)))))
    (setq all (concat all "\"" line "\",\n")))
  (insert-image (string-to-image all)))

(mandel-pic)

Erlang

Translation of: Haskell

Function seq_float/2 is copied from Andrew Fecheyr's GitHubGist.

Using module complex from Geoff Hulette's GitHub repository

Geoff Hulette's GitHub repository provides two alternative implementations which are very interesting.

-module(mandelbrot).

-export([test/0]).

magnitude(Z) ->
  R = complex:real(Z),
  I = complex:imaginary(Z),
  R * R + I * I.

mandelbrot(A, MaxI, Z, I) ->
    case (I < MaxI) and (magnitude(Z) < 2.0) of
        true ->
            NZ = complex:add(complex:mult(Z, Z), A),
            mandelbrot(A, MaxI, NZ, I + 1);
        false ->
            case I of 
                MaxI ->
                    $*;
                _ ->
                    $ 
            end
    end.

test() ->
    lists:map(
        fun(S) -> io:format("~s",[S]) end, 
        [
            [
                begin 
                    Z = complex:make(X, Y),
                    mandelbrot(Z, 50, Z, 1)
                end
            || X <- seq_float(-2, 0.5, 0.0315)
            ] ++ "\n"
        || Y <- seq_float(-1,1, 0.05)
        ] ),
    ok.

% **************************************************
% Copied from https://gist.github.com/andruby/241489
% **************************************************

seq_float(Min, Max, Inc, Counter, Acc) when (Counter*Inc + Min) >= Max -> 
  lists:reverse([Max|Acc]);
seq_float(Min, Max, Inc, Counter, Acc) -> 
  seq_float(Min, Max, Inc, Counter+1, [Inc * Counter + Min|Acc]).
seq_float(Min, Max, Inc) -> 
  seq_float(Min, Max, Inc, 0, []).

% **************************************************

Output:

                                                                                 
                                                                                 
                                                                                 
                                                           **                    
                                                         ******                  
                                                       ********                  
                                                         ******                  
                                                      ******** **   *            
                                              ***   *****************            
                                              ************************  ***      
                                              ****************************       
                                           ******************************        
                                            ******************************       
                                         ************************************    
                                *         **********************************     
                           ** ***** *     **********************************     
                           ***********   ************************************    
                         ************** ************************************     
                         ***************************************************     
                     *****************************************************       
                   *****************************************************         
                     *****************************************************       
                         ***************************************************     
                         ************** ************************************     
                           ***********   ************************************    
                           ** ***** *     **********************************     
                                *         **********************************     
                                         ************************************    
                                            ******************************       
                                           ******************************        
                                              ****************************       
                                              ************************  ***      
                                              ***   *****************            
                                                      ******** **   *            
                                                         ******                  
                                                       ********                  
                                                         ******                  
                                                           **                    
                                                                                 
                                                                                 
                                                                                 

ERRE

PROGRAM MANDELBROT

!$KEY
!$INCLUDE="PC.LIB"

BEGIN

SCREEN(7)
GR_WINDOW(-2,1.5,2,-1.5)
FOR X0=-2 TO 2 STEP 0.01 DO
    FOR Y0=-1.5 TO 1.5 STEP 0.01 DO
        X=0
        Y=0

        ITERATION=0
        MAX_ITERATION=223

        WHILE (X*X+Y*Y<=(2*2) AND ITERATION<MAX_ITERATION) DO
            X_TEMP=X*X-Y*Y+X0
            Y=2*X*Y+Y0

            X=X_TEMP

            ITERATION=ITERATION+1
        END WHILE

        IF ITERATION<>MAX_ITERATION THEN
            C=ITERATION
          ELSE
            C=0
        END IF

        PSET(X0,Y0,C)
    END FOR
END FOR
END PROGRAM

Note: This is a PC version which uses EGA 16-color 320x200. Graphic commands are taken from PC.LIB library.

F#

open System.Drawing 
open System.Windows.Forms
type Complex =
    { 
        re : float;
        im : float
    }
let cplus (x:Complex) (y:Complex) : Complex = 
    {
        re = x.re + y.re;
        im = x.im + y.im
    }
let cmult (x:Complex) (y:Complex) : Complex = 
    {
        re = x.re * y.re - x.im * y.im;
        im = x.re * y.im + x.im * y.re;
    }

let norm (x:Complex) : float =
    x.re*x.re + x.im*x.im

type Mandel = class
    inherit Form
    static member xPixels = 500
    static member yPixels = 500
    val mutable bmp : Bitmap
    member x.mandelbrot xMin xMax yMin yMax maxIter =
        let rec mandelbrotIterator z c n =
            if (norm z) > 2.0 then false else
                match n with
                    | 0 -> true
                    | n -> let z' = cplus ( cmult z z ) c in
                            mandelbrotIterator z' c (n-1)
        let dx = (xMax - xMin) / (float (Mandel.xPixels))
        let dy = (yMax - yMin) / (float (Mandel.yPixels))
        in
        for xi = 0 to Mandel.xPixels-1 do
            for yi = 0 to Mandel.yPixels-1 do
                let c = {re = xMin + (dx * float(xi) ) ;
                         im = yMin + (dy * float(yi) )} in
                if (mandelbrotIterator {re=0.;im=0.;} c maxIter) then
                    x.bmp.SetPixel(xi,yi,Color.Azure)
                else
                    x.bmp.SetPixel(xi,yi,Color.Black)
            done
        done

    member public x.generate () = x.mandelbrot (-1.5) 0.5 (-1.0) 1.0 200 ; x.Refresh()

    new() as x = {bmp = new Bitmap(Mandel.xPixels , Mandel.yPixels)} then
        x.Text <- "Mandelbrot set" ;
        x.Width <- Mandel.xPixels ;
        x.Height <- Mandel.yPixels ;
        x.BackgroundImage <- x.bmp;
        x.generate();
        x.Show();   
end

let f = new Mandel()
do Application.Run(f)

Alternate version, applicable to text and GUI

Basic generation code

let getMandelbrotValues width height maxIter ((xMin,xMax),(yMin,yMax)) =
  let mandIter (cr:float,ci:float) =
    let next (zr,zi) = (cr + (zr * zr - zi * zi)), (ci + (zr * zi + zi * zr))
    let rec loop = function
      | step,_ when step=maxIter->0
      | step,(zr,zi) when ((zr * zr + zi * zi) > 2.0) -> step
      | step,z -> loop ((step + 1), (next z))
    loop (0,(0.0, 0.0))
  let forPos =
    let dx, dy = (xMax - xMin) / (float width), (yMax - yMin) / (float height)
    fun y x -> mandIter ((xMin + dx * float(x)), (yMin + dy * float(y)))
  [0..height-1] |> List.map(fun y->[0..width-1] |> List.map (forPos y))

Text display

getMandelbrotValues 80 25 50 ((-2.0,1.0),(-1.0,1.0))
|> List.map(fun row-> row |> List.map (function | 0 ->" " |_->".") |> String.concat "")
|> List.iter (printfn "%s")

Results:

Output:
................................................................................
................................................................................
.................................................  .............................
................................................     ...........................
.................................................    ...........................
.......................................   .               ......................
........................................                       .................
....................................                          ..................
....................................                           .................
..........................  ......                              ................
.......................         ...                             ................
.....................            .                              ................
.................                                              .................
.................                                              .................
.....................            .                              ................
.......................         ...                             ................
..........................  ......                              ................
....................................                           .................
....................................                          ..................
........................................                       .................
.......................................   .               ......................
.................................................    ...........................
................................................     ...........................
.................................................  .............................
................................................................................

Graphics display

open System.Drawing 
open System.Windows.Forms

let showGraphic (colorForIter: int -> Color) (width: int) (height:int) maxIter view =
  new Form()
  |> fun frm ->
    frm.Width <- width
    frm.Height <- height
    frm.BackgroundImage <- 
      new Bitmap(width,height)
      |> fun bmp ->
        getMandelbrotValues width height maxIter view
        |> List.mapi (fun y row->row |> List.mapi (fun x v->((x,y),v))) |> List.collect id
        |> List.iter (fun ((x,y),v) -> bmp.SetPixel(x,y,(colorForIter v)))
        bmp
    frm.Show()

let toColor = (function | 0 -> (0,0,0) | n -> ((31 &&& n) |> fun x->(0, 18 + x * 5, 36 + x * 7))) >> Color.FromArgb

showGraphic toColor 640 480 5000 ((-2.0,1.0),(-1.0,1.0))

Factor

! with ("::") or without (":") generalizations:
! : [a..b] ( steps a b -- a..b ) 2dup swap - 4 nrot 1 - / <range> ;
::  [a..b] ( steps a b -- a..b ) a b b a - steps 1 - / <range> ;

: >char ( n -- c )
    dup -1 = [ drop 32 ] [ 26 mod CHAR: a + ] if ;

! iterates z' = z^2 + c, Factor does complex numbers!
: iter ( c z -- z' ) dup * + ;

: unbound ( c -- ? ) absq 4 > ;

:: mz ( c max i z -- n )
  {
    { [ i max >= ] [ -1 ] }
    { [ z unbound ] [ i ] }
    [ c max i 1 + c z iter mz ]
  } cond ;

: mandelzahl ( c max -- n ) 0 0 mz ;

:: mandel ( w h max -- )
    h -1. 1. [a..b] ! range over y
    [   w -2. 1. [a..b] ! range over x
        [ dupd swap rect> max mandelzahl >char ] map
        >string print
        drop ! old y
    ] each
    ;

70 25 1000 mandel
Output:
bbbbbbbcccccdddddddddddddddddddeeeeeeeffghjpjl feeeeedddddcccccccccccc
bbbbbbccccddddddddddddddddddeeeeeeeefffghikopjhgffeeeeedddddcccccccccc
bbbbbcccddddddddddddddddddeeeeeeeefffggjotx etiigfffeeeeddddddcccccccc
bbbbccddddddddddddddddddeeeeeeeffgggghhjq     iihgggfffeedddddddcccccc
bbbccddddddddddddddddeeeeeefffghvasjjqqyqt   upqlrjhhhkhfedddddddccccc
bbbcdddddddddddddddeeeeffffffgghks  c             qnbpfmgfedddddddcccc
bbcdddddddddddddeefffffffffgggipmt                    qhgfeedddddddccc
bbdddddddddeeeefhlggggggghhhhils                      ljigfeedddddddcc
bcddddeeeeeefffghmllkjiljjiijle                         yhfeedddddddcc
bddeeeeeeeffffghhjoj do   clmq                         qlgfeeedddddddc
bdeeeeeefffffhiijpu         sm                         ohffeeedddddddc
beffeefgggghhjocsu                                    higffeeedddddddc
                                                    cmihgffeeedddddddd
beffeefgggghhjocsu                                    higffeeedddddddc
bdeeeeeefffffhiijpu         sd                         ohffeeedddddddc
bddeeeeeeeffffghhjoj do   clmq                         qlgfeeedddddddc
bcddddeeeeeefffghmllkjiljjiijle                         yhfeedddddddcc
bbdddddddddeeeefhlggggggghhhhils                      ljigfeedddddddcc
bbcdddddddddddddeefffffffffgggipmt                    qhgfeedddddddccc
bbbcdddddddddddddddeeeeffffffgghks  c             qnbpfmgfedddddddcccc
bbbccddddddddddddddddeeeeeefffghvasjjqqyqt   upqlrjhhhkhfedddddddccccc
bbbbccddddddddddddddddddeeeeeeeffgggghhjq     iihgggfffeedddddddcccccc
bbbbbcccddddddddddddddddddeeeeeeeefffggjotx etiigfffeeeeddddddcccccccc
bbbbbbccccddddddddddddddddddeeeeeeeefffghikopjhgffeeeeedddddcccccccccc
bbbbbbbcccccdddddddddddddddddddeeeeeeeffghjpjl feeeeedddddcccccccccccc



Fennel

#!/usr/bin/env fennel

(fn mandelzahl [cr ci max i tr ti tr2 ti2]
  "Calculates the Mandelbrot escape number of a complex point c"
  (if (>= i max)         -1
      (>= (+ tr2 ti2) 4)  i
      (let [(tr ti) (values (+ (- tr2 ti2) cr)
                            (+ (* tr ti 2) ci))]
        (mandelzahl cr ci max (+ i 1)
                    tr ti (* tr tr) (* ti ti)))))

(fn mandel [w h max]
  "Entry point, generate a 'graphical' representation of the Mandelbrot set"
  (for [y -1.0 1.0 (/ 2.0 h)]
    (var line {})
    (for [x -2.0 1.0 (/ 3.0 w)]
      (let [mz (mandelzahl x y max 0 0 0 0 0)]
        (tset line (+ (length line) 1)
              (or (and (< mz 0) " ")
                  (string.char (+ (string.byte :a) (% mz 26)))))))
    (print (table.concat line))))

(fn arg-def [pos default]
  "A helper fn to extract command line parameter with defaults" 
  (or (tonumber (and arg (. arg pos))) default))

(let [width  (arg-def 1 140)
      height (arg-def 2 50)
      max    (arg-def 3 1e5)]
  (mandel width height max))

FOCAL

1.1 S I1=-1.2; S I2=1.2; S R1=-2; S R2=.5
1.2 S MIT=30
1.3 F Y=1,24; D 2
1.4 Q

2.1 T !
2.2 F X=1,70; D 3

3.1 S R=X*(R2-R1)/70+R1
3.2 S I=Y*(I2-I1)/24+I1
3.3 S C1=R; S C2=I
3.4 F T=1,MIT; D 4

4.1 S C3=C1
4.2 S C1=C1*C1 - C2*C2
4.3 S C2=C3*C2 + C2*C3
4.4 S C1=C1+R
4.5 S C2=C2+I
4.6 I (-FABS(C1)+2)5.1
4.7 I (-FABS(C2)+2)5.1
4.8 I (MIT-T-1)6.1

5.1 S T=MIT; T "*"; R

6.1 T " "; R
Output:
**********************************************************************
**********************************************************************
**************************************************** *****************
*************************************************      ***************
*************************************************      ***************
****************************************    *               **********
*************************************** *                       ******
*************************************                            *****
********************** **** *******                               ****
***********************          **                                 **
*********************                                             ****
*** *                                                          *******
*********************                                             ****
***********************          **                                 **
********************** **** *******                               ****
*************************************                            *****
*************************************** *                       ******
****************************************    *               **********
*************************************************      ***************
*************************************************      ***************
**************************************************** *****************
**********************************************************************
**********************************************************************
**********************************************************************

Forth

This uses grayscale image utilities.

500 value max-iter

: mandel ( gmp  F: imin imax rmin rmax -- )
  0e 0e { F: imin F: imax F: rmin F: rmax F: Zr F: Zi }
  dup bheight 0 do
    i s>f dup bheight s>f f/ imax imin f- f* imin f+ TO Zi
    dup bwidth 0 do
      i s>f dup bwidth s>f f/ rmax rmin f- f* rmin f+ TO Zr
      Zr Zi max-iter
      begin  1- dup
      while  fover fdup f* fover fdup f*
             fover fover f+ 4e f<
      while  f- Zr f+
             frot frot f* 2e f* Zi f+
      repeat fdrop fdrop
             drop 0        \ for a pretty grayscale image, replace with: 255 max-iter */
      else   drop 255
      then   fdrop fdrop
      over i j rot g!
    loop
  loop    drop ;

80 24 graymap
dup -1e 1e -2e 1e mandel
Works with: 4tH v3.64

This is a completely integer version without local variables, which uses 4tH's native graphics library.

include lib/graphics.4th               \ graphics support is needed

640 pic_width !                        \ width of the image
480 pic_height !                       \ height of the image

create shade                           \ map the shades of the image
  ' black ,                            \ this is the colorscheme
  ' blue ,
  ' cyan ,
  ' green ,
  ' yellow ,
  ' red ,
  ' magenta ,
  ' blue ,
  ' cyan ,
  ' green ,
  ' yellow ,
  ' white ,
does> swap cells + @c execute ;        \ loop through the shades available

color_image                            \ we're making a color image

15121 -15120 do                        \ do y-coordinate
  15481 -21000 do                      \ do x-coordinate
    j 0 0 0                            ( l u v i)
    200 0 do                           \ get color
      >r
      over dup 10 / * 1000 /           \ calculate X and Y
      over dup 10 / * 1000 /           \ if X+Y > 40000
      over over + r> swap 40000 >      \ use the color in the loop
      if
        drop drop drop i 11 min leave
      else                             \ otherwise try the next one
        j swap >r - - >r * 5000 / over + r> swap r>
      then
    loop                               \ drop all parameters and set the shade
    shade drop drop drop               \ now set the proper pixel
    j 15120 + 63 / i 21000 + 57 / set_pixel
  57 +loop                             \ we're scaling the x-coordinate
63 +loop                               \ we're scaling the y-coordinate

s" mandelbt.ppm" save_image            \ done, save the image
dup gshow
free bye

Fortran

Works with: Fortran version 90 and later
program mandelbrot

  implicit none
  integer  , parameter :: rk       = selected_real_kind (9, 99)
  integer  , parameter :: i_max    =  800
  integer  , parameter :: j_max    =  600
  integer  , parameter :: n_max    =  100
  real (rk), parameter :: x_centre = -0.5_rk
  real (rk), parameter :: y_centre =  0.0_rk
  real (rk), parameter :: width    =  4.0_rk
  real (rk), parameter :: height   =  3.0_rk
  real (rk), parameter :: dx_di    =   width / i_max
  real (rk), parameter :: dy_dj    = -height / j_max
  real (rk), parameter :: x_offset = x_centre - 0.5_rk * (i_max + 1) * dx_di
  real (rk), parameter :: y_offset = y_centre - 0.5_rk * (j_max + 1) * dy_dj
  integer, dimension (i_max, j_max) :: image
  integer   :: i
  integer   :: j
  integer   :: n
  real (rk) :: x
  real (rk) :: y
  real (rk) :: x_0
  real (rk) :: y_0
  real (rk) :: x_sqr
  real (rk) :: y_sqr

  do j = 1, j_max
    y_0 = y_offset + dy_dj * j
    do i = 1, i_max
      x_0 = x_offset + dx_di * i
      x = 0.0_rk
      y = 0.0_rk
      n = 0
      do
        x_sqr = x ** 2
        y_sqr = y ** 2
        if (x_sqr + y_sqr > 4.0_rk) then
          image (i, j) = 255
          exit
        end if
        if (n == n_max) then
          image (i, j) = 0
          exit
        end if
        y = y_0 + 2.0_rk * x * y
        x = x_0 + x_sqr - y_sqr
        n = n + 1
      end do
    end do
  end do
  open  (10, file = 'out.pgm')
  write (10, '(a/ i0, 1x, i0/ i0)') 'P2', i_max, j_max, 255
  write (10, '(i0)') image
  close (10)

end program mandelbrot
bs

Frink

This draws a graphical Mandelbrot set using Frink's built-in graphics and complex arithmetic.

// Maximum levels for each pixel.
levels = 60

// Create a random color for each level.
colors = new array[[levels]]
for a = 0 to levels-1
   colors@a = new color[randomFloat[0,1], randomFloat[0,1], randomFloat[0,1]]

// Make this number smaller for higher resolution.
stepsize = .005

g = new graphics
g.antialiased[false]

for im = -1.2 to 1.2 step stepsize
{
   imag = i * im
   for real = -2 to 1 step stepsize
   {  
      C = real + imag
      z = 0
      count = -1

      do
      {
         z = z^2 + C
         count=count+1;
      } while abs[z] < 4 and count < levels

      g.color[colors@((count-1) mod levels)]
      g.fillRectSize[real, im, stepsize, stepsize]
   }
}

g.show[]

Furor

###sysinclude X.uh
$ff0000 sto szin
300 sto maxiter
maxypixel sto YRES
maxxpixel sto XRES
myscreen "Mandelbrot" @YRES @XRES graphic
@YRES 2 / (#d) sto y2
@YRES 2 / (#d) sto x2
#g 0. @XRES (#d) 1.  i: {#d
#g 0. @YRES (#d) 1. {#d
#d
{#d}§i 400. - @x2 - @x2 /
sto x
{#d}  @y2 - @y2 /
sto y
zero#d xa zero#d ya zero iter
(( #d
@x @xa dup* @ya dup* -+
@y @xa *2 @ya *+ sto ya
sto xa #g inc iter
@iter @maxiter >= then((>))
#d ( @xa dup* @ya dup* + 4. > )))
#g @iter @maxiter == { #d
myscreen {d} {d}§i @szin [][]
}{ #d
myscreen {d} {d}§i #g @iter 64 * [][]
}
#d}
#d}
(( ( myscreen key? 10000 usleep )))
myscreen !graphic
end
{ „x” }
{ „x2” }
{ „y” }
{ „y2” }
{ „xa” }
{ „ya” }
{ „iter” }
{ „maxiter” }
{ „szin” }
{ „YRES” }
{ „XRES” }
{ „myscreen” }


Futhark

This example is incorrect. Please fix the code and remove this message.
Details: Futhark's syntax has changed, so this example will not compile

Computes escapes for each pixel, but not the colour.

default(f32)

type complex = (f32, f32)

fun dot(c: complex): f32 =
  let (r, i) = c
  in r * r + i * i

fun multComplex(x: complex, y: complex): complex =
  let (a, b) = x
  let (c, d) = y
  in (a*c - b * d,
      a*d + b * c)

fun addComplex(x: complex, y: complex): complex =
  let (a, b) = x
  let (c, d) = y
  in (a + c,
      b + d)

fun divergence(depth: int, c0: complex): int =
  loop ((c, i) = (c0, 0)) = while i < depth && dot(c) < 4.0 do
    (addComplex(c0, multComplex(c, c)),
     i + 1)
  in i

fun mandelbrot(screenX: int, screenY: int, depth: int, view: (f32,f32,f32,f32)): [screenX][screenY]int =
  let (xmin, ymin, xmax, ymax) = view
  let sizex = xmax - xmin
  let sizey = ymax - ymin
  in map (fn (x: int): [screenY]int  =>
           map  (fn (y: int): int  =>
                  let c0 = (xmin + (f32(x) * sizex) / f32(screenX),
                            ymin + (f32(y) * sizey) / f32(screenY))
                  in divergence(depth, c0))
                (iota screenY))
         (iota screenX)

fun main(screenX: int, screenY: int, depth: int, xmin: f32, ymin: f32, xmax: f32, ymax: f32): [screenX][screenY]int =
  mandelbrot(screenX, screenY, depth, (xmin, ymin, xmax, ymax))


FutureBasic

_xmin    = -8601
_xmax    =  2867
_ymin    = -4915
_ymax    =  4915
_maxiter =  32
_dx = ( _xmax - _xmin ) / 79
_dy = ( _ymax - _ymin ) / 24

void local fn MandelbrotSet
  printf @"\n"
  SInt32 cy = _ymin
  while ( cy <= _ymax )
    SInt32 cx = _xmin
    while ( cx <= _xmax )
      SInt32   x = 0
      SInt32   y = 0
      SInt32  x2 = 0
      SInt32  y2 = 0
      SInt32 iter = 0
      while ( iter < _maxiter )
        if ( x2 + y2 > 16384 ) then break
        y = ( ( x  * y ) >> 11 ) + (SInt32)cy
        x = x2 - y2 + (SInt32)cx
        x2 = ( x * x ) >> 12
        y2 = ( y * y ) >> 12
        iter++
      wend
      print fn StringWithFormat( @"%3c", iter + 32 );
      cx += _dx
    wend
    printf @"\n"
    cy += _dy
  wend
end fn

window 1, @"Mandelbrot Set", ( 0, 0, 820, 650 )
WindowSetBackgroundColor( 1, fn ColorBlack )
text @"Impact", 10.0, fn ColorWithRGB( 1.000, 0.800, 0.000, 1.0 )

fn MandelbrotSet

HandleEvents
Output:

!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'+)%%%$$$$$#####"""""""""""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(+,)++&%$$$$$$######""""""
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*5:/+('&%%$$$$$$#######"""
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),@@@@@@@,'&%%%%%$$$$########
!!!!!!!"""####################$$$$$$$$%%%&'())((())*,@@@@@@/+))('&&&&)'%$$######
!!!!!!""###################$$$$$%%%%%%&&&'+.@@=/<@@@@@@@@@@@@@@@/++@..93%%$#####
!!!!!"################$$$%%%%%%%%%%&&&&'),+2@@@@@@@@@@@@@@@@@@@@@@@@@1(&&%$$####
!!!!"##########$$$$$%%&(-(''''''''''''(*,5@@@@@@@@@@@@@@@@@@@@@@@@@@@@+)-&%$$###
!!!!####$$$$$$$$%%%%%&'(*-@1.+.@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4-(&%$$$##
!!!!#$$$$$$$$$%%%%%%'''++.6@@@@@@@@@8/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3(%%$$$$#
!!!#$$$$$$$%&&&&''()/-5.5@@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?'&%%$$$$#
!!!(**+/+<523/80/46@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+)'&&%%$$$$#
!!!#$$$$$$$%&&&&''().-2.@@@@@@@@@@@@@@?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$#
!!!!#$$$$$$$$$%%%%%&'''/,.7@@@@@@@@@;/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0'%%$$$$#
!!!!####$$$$$$$$%%%%%&'(*-:2.,/?-5+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+(&%$$$##
!!!!"##########$$$$$%%&(-(''''(''''''((*,4@@@@@@@@@@@@@@@@@@@@@@@@@@@4+).&%$$###
!!!!!"################$$$%%%%%%%%%%&&&&')<,4@@@@@@@@@@@@@@@@@@@@@@@@@/('&%%$####
!!!!!!""##################$$$$$$%%%%%%&&&'*.@@@0@@@@@@@@@@@@@@@@1,,@//9)%%$#####
!!!!!!!"""####################$$$$$$$$%%%&(())((()**-@@@@@@/+)))'&&&')'%$$######
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''(,@@@@@@@+'&&%%%%%$$$########
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*7@0+('&%%%$$$$$#######"""
!!!!!!!!!!!"""""""######################$$$$$$$$$%%%&&(+-).*&%$$$$$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$%%'3(%%%$$$$$######""""""""""
!!!!!!!!!!!!!!!""""""""""""#####################################"""""""""""""""


Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website.

In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.

Solution

We need first to generate a color palette, this is, a list of colors:

The following function draw the Mandelbrot set:

File:Fōrmulæ - Mandelbrot set 01.png

Test Case 1. Grayscale palette

File:Fōrmulæ - Mandelbrot set 02.png

File:Fōrmulæ - Mandelbrot set 03.png

Test case 2. Black & white palette

File:Fōrmulæ - Mandelbrot set 04.png

File:Fōrmulæ - Mandelbrot set 05.png

GLSL

Uses smooth coloring.

const int MaxIterations = 1000;
const vec2 Focus = vec2(-0.51, 0.54);
const float Zoom = 1.0;

vec3
color(int iteration, float sqLengthZ) {
    // If the point is within the mandlebrot set
    // just color it black
    if(iteration == MaxIterations)
        return vec3(0.0);
    
    // Else we give it a smoothed color
   	float ratio = (float(iteration) - log2(log2(sqLengthZ))) / float(MaxIterations);
    
    // Procedurally generated colors
    return mix(vec3(1.0, 0.0, 0.0), vec3(1.0, 1.0, 0.0), sqrt(ratio));
}

void
mainImage(out vec4 fragColor, in vec2 fragCoord) {      
    // C is the aspect-ratio corrected UV coordinate.
    vec2 c = (-1.0 + 2.0 * fragCoord / iResolution.xy) * vec2(iResolution.x / iResolution.y, 1.0);
    
    // Apply scaling, then offset to get a zoom effect
    c = (c * exp(-Zoom)) + Focus;
	vec2 z = c;
    
    int iteration = 0;
    
    while(iteration < MaxIterations) {
        // Precompute for efficiency
   	float zr2 = z.x * z.x;
        float zi2 = z.y * z.y;

        // The larger the square length of Z,
        // the smoother the shading
        if(zr2 + zi2 > 32.0) break;

        // Complex multiplication, then addition
    	z = vec2(zr2 - zi2, 2.0 * z.x * z.y) + c;
        ++iteration;
    }
    
    // Generate the colors
    fragColor = vec4(color(iteration, dot(z,z)), 1.0);
    
    // Apply gamma correction
    fragColor.rgb = pow(fragColor.rgb, vec3(0.5));
}

gnuplot

The output from gnuplot is controlled by setting the appropriate values for the options terminal and output.

set terminal png
set output 'mandelbrot.png'

The following script draws an image of the number of iterations it takes to escape the circle with radius rmax with a maximum of nmax.

rmax = 2
nmax = 100
complex (x, y) = x * {1, 0} + y * {0, 1}
mandelbrot (z, z0, n) = n == nmax || abs (z) > rmax ? n : mandelbrot (z ** 2 + z0, z0, n + 1)
set samples 200
set isosamples 200
set pm3d map
set size square
splot [-2 : .8] [-1.4 : 1.4] mandelbrot (complex (0, 0), complex (x, y), 0) notitle
Output:

Go

Text

Prints an 80-char by 41-line depiction.

package main

import "fmt"
import "math/cmplx"

func mandelbrot(a complex128) (z complex128) {
    for i := 0; i < 50; i++ {
        z = z*z + a
    }
    return
}

func main() {
    for y := 1.0; y >= -1.0; y -= 0.05 {
        for x := -2.0; x <= 0.5; x += 0.0315 {
            if cmplx.Abs(mandelbrot(complex(x, y))) < 2 {
                fmt.Print("*")
            } else {
                fmt.Print(" ")
            }
        }
        fmt.Println("")
    }
}
Graphical
.png image
package main

import (
    "fmt"
    "image"
    "image/color"
    "image/draw"
    "image/png"
    "math/cmplx"
    "os"
)

const (
    maxEsc = 100
    rMin   = -2.
    rMax   = .5
    iMin   = -1.
    iMax   = 1.
    width  = 750
    red    = 230
    green  = 235
    blue   = 255
)

func mandelbrot(a complex128) float64 {
    i := 0
    for z := a; cmplx.Abs(z) < 2 && i < maxEsc; i++ {
        z = z*z + a
    }
    return float64(maxEsc-i) / maxEsc
}

func main() {
    scale := width / (rMax - rMin)
    height := int(scale * (iMax - iMin))
    bounds := image.Rect(0, 0, width, height)
    b := image.NewNRGBA(bounds)
    draw.Draw(b, bounds, image.NewUniform(color.Black), image.ZP, draw.Src)
    for x := 0; x < width; x++ {
        for y := 0; y < height; y++ {
            fEsc := mandelbrot(complex(
                float64(x)/scale+rMin,
                float64(y)/scale+iMin))
            b.Set(x, y, color.NRGBA{uint8(red * fEsc),
                uint8(green * fEsc), uint8(blue * fEsc), 255})

        }
    }
    f, err := os.Create("mandelbrot.png")
    if err != nil {
        fmt.Println(err)
        return
    }
    if err = png.Encode(f, b); err != nil {
        fmt.Println(err)
    }
    if err = f.Close(); err != nil {
        fmt.Println(err)
    }
}


Golfscript

Código sacado de https://codegolf.stackexchange.com/

20{40{0.1{.{;..*2$.*\- 
20/3$-@@*10/3$-..*2$.*+1600<}*}32*' 
*'=\;\;@@(}60*;(n\}40*;]''+
Output:
000000000000000000000000000000000000000010000000000000000000
000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000001000000000000000000000000
000000000000000000000000000000000000001000000000000000000000
000000000000000000000000000000000000111000000000000000000000
000000000000000000000000000000000000111110000000000000000000
000000000000000000000000000000000000011100000000000000000000
000000000000000000000000000001000110111100010000000000000000
000000000000000000000000000000100111111111110000000000000000
000000000000000000000000000001011111111111110111000000000000
000000000000000000000000000001111111111111111110000000000000
000000000000000000000000000000111111111111111110000000000000
000000000000001000000000000011111111111111111111000000000000
000000000000000000000000000011111111111111111111000000000000
000000000000000000000000000111111111111111111111000000000000
000000000000000000000000001111111111111111111111100000000000
000000000000000001111110001111111111111111111111100000000000
000000000000000011111111101111111111111111111111100000000000
000000000000100111111111111111111111111111111111000000000000
000000000001101111111111111111111111111111111111000000000000
011111111111111111111111111111111111111111111100000000000000
000000000000001111111111111111111111111111111110000000000000
000000000000000111111111111111111111111111111111000000000000
000000000000000001111111111111111111111111111111100000000000
000000000000000001111111101111111111111111111111000000000000
000000000000000001011100000111111111111111111111100000000000
000000000000000000000100000111111111111111111111000000000000
000000000000000100000000001111111111111111111111100000000000
000000000000000100000000000011111111111111111111000000000000
000000000000000000000000000011111111111111111110000000000000
000000000000000000000000000001111111111111111111000000000000
000000000000000000000000000000111111111111111111000000000000
000000000000000000000000000001101111111111111000000000000000
000000000000000000000000000011000011111110100000000000000000
000000000000000000000000000000000000111100000000000000000000
000000000000000000000000000000000000111110000000000000000000
000000000000000000000000000000000000111100000000000000000000
000000000000000000000000000000000000011000000000000000000000
000000000000000000000000000000000000001000000000000000000000
000000000000000000000000000000000000000000000000000000000000

Hare

Translation of: D
use fmt;
use math;

type complex = struct {
	re: f64,
	im: f64
};

export fn main() void = {
	for (let y = -1.2; y < 1.2; y += 0.05) {
		for (let x = -2.05; x < 0.55; x += 0.03) {
			let z = complex {re = 0.0, im = 0.0};

			for (let m = 0z; m < 100; m += 1) {
				let tz = z;

				z.re = tz.re*tz.re - tz.im*tz.im;
				z.im = tz.re*tz.im + tz.im*tz.re;
				z.re += x;
				z.im += y;
			};
			fmt::print(if (abs(z) < 2f64) '#' else '.')!;
		};
		fmt::println()!;
	};
};

fn abs(z: complex) f64 = {
	return math::sqrtf64(z.re*z.re + z.im*z.im);
};
Output:
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
................................................................##.....................
.............................................................######....................
.............................................................#######...................
..............................................................######...................
..........................................................#.#.###..#.#.................
...................................................##....################..............
..................................................###.######################.###.......
...................................................############################........
................................................###############################........
................................................################################.......
.............................................#####################################.....
..............................................###################################......
..............................##.####.#......####################################......
..............................###########....####################################......
............................###############.######################################.....
............................###############.#####################################......
........................##.#####################################################.......
......#.###...#.#############################################################..........
........................##.#####################################################.......
............................###############.#####################################......
............................###############.######################################.....
..............................###########....####################################......
..............................##.####.#......####################################......
..............................................###################################......
.............................................#####################################.....
................................................################################.......
................................................###############################........
...................................................############################........
..................................................###.######################.###.......
...................................................##....################..............
..........................................................#.#.###..#.#.................
..............................................................######...................
.............................................................#######...................
.............................................................######....................
................................................................##.....................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
.......................................................................................

Haskell

Translation of: Ruby
import Data.Bool ( bool )
import Data.Complex (Complex ((:+)), magnitude)

mandelbrot :: RealFloat a => Complex a -> Complex a
mandelbrot a = iterate ((a +) . (^ 2)) 0 !! 50

main :: IO ()
main =
  mapM_
    putStrLn
    [ [ bool ' ' '*' (2 > magnitude (mandelbrot (x :+ y)))
        | x <- [-2, -1.9685 .. 0.5]
      ]
      | y <- [1, 0.95 .. -1]
    ]
Output:
                            
                                                           **                   
                                                         ******                 
                                                       ********                 
                                                         ******                 
                                                      ******** **   *           
                                              ***   *****************           
                                              ************************  ***     
                                              ****************************      
                                           ******************************       
                                            ******************************      
                                         ************************************   
                                *         **********************************    
                           ** ***** *     **********************************    
                           ***********   ************************************   
                         ************** ************************************    
                         ***************************************************    
                     *****************************************************      
 ***********************************************************************        
                     *****************************************************      
                         ***************************************************    
                         ************** ************************************    
                           ***********   ************************************   
                           ** ***** *     **********************************    
                                *         **********************************    
                                         ************************************   
                                            ******************************      
                                           ******************************       
                                              ****************************      
                                              ************************  ***     
                                              ***   *****************           
                                                      ******** **   *           
                                                         ******                 
                                                       ********                 
                                                         ******                 
                                                           **  

haskell one-liners :

-- first attempt
-- putStrLn $ foldr (++) "" [ if x==(-2) then "\n" else let (a, b) = iterate (\(x', y') -> (x'^2-y'^2+x, 2*x'*y'+y)) (0, 0) !! 500 in (snd.head.filter (\(v, c)->v) $ zip ([(<0.01), (<0.025), (<0.05), (<0.1), (<0.5), (<1), (<4), (\_ -> True)] <*> [a^2 + b^2]) [".", "\'", ":", "!", "|", "}", "#", " "]) | y <- [1, 0.98 .. -1], x <- [-2, -1.98 .. 0.5]]

-- replaced iterate with foldr, modified the snd.head part and a introduced a check to stop the magnitude from exploding
-- foldr(>>)(return())[putStrLn[let(a,b)=foldr(\_(u,w)->if(u^2+w^2<4)then(u^2-w^2+x,2*u*w+y)else(u,w))(0,0)[1..500]in snd.last$(filter(\(f,v)->f)$zip(map(a^2+b^2>)[0,0.01,0.025,0.05,0.1,0.5,1,4])['.','\'',':','!','|','}','#',' '])|x<-[-2,-1.98..0.5]]|y<-[1,0.98.. -1]]

-- without different characters in the output
-- foldr(>>)(return())[putStrLn[let(a,b)=foldr(\_(u,w)->(u^2-w^2+x,2*u*w+y))(0,0)[1..500]in if a^2+b^2<4 then '*' else ' '|x<-[-2,-1.98..0.5]]|y<-[1,0.98.. -1]]

-- using mapM_ instead of foldr, bind operator instead of list comprehension and replacing 'let' with a lambda function
 -- mapM_ putStrLn $[1,0.98.. -1]>>= \y->return $[-2,-1.98..0.5]>>= \x->return (if(\(a,b)->a^2+b^2<4)(foldr(\_(u,w)->(u^2-w^2+x,2*u*w+y))(0,0)[1..500]) then '*' else ' ')

-- open GHCI > Copy and paste any of above one-liners > Hit enter

A legible variant of the first of the "one-liner" contributions above:

main :: IO ()
main =
  putStrLn $
    concat
      [ go x y
        | y <- [1, 0.98 .. -1],
          x <- [-2, -1.98 .. 0.5]
      ]
  where
    go x y
      | x == (-2) = "\n"
      | otherwise =
        let (a, b) =
              iterate
                (\(x', y') -> (x' ^ 2 - y' ^ 2 + x, 2 * x' * y' + y))
                (0, 0)
                !! 500
         in ( snd . head . filter fst $
                zip
                  ( [ (< 0.01),
                      (< 0.025),
                      (< 0.05),
                      (< 0.1),
                      (< 0.5),
                      (< 1),
                      (< 4),
                      const True
                    ]
                      <*> [a ^ 2 + b ^ 2]
                  )
                  [".", "\'", ":", "!", "|", "}", "#", " "]
            )
Output:
                                                                                             #                               
                                                                                             ##                              
                                                                                             #                               
                                                                                          }}}}}}}                            
                                                                                        #}}}}}}}}                            
                                                                                         }}}}}}}}}                           
                                                                                         }}}}}}}}}                           
                                                                                         }}}}}}}}}#                          
                                                                                        }}}}}}}}}}                           
                                                                                         }}}}}}}}                            
                                                                                          }}}}}}}                            
                                                                                           |||}}                             
                                                                                      } |||||||||||                          
                                                                                 } |||||||||||||||||||   |                   
                                                                        . '      |||||||||||||||||||||||||                   
                                                                         ..'   ||||||||||||||||||||||||||||                  
                                                                        '... |||||||||||||||||||||||||||||||    '.':         
                                                                         '':|||||||||||||||||||||||||||||||||| :...'         
                                                                           ||||||||||||||||||||||||||||||||||||:'..'         
                                                                         |||||||||||||||||||||||||||||||||||||||:''          
                                                                       }|||||||||||||||||||||||||||||||||||||||||            
                                                                       |||||||||||||||||||||||||||||||||||||||||||           
                                                                   || ||||||||||||||||||||||||||||||||||||||||||||!          
                                                                   ||}|||||||||||||||||||||||||||||||||||||||||||||          
                                                                     |||||||||||||||||||||||||||||||||||||||||||||||         
                                                                    |||||||||||||||||||||||||||||||||||||||||||||||||        
                                                                   |||||||||||||||||||||||||||!!!!!|||||||||||||||||| :      
                                                                 |||||||||||||||||||||||||!!!!!!!!!!!!|||||||||||||||'.'     
                                                                  ||||||||||||||||||||||!!!!!!!!!!!!!!!!||||||||||||| .      
                                                                 .||||||||||||||||||||!!!!!!!!!!!!!!!!!!!!||||||||||||       
                                                 |              |||||||||||||||||||||!!!!!!!!!!!!!!!!!!!!!!|||||||||||       
                                          |      |               |||||||||||||||||||!!!!!!!!!!!!!!!!!!!!!!!!||||||||||       
                                         ||! .:::!!!!.         ||||||||||||||||||||!!!!!!!!!!!!!:::!!!!!!!!!||||||||||       
                                          !'::::::::!!!         ||||||||||||||||||!!!!!!!!!!!:::::::::!!!!!!!|||||||||||     
                                          ::::::::::::!!!|     |||||||||||||||||||!!!!!!!!!:::::::::::::!!!!!!||||||||       
                                        !::::::::::::::!!!!    ||||||||||||||||||!!!!!!!!!:::::::::::::::!!!!!||||||||       
                                      . ::::::''''::::::!!!    |||||||||||||||||!!!!!!!!!:::::::''''::::::!!!!||||||||       
                                       :::::'''''''''::::!!!   |||||||||||||||||!!!!!!!!::::::'''''''''::::!!!!||||||||      
                                      !::::''''''''''':::!!!  ||||||||||||||||||!!!!!!!::::::''''''''''':::!!!!||||||!       
                                      ::::''''''..''''':::!!! |||||||||||||||||!!!!!!!!:::::''''''..''''':::!!!||||||}       
                                      :::'''''......''':::!!! |||||||||||||||||!!!!!!!:::::'''''......''':::!!!||||||        
                                     ::::''''........'''::!!!||||||||||||||||||!!!!!!!:::::''''........'''::!!!|||||         
                                .... ::::'''..........''::!!!||||||||||||||||||!!!!!!!:::::'''..........''::!!||||||         
                               .....':::''''..........''::!!|||||||||||||||||||!!!!!!!::::''''..........''::!!||||           
          ##             |   ::.....':::''''..........''::!!|||||||||||||||||||!!!!!!!::::''''..........''::!!||             
                               .....':::''''..........''::!!|||||||||||||||||||!!!!!!!::::''''..........''::!!||||           
                                .... ::::'''..........''::!!!||||||||||||||||||!!!!!!!:::::'''..........''::!!||||||         
                                     ::::''''........'''::!!!||||||||||||||||||!!!!!!!:::::''''........'''::!!!|||||         
                                      :::'''''......''':::!!! |||||||||||||||||!!!!!!!:::::'''''......''':::!!!||||||        
                                      ::::''''''..''''':::!!! |||||||||||||||||!!!!!!!!:::::''''''..''''':::!!!||||||}       
                                      !::::''''''''''':::!!!  ||||||||||||||||||!!!!!!!::::::''''''''''':::!!!!||||||!       
                                       :::::'''''''''::::!!!   |||||||||||||||||!!!!!!!!::::::'''''''''::::!!!!||||||||      
                                      . ::::::''''::::::!!!    |||||||||||||||||!!!!!!!!!:::::::''''::::::!!!!||||||||       
                                        !::::::::::::::!!!!    ||||||||||||||||||!!!!!!!!!:::::::::::::::!!!!!||||||||       
                                          ::::::::::::!!!|     |||||||||||||||||||!!!!!!!!!:::::::::::::!!!!!!||||||||       
                                          !'::::::::!!!         ||||||||||||||||||!!!!!!!!!!!:::::::::!!!!!!!|||||||||||     
                                         ||! .:::!!!!.         ||||||||||||||||||||!!!!!!!!!!!!!:::!!!!!!!!!||||||||||       
                                          |      |               |||||||||||||||||||!!!!!!!!!!!!!!!!!!!!!!!!||||||||||       
                                                 |              |||||||||||||||||||||!!!!!!!!!!!!!!!!!!!!!!|||||||||||       
                                                                 .||||||||||||||||||||!!!!!!!!!!!!!!!!!!!!||||||||||||       
                                                                  ||||||||||||||||||||||!!!!!!!!!!!!!!!!||||||||||||| .      
                                                                 |||||||||||||||||||||||||!!!!!!!!!!!!|||||||||||||||'.'     
                                                                   |||||||||||||||||||||||||||!!!!||||||||||||||||||| :      
                                                                    |||||||||||||||||||||||||||||||||||||||||||||||||        
                                                                     |||||||||||||||||||||||||||||||||||||||||||||||         
                                                                   ||}|||||||||||||||||||||||||||||||||||||||||||||          
                                                                   || ||||||||||||||||||||||||||||||||||||||||||||!          
                                                                       |||||||||||||||||||||||||||||||||||||||||||           
                                                                       }|||||||||||||||||||||||||||||||||||||||||            
                                                                         |||||||||||||||||||||||||||||||||||||||:''          
                                                                           ||||||||||||||||||||||||||||||||||||:'..'         
                                                                         '':|||||||||||||||||||||||||||||||||| :...'         
                                                                        '... |||||||||||||||||||||||||||||||    '.':         
                                                                         ..'   ||||||||||||||||||||||||||||                  
                                                                        . '      |||||||||||||||||||||||||                   
                                                                                 } |||||||||||||||||||   |                   
                                                                                      } |||||||||||                          
                                                                                           |||}}                             
                                                                                          }}}}}}}                            
                                                                                         }}}}}}}}                            
                                                                                        }}}}}}}}}}                           
                                                                                         }}}}}}}}}#                          
                                                                                         }}}}}}}}}                           
                                                                                         }}}}}}}}}                           
                                                                                        #}}}}}}}}                            
                                                                                          }}}}}}}                            
                                                                                             #                               
                                                                                             ##                              
                                                                                             #  

and a legible variant of the last of the "one-liner" contributions above:

main :: IO ()
main =
  mapM_
    putStrLn
    $ [1, 0.98 .. -1]
      >>= \y ->
        [ [-2, -1.98 .. 0.5]
            >>= \x ->
              [ if (\(a, b) -> a ^ 2 + b ^ 2 < 4)
                  ( foldr
                      ( \_ (u, w) ->
                          (u ^ 2 - w ^ 2 + x, 2 * u * w + y)
                      )
                      (0, 0)
                      [1 .. 500]
                  )
                  then '*'
                  else ' '
              ]
        ]

Haxe

This version compiles for flash version 9 or greater. The compilation command is

haxe -swf mandelbrot.swf -main Mandelbrot
class Mandelbrot extends flash.display.Sprite
{
    inline static var MAX_ITER = 255;

    public static function main() {
        var w = flash.Lib.current.stage.stageWidth;
        var h = flash.Lib.current.stage.stageHeight;
        var mandelbrot = new Mandelbrot(w, h);
        flash.Lib.current.stage.addChild(mandelbrot);
        mandelbrot.drawMandelbrot();
    }

    var image:flash.display.BitmapData;
    public function new(width, height) {
        super();
        var bitmap:flash.display.Bitmap;
        image = new flash.display.BitmapData(width, height, false);
        bitmap = new flash.display.Bitmap(image);
        this.addChild(bitmap);
    }

    public function drawMandelbrot() {
        image.lock();
        var step_x = 3.0 / (image.width-1);
        var step_y = 2.0 / (image.height-1);
        for (i in 0...image.height) {
            var ci = i * step_y - 1.0;
            for (j in 0...image.width) {
                var k = 0;
                var zr = 0.0;
                var zi = 0.0;
                var cr = j * step_x - 2.0;
                while (k <= MAX_ITER && (zr*zr + zi*zi) <= 4) {
                    var temp = zr*zr - zi*zi + cr;
                    zi = 2*zr*zi + ci;
                    zr = temp;
                    k ++;
                }
                paint(j, i, k);
            }
        }
        image.unlock();
    }

    inline function paint(x, y, iter) {
        var color = iter > MAX_ITER? 0 : iter * 0x100;
        image.setPixel(x, y, color);
    }
}

Huginn

#! /bin/sh
exec huginn -E "${0}" "${@}"
#! huginn

import Algorithms as algo;
import Mathematics as math;
import Terminal as term;

mandelbrot( x, y ) {
  c = math.Complex( x, y );
  z = math.Complex( 0., 0. );
  s = -1;
  for ( i : algo.range( 50 ) ) {
    z = z * z + c;
    if ( | z | > 2. ) {
      s = i;
      break;
    }
  }
  return ( s );
}

main( argv_ ) {
  imgSize = term_size( argv_ );
  yRad = 1.2;
  yScale = 2. * yRad / real( imgSize[0] );
  xScale = 3.3 / real( imgSize[1] );
  glyphTab = [ ".", ":", "-", "+", "+" ].resize( 12, "*" ).resize( 26, "%" ).resize( 50, "@" ).push( " " );
  for ( y : algo.range( imgSize[0] ) ) {
    line = "";
    for ( x : algo.range( imgSize[1] ) ) {
      line += glyphTab[ mandelbrot( xScale * real( x ) - 2.3, yScale * real( y ) - yRad ) ];
    }
    print( line + "\n" );
  }
  return ( 0 );
}

term_size( argv_ ) {
  lines = 25;
  columns = 80;
  if ( size( argv_ ) == 3 ) {
    lines = integer( argv_[1] );
    columns = integer( argv_[2] );
  } else {
    lines = term.lines();
    columns = term.columns();
    if ( ( lines % 2 ) == 0 ) {
      lines -= 1;
    }
  }
  lines -= 1;
  columns -= 1;
  return ( ( lines, columns ) );
}
Output:

........................:::::::::::::::::::------------------------------------------------------::::::::::::::::::::::::::::::::::::
......................::::::::::::::::------------------------------------++++++++++++++++++++---------::::::::::::::::::::::::::::::
....................:::::::::::::-----------------------------------+++++++++++++*******+++++++++++--------::::::::::::::::::::::::::
...................:::::::::::----------------------------------++++++++++++++++****%%******++++++++++---------::::::::::::::::::::::
.................:::::::::----------------------------------++++++++++++++++++++******% %****++++++++++++---------:::::::::::::::::::
................::::::::---------------------------------+++++++++++++++++++++******%%%%%*****+++++++++++++----------::::::::::::::::
...............::::::---------------------------------++++++++++++++++++++*****%%%%%   @%%%@***++++++++++++++----------::::::::::::::
..............:::::--------------------------------++++++++++++++++++***********@%        @%******+++++++++++++-----------:::::::::::
.............::::-------------------------------+++++++++++++++++****************@        %%***************+++++------------:::::::::
............:::------------------------------+++++++++++++++++****@%%%****%@@%@% %%@    @%%%% %*% ********%**++++------------::::::::
...........:::----------------------------+++++++++++++++++********%   @%@@                      %%%**%@%%@@**+++++------------::::::
..........:::-------------------------+++++++++++++++++++**********%                                @    %%***++++++------------:::::
..........:----------------------+++++++++++++++++++++*********%%%%                                    %%******++++++------------::::
.........:-----------------++++++++****************************                                           %*****+++++-------------:::
.........----------+++++++++++++++****%********%%*********** @%%                                          % %%**++++++-------------::
........:------++++++++++++++++++*******%@@%%**%% %%%*******%%                                             %%***+++++++-------------:
........---+++++++++++++++++++++********%@           @%%%**%                                               %%***+++++++-------------:
.......:-+++++++++++++++++++++*******%%%%                @%%                                               @****++++++++-------------
.......-+++++++++++++***********%**@*%@                    %                                               %***+++++++++-------------
.......++++++*******************%%    @                                                                  %*****+++++++++-------------
.......                                                                                               %%******++++++++++-------------
.......++++++*******************%%    @                                                                  %*****+++++++++-------------
.......-+++++++++++++***********%**@*%@                    %                                               %***+++++++++-------------
.......:-+++++++++++++++++++++*******%%%%                @%%                                               @****++++++++-------------
........---+++++++++++++++++++++********%@           @%%%**%                                               %%***+++++++-------------:
........:------++++++++++++++++++*******%@@%%**%% %%%*******%%                                             %%***+++++++-------------:
.........----------+++++++++++++++****%********%%*********** @%%                                          % %%**++++++-------------::
.........:-----------------++++++++****************************                                           %*****+++++-------------:::
..........:----------------------+++++++++++++++++++++*********%%%%                                    %%******++++++------------::::
..........:::-------------------------+++++++++++++++++++**********%                                @    %%***++++++------------:::::
...........:::----------------------------+++++++++++++++++********%   @%@@                      %%%**%@%%@@**+++++------------::::::
............:::------------------------------+++++++++++++++++****@%%%****%@@%@% %%@    @%%%% %*% ********%**++++------------::::::::
.............::::-------------------------------+++++++++++++++++****************@        %%***************+++++------------:::::::::
..............:::::--------------------------------++++++++++++++++++***********@%        @%******+++++++++++++-----------:::::::::::
...............::::::---------------------------------++++++++++++++++++++*****%%%%%   @%%%@***++++++++++++++----------::::::::::::::
................::::::::---------------------------------+++++++++++++++++++++******%%%%%*****+++++++++++++----------::::::::::::::::
.................:::::::::----------------------------------++++++++++++++++++++******% %****++++++++++++---------:::::::::::::::::::
...................:::::::::::----------------------------------++++++++++++++++****%%******++++++++++---------::::::::::::::::::::::
....................:::::::::::::-----------------------------------+++++++++++++*******+++++++++++--------::::::::::::::::::::::::::
......................::::::::::::::::------------------------------------++++++++++++++++++++---------::::::::::::::::::::::::::::::

Icon and Unicon

link graphics

procedure main()
    width := 750
    height := 600
    limit := 100
    WOpen("size="||width||","||height)
    every x:=1 to width & y:=1 to height do
    {
        z:=complex(0,0)
        c:=complex(2.5*x/width-2.0,(2.0*y/height-1.0))
        j:=0
        while j<limit & cAbs(z)<2.0 do
        {
           z := cAdd(cMul(z,z),c)
           j+:= 1
        }
        Fg(mColor(j,limit))
        DrawPoint(x,y)
    }
    WriteImage("./mandelbrot.gif")
    WDone()
end

procedure mColor(x,limit)
   max_color := 2^16-1
   color := integer(max_color*(real(x)/limit))

   return(if x=limit
          then "black"
          else color||","||color||",0")
end

record complex(r,i)

procedure cAdd(x,y)
    return complex(x.r+y.r,x.i+y.i)
end

procedure cMul(x,y)
    return complex(x.r*y.r-x.i*y.i,x.r*y.i+x.i*y.r)
end

procedure cAbs(x)
    return sqrt(x.r*x.r+x.i*x.i)
end

graphics is required


This example is in need of improvement:
The example is correct; however, Unicon implemented additional graphical features and a better example may be possible.

IDL

IDL - Interactive Data Language (free implementation: GDL - GNU Data Language http://gnudatalanguage.sourceforge.net)

PRO Mandelbrot,xRange,yRange,xPixels,yPixels,iterations

xPixelstartVec = Lindgen( xPixels) * Float(xRange[1]-xRange[0]) / $
                 xPixels + xRange[0]
yPixelstartVec = Lindgen( yPixels) * Float(YRANGE[1]-yrange[0])$
                 / yPixels + yRange[0]

constArr = Complex( Rebin( xPixelstartVec, xPixels, yPixels),$
                     Rebin( Transpose(yPixelstartVec), xPixels, yPixels))

valArr = ComplexArr( xPixels, yPixels)

res = IntArr( xPixels, yPixels)

oriIndex = Lindgen( Long(xPixels) * yPixels)

FOR i = 0, iterations-1 DO BEGIN ; only one loop needed

    ; calculation for whole array at once
    valArr = valArr^2 - constArr

    whereIn = Where( Abs( valArr) LE 4.0d, COMPLEMENT=whereOut)

    IF whereIn[0] EQ -1 THEN BREAK

    valArr = valArr[ whereIn]

    constArr = constArr[ whereIn]

    IF whereOut[0] NE -1 THEN BEGIN

        res[ oriIndex[ whereOut]] = i+1

        oriIndex = oriIndex[ whereIn]
    ENDIF
ENDFOR

tv,res ; open a window and show the result

END


Mandelbrot,[-1.,2.3],[-1.3,1.3],640,512,200

END

from the command line:

GDL>.run mandelbrot

or

GDL> Mandelbrot,[-1.,2.3],[-1.3,1.3],640,512,200

Inform 7

"Mandelbrot"

The story headline is "A Non-Interactive Set".

Include Glimmr Drawing Commands by Erik Temple.

[Q20 fixed-point or floating-point: see definitions below]
Use floating-point math.

Finished is a room.

The graphics-window is a graphics g-window spawned by the main-window.
The position is g-placeabove.

When play begins:
	let f10 be 10 as float;
	now min re is ( -20 as float ) fdiv f10;
	now max re is ( 6 as float ) fdiv f10;
	now min im is ( -12 as float ) fdiv f10;
	now max im is ( 12 as float ) fdiv f10;
	now max iterations is 100;
	add color g-Black to the palette;
	add color g-Red to the palette;
	add hex "#FFA500" to the palette;
	add color g-Yellow to the palette;
	add color g-Green to the palette;
	add color g-Blue to the palette;
	add hex "#4B0082" to the palette;
	add hex "#EE82EE" to the palette;
	open up the graphics-window.

Min Re is a number that varies.
Max Re is a number that varies.
Min Im is a number that varies.
Max Im is a number that varies.

Max Iterations is a number that varies.

Min X is a number that varies.
Max X is a number that varies.
Min Y is a number that varies.
Max Y is a number that varies.

The palette is a list of numbers that varies.

[vertically mirrored version]
Window-drawing rule for the graphics-window when max im is fneg min im:
	clear the graphics-window;
	let point be { 0, 0 };
	now min X is 0 as float;
	now min Y is 0 as float;
	let mX be the width of the graphics-window minus 1;
	let mY be the height of the graphics-window minus 1;
	now max X is mX as float;
	now max Y is mY as float;
	let L be the column order with max mX;
	repeat with X running through L:
		now entry 1 in point is X;
		repeat with Y running from 0 to mY / 2:
			now entry 2 in point is Y;
			let the scaled point be the complex number corresponding to the point;
			let V be the Mandelbrot result for the scaled point;
			let C be the color corresponding to V;
			if C is 0, next;
			draw a rectangle (C) in the graphics-window at the point with size 1 by 1;
			now entry 2 in point is mY - Y;
			draw a rectangle (C) in the graphics-window at the point with size 1 by 1;
		yield to VM;
	rule succeeds.

[slower non-mirrored version]
Window-drawing rule for the graphics-window:
	clear the graphics-window;
	let point be { 0, 0 };
	now min X is 0 as float;
	now min Y is 0 as float;
	let mX be the width of the graphics-window minus 1;
	let mY be the height of the graphics-window minus 1;
	now max X is mX as float;
	now max Y is mY as float;
	let L be the column order with max mX;
	repeat with X running through L:
		now entry 1 in point is X;
		repeat with Y running from 0 to mY:
			now entry 2 in point is Y;
			let the scaled point be the complex number corresponding to the point;
			let V be the Mandelbrot result for the scaled point;
			let C be the color corresponding to V;
			if C is 0, next;
			draw a rectangle (C) in the graphics-window at the point with size 1 by 1;
		yield to VM;
	rule succeeds.

To decide which list of numbers is column order with max (N - number):
	let L be a list of numbers;
	let L2 be a list of numbers;
	let D be 64;
	let rev be false;
	while D > 0:
		let X be 0;
		truncate L2 to 0 entries;
		while X <= N:
			if D is 64 or X / D is odd, add X to L2;
			increase X by D;
		if rev is true:
			reverse L2;
			let rev be false;
		otherwise:
			let rev be true;
		add L2 to L;
		let D be D / 2;
	decide on L.

To decide which list of numbers is complex number corresponding to (P - list of numbers):
	let R be a list of numbers;
	extend R to 2 entries;
	let X be entry 1 in P as float;
	let X be (max re fsub min re) fmul (X fdiv max X);
	let X be X fadd min re;
	let Y be entry 2 in P as float;
	let Y be (max im fsub min im) fmul (Y fdiv max Y);
	let Y be Y fadd min im;
	now entry 1 in R is X;
	now entry 2 in R is Y;
	decide on R.

To decide which number is Mandelbrot result for (P - list of numbers):
	let c_re be entry 1 in P;
	let c_im be entry 2 in P;
	let z_re be 0 as float;
	let z_im be z_re;
	let threshold be 4 as float;
	let runs be 0;
	while 1 is 1:
		[ z = z * z ]
		let r2 be z_re fmul z_re;
		let i2 be z_im fmul z_im;
		let ri be z_re fmul z_im;
		let z_re be r2 fsub i2;
		let z_im be ri fadd ri;
		[ z = z + c ]
		let z_re be z_re fadd c_re;
		let z_im be z_im fadd c_im;
		let norm be (z_re fmul z_re) fadd (z_im fmul z_im);
		increase runs by 1;
		if norm is greater than threshold, decide on runs;
		if runs is max iterations, decide on 0.

To decide which number is color corresponding to (V - number):
	let L be the number of entries in the palette;
	let N be the remainder after dividing V by L;
	decide on entry (N + 1) in the palette.

Section - Fractional numbers (for Glulx only)

To decide which number is (N - number) as float: (- (numtof({N})) -).
To decide which number is (N - number) fadd (M - number): (- (fadd({N}, {M})) -).
To decide which number is (N - number) fsub (M - number): (- (fsub({N}, {M})) -).
To decide which number is (N - number) fmul (M - number): (- (fmul({N}, {M})) -).
To decide which number is (N - number) fdiv (M - number): (- (fdiv({N}, {M})) -).
To decide which number is fneg (N - number): (- (fneg({N})) -).
To yield to VM: (- glk_select_poll(gg_event); -).

Use Q20 fixed-point math translates as (- Constant Q20_MATH; -).
Use floating-point math translates as (- Constant FLOAT_MATH; -).

Include (-
#ifdef Q20_MATH;
! Q11.20 format: 1 sign bit, 11 integer bits, 20 fraction bits
[ numtof n r; @shiftl n 20 r; return r; ];
[ fadd n m; return n+m; ];
[ fsub n m; return n-m; ];
[ fmul n m; n = n + $$1000000000; @sshiftr n 10 n; m = m + $$1000000000; @sshiftr m 10 m; return n * m; ]; 
[ fdiv n m; @sshiftr m 20 m; return n / m; ];
[ fneg n; return -n; ];
#endif;

#ifdef FLOAT_MATH;
[ numtof f; @"S2:400" f f; return f; ];
[ fadd n m; @"S3:416" n m n; return n; ];
[ fsub n m; @"S3:417" n m n; return n; ];
[ fmul n m; @"S3:418" n m n; return n; ];
[ fdiv n m; @"S3:419" n m n; return n; ];
[ fneg n; @bitxor n $80000000 n; return n; ];
#endif;
-).

Newer Glulx interpreters provide 32-bit floating-point operations, but this solution also supports fixed-point math which is more widely supported and accurate enough for a zoomed-out view. Inform 6 inclusions are used for the low-level math functions in either case. The rendering process is extremely slow, since the graphics system is not optimized for pixel-by-pixel drawing, so this solution includes an optimization for vertical symmetry (as in the default view) and also includes extra logic to draw the lines in a more immediately useful order.

Insitux

(function mandelbrot width height depth
  (.. str 
    (for yy (range height)
         xx (range width)
      (let c_re (/ (* (- xx (/ width 2)) 4) width)
           c_im (/ (* (- yy (/ height 2)) 4) width)
           x 0 y 0 i 0)
      (while (and (<= (+ (** x) (** y)) 4)
                  (< i depth))
        (let x2 (+ c_re (- (** x) (** y)))
             y  (+ c_im (* 2 x y))
             x  x2
             i  (inc i)))
      (strn ((zero? xx) "\n") (i "ABCDEFGHIJ ")))))

(mandelbrot 48 24 10)
Output:

BBBBCCCDDDDDDDDDEEEEFGJJ EEEDDCCCCCCCCCCCCCCCBBB
BBBCCDDDDDDDDDDEEEEFFH  HFEEEDDDCCCCCCCCCCCCCCBB
BBBCDDDDDDDDDDEEEEFFH    GFFEEDDDCCCCCCCCCCCCCBB
BBCCDDDDDDDDDEEEEGGHI    HGFFEDDDCCCCCCCCCCCCCCB
BBCDDDDDDDDEEEEFG          HIGEDDDCCCCCCCCCCCCCB
BBDDDDDDDDEEFFFGH            IEDDDDCCCCCCCCCCCCB
BCDDDDDDEEFFFFGG             GFEDDDCCCCCCCCCCCCC
BDDDDDEEFJGGGHHI             IFEDDDDCCCCCCCCCCCC
BDDEEEEFG  J JI               GEDDDDCCCCCCCCCCCC
BDEEEFFFHJ                    FEDDDDCCCCCCCCCCCC
BEEEFFFIJ                     FEEDDDCCCCCCCCCCCC
BEEFGGH                      HFEEDDDCCCCCCCCCCCC
                            JGFEEDDDDCCCCCCCCCCC
BEEFGGH                      HFEEDDDCCCCCCCCCCCC
BEEEFFFIJ                     FEEDDDCCCCCCCCCCCC
BDEEEFFFHJ                    FEDDDDCCCCCCCCCCCC
BDDEEEEFG  J JI               GEDDDDCCCCCCCCCCCC
BDDDDDEEFJGGGHHI             IFEDDDDCCCCCCCCCCCC
BCDDDDDDEEFFFFGG             GFEDDDCCCCCCCCCCCCC
BBDDDDDDDDEEFFFGH            IEDDDDCCCCCCCCCCCCB
BBCDDDDDDDDEEEEFG          HIGEDDDCCCCCCCCCCCCCB
BBCCDDDDDDDDDEEEEGGHI    HGFFEDDDCCCCCCCCCCCCCCB
BBBCDDDDDDDDDDEEEEFFH    GFFEEDDDCCCCCCCCCCCCCBB
BBBCCDDDDDDDDDDEEEEFFH  HFEEEDDDCCCCCCCCCCCCCCBB

J

The characteristic function of the Mandelbrot can be defined as follows:

mcf=. (<: 2:)@|@(] ((*:@] + [)^:((<: 2:)@|@])^:1000) 0:) NB. 1000 iterations test

The Mandelbrot set can be drawn as follows:

domain=. |.@|:@({.@[ + ] *~ j./&i.&>/@+.@(1j1 + ] %~ -~/@[))&>/

load 'viewmat'
viewmat mcf "0 @ domain (_2j_1 1j1) ; 0.01 NB. Complex interval and resolution

A smaller version, based on a black&white implementation of viewmat (and paraphrased, from html markup to wiki markup), is shown here (The output is HTML-heavy and was split out to make editing this page easier):

   viewmat mcf "0 @ domain (_2j_1 1j1) ; 0.1 NB. Complex interval and resolution

Java

Library: Swing
Library: AWT
import java.awt.Graphics;
import java.awt.image.BufferedImage;
import javax.swing.JFrame;

public class Mandelbrot extends JFrame {

    private final int MAX_ITER = 570;
    private final double ZOOM = 150;
    private BufferedImage I;
    private double zx, zy, cX, cY, tmp;

    public Mandelbrot() {
        super("Mandelbrot Set");
        setBounds(100, 100, 800, 600);
        setResizable(false);
        setDefaultCloseOperation(EXIT_ON_CLOSE);
        I = new BufferedImage(getWidth(), getHeight(), BufferedImage.TYPE_INT_RGB);
        for (int y = 0; y < getHeight(); y++) {
            for (int x = 0; x < getWidth(); x++) {
                zx = zy = 0;
                cX = (x - 400) / ZOOM;
                cY = (y - 300) / ZOOM;
                int iter = MAX_ITER;
                while (zx * zx + zy * zy < 4 && iter > 0) {
                    tmp = zx * zx - zy * zy + cX;
                    zy = 2.0 * zx * zy + cY;
                    zx = tmp;
                    iter--;
                }
                I.setRGB(x, y, iter | (iter << 8));
            }
        }
    }

    @Override
    public void paint(Graphics g) {
        g.drawImage(I, 0, 0, this);
    }

    public static void main(String[] args) {
        new Mandelbrot().setVisible(true);
    }
}

Interactive

Library: AWT
Library: Swing
import static java.awt.Color.HSBtoRGB;
import static java.awt.Color.black;
import static java.awt.event.KeyEvent.VK_BACK_SLASH;
import static java.awt.event.KeyEvent.VK_ESCAPE;
import static java.awt.image.BufferedImage.TYPE_INT_RGB;
import static java.lang.Integer.signum;
import static java.lang.Math.abs;
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.System.currentTimeMillis;
import static java.util.Locale.ROOT;

import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.Insets;
import java.awt.event.KeyAdapter;
import java.awt.event.KeyEvent;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;
import java.awt.image.BufferedImage;
import java.util.function.Consumer;
import java.util.function.Predicate;

import javax.swing.JFrame;

/* 
 *      click: point to center
 * ctrl-click: point to origin
 *       drag: point to mouse release point
 *  ctrl-drag: point to origin + zoom
 * back-slash: back to previous point      
 *        esc: back to previous zoom point - zoom     
 */

public class Mandelbrot extends JFrame {
	private static final long serialVersionUID = 1L;
	
	private Insets insets;
	private int width, height;
	private double widthHeightRatio;
	private int minX, minY;
	private double Zoom;
		
	private int mpX, mpY, mdX, mdY;
	private boolean isCtrlDown, ctrl;
	private Stack stack = new Stack();
	
	private BufferedImage image;
	private boolean newImage = true;
	
	public static void main(String[] args) {
		new Mandelbrot(800, 600); // (800, 600), (1024, 768), (1600, 900), (1920, 1080)
		//new Mandelbrot(800, 600, 4.5876514379235943e-09, -0.6092161175392330, -0.4525577210859453);
		//new Mandelbrot(800, 600, 5.9512354925205320e-10, -0.6092146769531246, -0.4525564820098262);
		//new Mandelbrot(800, 600, 6.7178527589983420e-08, -0.7819036465400592, -0.1298363433443265);
		//new Mandelbrot(800, 600, 4.9716091454775210e-09, -0.7818800036717134, -0.1298044093748981);
		//new Mandelbrot(800, 600, 7.9333341281639390e-06, -0.7238770725243187, -0.2321214232559487); 
		/*
		new Mandelbrot(800, 600, new double[][] {
			{5.0000000000000000e-03, -2.6100000000000000, -1.4350000000000000}, // done!
			{3.5894206549118390e-04, -0.7397795969773300, -0.4996473551637279}, // done!
			{3.3905106941862460e-05, -0.6270410477828043, -0.4587021918164572}, // done!
			{6.0636337351945460e-06, -0.6101531446039512, -0.4522561221394852}, // done!
			{1.5502741161769430e-06, -0.6077214060084073, -0.4503995886987711}, // done!
		});
		//*/
	}
	
	public Mandelbrot(int width, int height) {
		this(width, height, .005, -2.61, -1.435);
	}
	
	public Mandelbrot(int width, int height, double Zoom, double r, double i) {
		this(width, height, new double[] {Zoom, r, i});
	}
	
	public Mandelbrot(int width, int height, double[] ... points) {
		super("Mandelbrot Set");
		setResizable(false);
		setDefaultCloseOperation(EXIT_ON_CLOSE);
		Dimension screen = getToolkit().getScreenSize();
		setBounds(
			rint((screen.getWidth() - width) / 2),
			rint((screen.getHeight() - height) / 2),
			width,
			height
		);
		addMouseListener(mouseAdapter);
		addMouseMotionListener(mouseAdapter);
		addKeyListener(keyAdapter);
		Point point = stack.push(points);
		this.Zoom = point.Zoom;
		this.minX = point.minX;
		this.minY = point.minY;
		setVisible(true);
		insets = getInsets();
		this.width = width -= insets.left + insets.right;
		this.height = height -= insets.top + insets.bottom;
		widthHeightRatio = (double) width / height;
	}
	
	private int rint(double d) {
		return (int) Math.rint(d); // half even
	}

	private void repaint(boolean newImage) {
		this.newImage = newImage;
		repaint();
	}

	private MouseAdapter mouseAdapter = new MouseAdapter() {
		public void mouseClicked(MouseEvent e) {
			stack.push(false);
			if (!ctrl) {
				minX -= width / 2 ;
				minY -= height / 2;
			}
			minX += e.getX() - insets.left;
			minY += e.getY() - insets.top;
			ctrl = false;
			repaint(true);
	 	}
		public void mousePressed(MouseEvent e) {
			mpX = e.getX();
			mpY = e.getY();
			ctrl = isCtrlDown;
		}
		public void mouseDragged(MouseEvent e) {
			if (!ctrl) return;
			setMdCoord(e);
			repaint();
		}
		private void setMdCoord(MouseEvent e) {
			int dx = e.getX() - mpX;
			int dy = e.getY() - mpY;
			mdX = mpX + max(abs(dx), rint(abs(dy) * widthHeightRatio) * signum(dx));
			mdY = mpY + max(abs(dy), rint(abs(dx) / widthHeightRatio) * signum(dy));
			acceptIf(insets.left, ge(mdX), setMdXY); 
			acceptIf(insets.top,  ge(mdY), setMdYX);
			acceptIf(insets.left+width-1, le(mdX), setMdXY); 
			acceptIf(insets.top+height-1, le(mdY), setMdYX);
		}
		private void acceptIf(int value, Predicate<Integer> p, Consumer<Integer> c) { if (p.test(value)) c.accept(value); }
		private Predicate<Integer> ge(int md) { return v-> v >= md; }
		private Predicate<Integer> le(int md) { return v-> v <= md; }
		private Consumer<Integer> setMdXY = v-> mdY = mpY + rint(abs((mdX=v)-mpX) / widthHeightRatio) * signum(mdY-mpY);
		private Consumer<Integer> setMdYX = v-> mdX = mpX + rint(abs((mdY=v)-mpY) * widthHeightRatio) * signum(mdX-mpX);
		public void mouseReleased(MouseEvent e) {
			if (e.getX() == mpX && e.getY() == mpY) return; 
			stack.push(ctrl);
			if (!ctrl) {
				minX += mpX - (mdX = e.getX());
				minY += mpY - (mdY = e.getY());
			}
			else {
				setMdCoord(e);
				if (mdX < mpX) { int t=mpX; mpX=mdX; mdX=t; } 
				if (mdY < mpY) { int t=mpY; mpY=mdY; mdY=t; } 
				minX += mpX - insets.left;
				minY += mpY - insets.top;
				double rZoom = (double) width / abs(mdX - mpX);
				minX *= rZoom;
				minY *= rZoom;
				Zoom /= rZoom;
			}
			ctrl = false;
			repaint(true);		
		}
	};
	
	private KeyAdapter keyAdapter = new KeyAdapter() {
		public void keyPressed(KeyEvent e) {
			isCtrlDown = e.isControlDown();
		}
		public void keyReleased(KeyEvent e) {
			isCtrlDown = e.isControlDown();
		}
		public void keyTyped(KeyEvent e) {
			char c = e.getKeyChar();
			boolean isEsc = c == VK_ESCAPE;
			if (!isEsc && c != VK_BACK_SLASH) return;
			repaint(stack.pop(isEsc));
		}
	};
	
	private class Point {
		public boolean type;
		public double Zoom;
		public int minX;
		public int minY;
		Point(boolean type, double Zoom, int minX, int minY) {
			this.type = type;
			this.Zoom = Zoom;
			this.minX = minX;
			this.minY = minY;
		}
	}
	private class Stack extends java.util.Stack<Point> {
		private static final long serialVersionUID = 1L;
		public Point push(boolean type) {
			return push(type, Zoom, minX, minY);
		}
		public Point push(boolean type, double ... point) {
			double Zoom = point[0];
			return push(type, Zoom, rint(point[1]/Zoom), rint(point[2]/Zoom));
		}
		public Point push(boolean type, double Zoom, int minX, int minY) {
			return push(new Point(type, Zoom, minX, minY));
		}
		public Point push(double[] ... points) {
			Point lastPoint = push(false, points[0]);
			for (int i=0, e=points.length-1; i<e; i+=1) {
				double[] point = points[i];
				lastPoint = push(point[0] != points[i+1][0], point);
				done(printPoint(lastPoint));
			}
			return lastPoint;
		}
		public boolean pop(boolean type) {
			for (;;) {
				if (empty()) return false;
				Point d = super.pop();
				Zoom = d.Zoom;
				minX = d.minX;
				minY = d.minY;
				if (!type || d.type) return true;
			}
		}
	}
	
	@Override
	public void paint(Graphics g) {
		if (newImage) newImage();
		g.drawImage(image, insets.left, insets.top, this);
		//g.drawLine(insets.left+width/2, insets.top+0,        insets.left+width/2, insets.top+height);
		//g.drawLine(insets.left+0,       insets.top+height/2, insets.left+width,   insets.top+height/2);
		if (!ctrl) return;
		g.drawRect(min(mpX, mdX), min(mpY, mdY), abs(mpX - mdX), abs(mpY - mdY));
	}

	private void newImage() {
		long milli = printPoint();
		image = new BufferedImage(width, height, TYPE_INT_RGB);
		int maxX = minX + width;
		int maxY = minY + height;
		for (int x = minX; x < maxX; x+=1) {
			double r = x * Zoom;
			for (int y = minY; y < maxY; y+=1) {
				double i = y * Zoom;
				//System.out.printf("%+f%+fi\n", r, i);
				//             0f    1/6f  1/3f 1/2f 2/3f    5/6f
				//straight -> red  yellow green cian blue magenta <- reverse 
				image.setRGB(x-minX, y-minY, color(r, i, 360, false, 2/3f));
			}
		}
		newImage = false;
		done(milli);
	}

	private long printPoint() {
		return printPoint(Zoom, minX, minY);
	}
	private long printPoint(Point point) {
		return printPoint(point.Zoom, point.minX, point.minY);
	}
	private long printPoint(double Zoom, int minX, int minY) {
		return printPoint(Zoom, minX*Zoom, minY*Zoom);
	}
	private long printPoint(Object ... point) {
		System.out.printf(ROOT,	"{%.16e, %.16g, %.16g},", point);
		return currentTimeMillis();
	}
	
	private void done(long milli) {
		milli = currentTimeMillis() - milli;
		System.out.println(" // " + milli + "ms done!");
	}

	private int color(double r0, double i0, int max, boolean straight, float shift) {
		int n = -1;
		double r=0, i=0, r2=0, i2=0;
		do {
			i = r*(i+i) + i0;
			r = r2-i2 + r0;
			r2 = r*r;
			i2 = i*i;
		}
		while (++n < max && r2 + i2 < 4); 
		return n == max
			? black.getRGB()
			: HSBtoRGB(shift + (float) (straight ? n : max-n) / max * 11/12f + (straight ? 0f : 1/12f), 1, 1)
		;		
	}
}

JavaScript

Works with: Firefox version 3.5.11

This needs the canvas tag of HTML 5 (it will not run on IE8 and lower or old browsers).

The code can be run directly from the Javascript console in modern browsers by copying and pasting it.

function mandelIter(cx, cy, maxIter) {
  var x = 0.0;
  var y = 0.0;
  var xx = 0;
  var yy = 0;
  var xy = 0;

  var i = maxIter;
  while (i-- && xx + yy <= 4) {
    xy = x * y;
    xx = x * x;
    yy = y * y;
    x = xx - yy + cx;
    y = xy + xy + cy;
  }
  return maxIter - i;
}

function mandelbrot(canvas, xmin, xmax, ymin, ymax, iterations) {
  var width = canvas.width;
  var height = canvas.height;

  var ctx = canvas.getContext('2d');
  var img = ctx.getImageData(0, 0, width, height);
  var pix = img.data;
  
  for (var ix = 0; ix < width; ++ix) {
    for (var iy = 0; iy < height; ++iy) {
      var x = xmin + (xmax - xmin) * ix / (width - 1);
      var y = ymin + (ymax - ymin) * iy / (height - 1);
      var i = mandelIter(x, y, iterations);
      var ppos = 4 * (width * iy + ix);
      
      if (i > iterations) {
        pix[ppos] = 0;
        pix[ppos + 1] = 0;
        pix[ppos + 2] = 0;
      } else {
        var c = 3 * Math.log(i) / Math.log(iterations - 1.0);
        
        if (c < 1) {
          pix[ppos] = 255 * c;
          pix[ppos + 1] = 0;
          pix[ppos + 2] = 0;
        }
        else if ( c < 2 ) {
          pix[ppos] = 255;
          pix[ppos + 1] = 255 * (c - 1);
          pix[ppos + 2] = 0;
        } else {
          pix[ppos] = 255;
          pix[ppos + 1] = 255;
          pix[ppos + 2] = 255 * (c - 2);
        }
      }
      pix[ppos + 3] = 255;
    }
  }
  
  ctx.putImageData(img, 0, 0);
}

var canvas = document.createElement('canvas');
canvas.width = 900;
canvas.height = 600;

document.body.insertBefore(canvas, document.body.childNodes[0]);

mandelbrot(canvas, -2, 1, -1, 1, 1000);
Output:
with default parameters

ES6/WebAssembly

With ES6 and WebAssembly, the program can run faster. Of course, this requires a compiled WASM file, but one can easily build one for instance with the WebAssembly explorer

var mandelIter;
fetch("./mandelIter.wasm")
    .then(res => {
        if (res.ok) return res.arrayBuffer();
        throw new Error('Unable to fetch WASM.');
    })
    .then(bytes => { return WebAssembly.compile(bytes); })
    .then(module => { return WebAssembly.instantiate(module); })
    .then(instance => { WebAssembly.instance = instance; draw(); })

function mandelbrot(canvas, xmin, xmax, ymin, ymax, iterations) {
    // ...
    var i = WebAssembly.instance.exports.mandelIter(x, y, iterations);
    // ...
}

function draw() {
    // canvas initialization if necessary
    // ...
    mandelbrot(canvas, -2, 1, -1, 1, 1000);
    // ...
}

jq

Thumbnail of SVG produced by jq program
Works with: jq version 1.4

The Mandelbrot function as defined here is similar to the JavaScript implementation but generates SVG. The resulting picture is the same.

Preliminaries

# SVG STUFF
  def svg(id; width; height): 
    "<svg width='\(width // "100%")' height='\(height // "100%") '
        id='\(id)'
        xmlns='http://www.w3.org/2000/svg'>";

  def pixel(x;y;r;g;b;a):
    "<circle cx='\(x)' cy='\(y)' r='1' fill='rgb(\(r|floor),\(g|floor),\(b|floor))' />";

# "UNTIL"
  # As soon as "condition" is true, then emit . and stop:
  def do_until(condition; next):
    def u: if condition then . else (next|u) end;
    u;
def Mandeliter( cx; cy; maxiter ):
  # [i, x, y, x^2+y^2]
  [ maxiter, 0.0, 0.0, 0.0 ]
  | do_until( .[0] == 0 or .[3] > 4;
      .[1] as $x | .[2] as $y
      | ($x * $y) as $xy
      | ($x * $x) as $xx
      | ($y * $y) as $yy
      | [ (.[0] - 1),         # i
          ($xx - $yy + cx),   # x
          ($xy + $xy + cy),   # y
          ($xx+$yy)           # xx+yy
        ] )
    | maxiter - .[0];
 
# width and height should be specified as the number of pixels.
# obj == { xmin: _, xmax: _, ymin: _, ymax: _ }
def Mandelbrot( obj; width; height; iterations ):
  def pixies:
    range(0; width) as $ix
    | (obj.xmin + ((obj.xmax - obj.xmin) * $ix / (width - 1))) as $x 
    | range(0; height) as $iy
    | (obj.ymin + ((obj.ymax - obj.ymin) * $iy / (height - 1))) as $y
    | Mandeliter( $x; $y; iterations ) as $i
    | if $i == iterations then
        pixel($ix; $iy; 0; 0; 0; 255)
      else
        (3 * ($i|log)/((iterations - 1.0)|log)) as $c  # redness
        | if $c < 1 then
            pixel($ix;$iy; 255*$c; 0; 0; 255)
          elif $c < 2 then
            pixel($ix;$iy; 255; 255*($c-1); 0; 255)
          else
            pixel($ix;$iy; 255; 255; 255*($c-2); 255)
          end
      end;

  svg("mandelbrot"; "100%"; "100%"),
  pixies,
  "</svg>";

Example:

 Mandelbrot( {"xmin": -2, "xmax": 1, "ymin": -1, "ymax":1}; 900; 600; 1000 )

Execution:

 $ jq -n -r -f mandelbrot.jq > mandelbrot.svg

The output can be viewed in a web browser such as Chrome, Firefox, or Safari.

Julia

Generates an ASCII representation:

function mandelbrot(a)
    z = 0
    for i=1:50
        z = z^2 + a
    end
    return z
end

for y=1.0:-0.05:-1.0
    for x=-2.0:0.0315:0.5
        abs(mandelbrot(complex(x, y))) < 2 ? print("*") : print(" ")
    end
    println()
end

This generates a PNG image file:

using Images

@inline function hsv2rgb(h, s, v)
    c = v * s
    x = c * (1 - abs(((h/60) % 2) - 1))
    m = v - c
    r,g,b = if     h < 60   (c, x, 0)
            elseif h < 120  (x, c, 0)
            elseif h < 180  (0, c, x)
            elseif h < 240  (0, x, c)
            elseif h < 300  (x, 0, c)
            else            (c, 0, x) end
    (r + m), (b + m), (g + m)
end

function mandelbrot()
    w       = 1600
    h       = 1200
    zoom    = 0.5
    moveX   = -0.5
    moveY   = 0
    maxIter = 30
    img = Array{RGB{Float64},2}(undef,h,w)
    for x in 1:w
      for y in 1:h
        i = maxIter
        z = c = Complex( (2*x - w) / (w * zoom) + moveX,
                         (2*y - h) / (h * zoom) + moveY )
        while abs(z) < 2 && (i -= 1) > 0
            z = z^2 + c
        end
        r,g,b = hsv2rgb(i / maxIter * 360, 1, i / maxIter)
        img[y,x] = RGB{Float64}(r, g, b)
      end
    end
    return img
end

img = mandelbrot()
save("mandelbrot.png", img)

Mandelbrot Set with Julia Animation

This is an extension of the corresponding R section: e^(-|z|)-smoothing was added. See Javier Barrallo & Damien M. Jones: Coloring Algorithms for Dynamical Systems in the Complex Plane (II. Distance Estimators).

using Plots
gr(aspect_ratio=:equal, legend=false, axis=false, ticks=false, dpi=100)

d, h = 400, 300  # pixel density (= image width) and image height
n, r = 40, 1000  # number of iterations and escape radius (r > 2)

x = range(-1.0, 1.0, length=d+1)
y = range(-h/d, h/d, length=h+1)

C = 2.0 .* (x' .+ y .* im) .- 0.5
Z, S = zero(C), zeros(size(C))

animation = Animation()
smoothing = Animation()

for k in 1:n
    M = abs.(Z) .< r
    S[M] = S[M] .+ exp.(.-abs.(Z[M]))
    Z[M] = Z[M] .^ 2 .+ C[M]
    heatmap(exp.(.-abs.(Z)), c=:jet)
    frame(animation)
    heatmap(S .+ exp.(.-abs.(Z)), c=:jet)
    frame(smoothing)
end

gif(animation, "Mandelbrot_animation.gif", fps=2)
gif(smoothing, "Mandelbrot_smoothing.gif", fps=2)

Normal Map Effect, Mercator Projection and Perturbation Theory

Normalization, Distance Estimation and Boundary Detection

This is a translation of the corresponding Python section: see there for more explanations. The e^(-|z|)-smoothing, normalized iteration count and exterior distance estimation algorithms are used. Partial antialiasing is used for boundary detection.

using Plots
gr(aspect_ratio=:equal, axis=true, ticks=true, legend=false, dpi=200)

d, h = 800, 500  # pixel density (= image width) and image height
n, r = 200, 500  # number of iterations and escape radius (r > 2)

x = range(0, 2, length=d+1)
y = range(0, 2 * h / d, length=h+1)

A, B = collect(x) .- 1, collect(y) .- h / d
C = 2.0 .* (A' .+ B .* im) .- 0.5

Z, dZ = zero(C), zero(C)
D, S, T = zeros(size(C)), zeros(size(C)), zeros(size(C))

for k in 1:n
    M = abs.(Z) .< r
    S[M], T[M] = S[M] .+ exp.(.- abs.(Z[M])), T[M] .+ 1
    Z[M], dZ[M] = Z[M] .^ 2 .+ C[M], 2 .* Z[M] .* dZ[M] .+ 1
end

heatmap(S .^ 0.1, c=:balance)
savefig("Mandelbrot_set_1.png")

N = abs.(Z) .>= r  # normalized iteration count
T[N] = T[N] .- log2.(log.(abs.(Z[N])) ./ log(r))

heatmap(T .^ 0.1, c=:balance)
savefig("Mandelbrot_set_2.png")

N = abs.(Z) .> 2  # exterior distance estimation
D[N] = log.(abs.(Z[N])) .* abs.(Z[N]) ./ abs.(dZ[N])

heatmap(D .^ 0.1, c=:balance)
savefig("Mandelbrot_set_3.png")

N, thickness = D .> 0, 0.01  # boundary detection
D[N] = max.(1 .- D[N] ./ thickness, 0)

heatmap(D .^ 2.0, c=:binary)
savefig("Mandelbrot_set_4.png")

Normal Map Effect and Stripe Average Coloring

The Mandelbrot set is represented using Normal Maps and Stripe Average Coloring by Jussi Härkönen (cf. Arnaud Chéritat: Normal map effect). See also the picture in section Mixing it all and Julia Stripes on Shadertoy. To get a stripe pattern similar to that of Arnaud Chéritat, one can increase the density of the stripes, use cos instead of sin, and set the colormap to binary.

using Plots
gr(aspect_ratio=:equal, axis=true, ticks=true, legend=false, dpi=200)

d, h = 800, 500  # pixel density (= image width) and image height
n, r = 200, 500  # number of iterations and escape radius (r > 2)

direction, height = 45.0, 1.5  # direction and height of the light
density, intensity = 4.0, 0.5  # density and intensity of the stripes

x = range(0, 2, length=d+1)
y = range(0, 2 * h / d, length=h+1)

A, B = collect(x) .- 1, collect(y) .- h / d
C = (2.0 + 1.0im) .* (A' .+ B .* im) .- 0.5

Z, dZ, ddZ = zero(C), zero(C), zero(C)
D, S, T = zeros(size(C)), zeros(size(C)), zeros(size(C))

for k in 1:n
    M = abs.(Z) .< r
    S[M], T[M] = S[M] .+ sin.(density .* angle.(Z[M])), T[M] .+ 1
    Z[M], dZ[M], ddZ[M] = Z[M] .^ 2 .+ C[M], 2 .* Z[M] .* dZ[M] .+ 1, 2 .* (dZ[M] .^ 2 .+ Z[M] .* ddZ[M])
end

N = abs.(Z) .>= r  # basic normal map effect and stripe average coloring (potential function)
P, Q = S[N] ./ T[N], (S[N] .+ sin.(density .* angle.(Z[N]))) ./ (T[N] .+ 1)
U, V = Z[N] ./ dZ[N], 1 .+ (log2.(log.(abs.(Z[N])) ./ log(r)) .* (P .- Q) .+ Q) .* intensity
U, v = U ./ abs.(U), exp(direction / 180 * pi * im)  # unit normal vectors and light vector
D[N] = max.((real.(U) .* real(v) .+ imag.(U) .* imag(v) .+ V .* height) ./ (1 + height), 0)

heatmap(D .^ 1.0, c=:bone_1)
savefig("Mandelbrot_normal_map_1.png")

N = abs.(Z) .> 2  # advanced normal map effect using higher derivatives (distance estimation)
U = Z[N] .* dZ[N] .* ((1 .+ log.(abs.(Z[N]))) .* conj.(dZ[N] .^ 2) .- log.(abs.(Z[N])) .* conj.(Z[N] .* ddZ[N]))
U, v = U ./ abs.(U), exp(direction / 180 * pi * im)  # unit normal vectors and light vector
D[N] = max.((real.(U) .* real(v) .+ imag.(U) .* imag(v) .+ height) ./ (1 + height), 0)

heatmap(D .^ 1.0, c=:afmhot)
savefig("Mandelbrot_normal_map_2.png")

Mercator Mandelbrot Maps and Zoom Images

A small change in the code above creates Mercator maps and zoom images of the Mandelbrot set. See also the album Mercator Mandelbrot Maps by Anders Sandberg and Mandelbrot sequence new on Wikimedia for a zoom animation to the given coordinates.

using Plots
gr(aspect_ratio=:equal, axis=true, ticks=true, legend=false, dpi=200)

d, h = 200, 1200  # pixel density (= image width) and image height
n, r = 8000, 10000  # number of iterations and escape radius (r > 2)

a = -.743643887037158704752191506114774  # https://mathr.co.uk/web/m-location-analysis.html
b = 0.131825904205311970493132056385139  # try: a, b, n = -1.748764520194788535, 3e-13, 800

x = range(0, 2, length=d+1)
y = range(0, 2 * h / d, length=h+1)

A, B = collect(x) .* pi, collect(y) .* pi
C = 8.0 .* exp.((A' .+ B .* im) .* im) .+ (a + b * im)

Z, dZ = zero(C), zero(C)
D = zeros(size(C))

for k in 1:n
    M = abs2.(Z) .< abs2(r)
    Z[M], dZ[M] = Z[M] .^ 2 .+ C[M], 2 .* Z[M] .* dZ[M] .+ 1
end

N = abs.(Z) .> 2  # exterior distance estimation
D[N] = log.(abs.(Z[N])) .* abs.(Z[N]) ./ abs.(dZ[N])

heatmap(D' .^ 0.05, c=:nipy_spectral)
savefig("Mercator_Mandelbrot_map.png")

X, Y = real(C), imag(C)  # zoom images (adjust circle size 50 and zoom level 20 as needed)
R, c, z = 50 * (2 / d) * pi .* exp.(.- B), min(d, h) + 1, max(0, h - d) ÷ 20

gr(c=:nipy_spectral, axis=true, ticks=true, legend=false, markerstrokewidth=0)
p1 = scatter(X[1z+1:1z+c,1:d], Y[1z+1:1z+c,1:d], markersize=R[1:c].^.5, marker_z=D[1z+1:1z+c,1:d].^.5)
p2 = scatter(X[2z+1:2z+c,1:d], Y[2z+1:2z+c,1:d], markersize=R[1:c].^.5, marker_z=D[2z+1:2z+c,1:d].^.4)
p3 = scatter(X[3z+1:3z+c,1:d], Y[3z+1:3z+c,1:d], markersize=R[1:c].^.5, marker_z=D[3z+1:3z+c,1:d].^.3)
p4 = scatter(X[4z+1:4z+c,1:d], Y[4z+1:4z+c,1:d], markersize=R[1:c].^.5, marker_z=D[4z+1:4z+c,1:d].^.2)
plot(p1, p2, p3, p4, layout=(2, 2))
savefig("Mercator_Mandelbrot_zoom.png")

Perturbation Theory and Deep Mercator Maps

For deep zoom images it is sufficient to calculate a single point with high accuracy. A good approximation can then be found for all other points by means of a perturbation calculation with standard accuracy. Rebasing is used to reduce glitches. See Another solution to perturbation glitches (Fractalforums) for details. See also the image Deeper Mercator Mandelbrot by Anders Sandberg.

using Plots
gr(aspect_ratio=:equal, axis=true, ticks=true, legend=false, dpi=200)

setprecision(BigFloat, 256)  # set precision to 256 bits (default)
setrounding(BigFloat, RoundNearest)  # set rounding mode (default)

d, h = 50, 1000  # pixel density (= image width) and image height
n, r = 80000, 100000  # number of iterations and escape radius (r > 2)

a = BigFloat("-1.256827152259138864846434197797294538253477389787308085590211144291")
b = BigFloat(".37933802890364143684096784819544060002129071484943239316486643285025")

S = zeros(Complex{Float64}, n+1)
let c = a + b * im, z = zero(c)
    for k in 1:n+1
        S[k] = z
        if abs2(z) < abs2(r)
            z = z ^ 2 + c
        else
            println("The reference sequence diverges within $(k-1) iterations.")
            break
        end
    end
end

x = range(0, 2, length=d+1)
y = range(0, 2 * h / d, length=h+1)

A, B = collect(x) .* pi, collect(y) .* pi
C = 8.0 .* exp.((A' .+ B .* im) .* im)

E, Z, dZ = zero(C), zero(C), zero(C)
D, I, J = zeros(size(C)), ones(Int64, size(C)), ones(Int64, size(C))

for k in 1:n
    M, R = abs2.(Z) .< abs2(r), abs2.(Z) .< abs2.(E)
    E[R], I[R] = Z[R], J[R]  # rebase when z is closer to zero
    E[M], I[M] = (2 .* S[I[M]] .+ E[M]) .* E[M] .+ C[M], I[M] .+ 1
    Z[M], dZ[M] = S[I[M]] .+ E[M], 2 .* Z[M] .* dZ[M] .+ 1
end

N = abs.(Z) .> 2  # exterior distance estimation
D[N] = log.(abs.(Z[N])) .* abs.(Z[N]) ./ abs.(dZ[N])

heatmap(D' .^ 0.015, c=:nipy_spectral)
savefig("Mercator_Mandelbrot_deep_map.png")

Kotlin

Translation of: Java
// version 1.1.2

import java.awt.Graphics
import java.awt.image.BufferedImage
import javax.swing.JFrame

class Mandelbrot: JFrame("Mandelbrot Set") {
    companion object {
        private const val MAX_ITER = 570
        private const val ZOOM = 150.0
    }

    private val img: BufferedImage

    init {
        setBounds(100, 100, 800, 600)
        isResizable = false
        defaultCloseOperation = EXIT_ON_CLOSE
        img = BufferedImage(width, height, BufferedImage.TYPE_INT_RGB)
        for (y in 0 until height) {
            for (x in 0 until width) {
                var zx = 0.0
                var zy = 0.0
                val cX = (x - 400) / ZOOM
                val cY = (y - 300) / ZOOM
                var iter = MAX_ITER
                while (zx * zx + zy * zy < 4.0 && iter > 0) {
                    val tmp = zx * zx - zy * zy + cX
                    zy = 2.0 * zx * zy + cY
                    zx = tmp
                    iter--
                }
                img.setRGB(x, y, iter or (iter shl 7))
            }
        }
    }

    override fun paint(g: Graphics) {
        g.drawImage(img, 0, 0, this)
    }
}

fun main(args: Array<String>) {
    Mandelbrot().isVisible = true
}

LabVIEW

Works with: LabVIEW version 8.0 Full Development Suite


Lang5

: d2c(*,*) 2 compress 'c dress ;        # Make a complex number.

: iterate(c) [0 0](c) "dup * over +" steps reshape execute ;

: print_line(*) "#*+-. " "" split swap subscript "" join . "\n" . ;

75 iota 45 - 20 /                       # x coordinates
29 iota 14 - 10 /                       # y cordinates
'd2c outer                              # Make complex matrix.

10 'steps set                           # How many iterations?

iterate abs int 5 min 'print_line apply # Compute & print

Lambdatalk

Lambdatalk working in any web browser has access to javascript and could draw the mandelbrot set very quickly in a canvas, for instance here: - http: // lambdaway.free.fr/lambdawalks/?view=mandel_canvas

Here we show a pure lambdatalk code, a slow but minimalistic and easy to understand version without the burden of any canvas. We just compute if a point is inside or outside the mandelbrot set and just write "o" or "." directly in the wiki page.

{def mandel

 {def mandel.r
  {lambda {:iter :cx :cy :norm :x :y :count}
   {if {> :count :iter}                       // then norm < 4
    then o                                    // inside the set
    else {if {> :norm 4}                      // then iter > max
    then .                                    // outside the set
    else {let { {:cx :cx} {:cy :cy} {:iter :iter}
                {:X {+ {* :x :x} -{* :y :y} :cx}}  // compute
                {:Y {+ {* 2 :x :y} :cy}}           // z = z^2+c
                {:count {+ :count 1}}
              } {mandel.r :iter :cx :cy
                          {+ {* :X :X} {* :Y :Y}}  // the norm
                          :X :Y :count} }}}}}

 {lambda {:iter :cx :cy}
  {mandel.r :iter
            {+ {* :cx 0.05} -1.50}       // centering the set
            {+ {* :cy 0.05} -0.75}       // inside the frame
            0 0 0 0} }}
-> mandel

We call mandel directly in the wiki page

{S.map {lambda {:i} {br}     // loop on y
  {S.map {{lambda {:i :j}    // loop on x
    {mandel 20 :i :j}} :i}   // compute
  {S.serie 0 30}}}           // x resolution
{S.serie 0 40}}              // y resolution
 . . . . . . . . . . . . . . . o . . . . . . . . . . . . . . . 
 . . . . . . . . . . . . . . . o . . . . . . . . . . . . . . . 
 . . . . . . . . . . . . . . . o . . . . . . . . . . . . . . . 
 . . . . . . . . . . . . . . o o o . . . . . . . . . . . . . . 
 . . . . . . . . . . . . . . o o o . . . . . . . . . . . . . . 
 . . . . . . . . . . . . . o o o o o . . . . . . . . . . . . . 
 . . . . . . . . . . . . o o o o o o o . . . . . . . . . . . . 
 . . . . . . . . . . o o o o o o o o o o o . . . . . . . . . . 
 . . . . . . . . . . o o o o o o o o o o o . . . . . . . . . . 
 . . . . . . . . . . o o o o o o o o o o o . . . . . . . . . . 
 . . . . . . . . . o o o o o o o o o o o o o . . . . . . . . . 
 . . . . . . . . . . o o o o o o o o o o o . . . . . . . . . . 
 . . . . . . . . . . o o o o o o o o o o o . . . . . . . . . . 
 . . . . . . . . . . . o o o o o o o o o . . . . . . . . . . . 
 . . . . . . . . . . . . o o o o o o o . . . . . . . . . . . . 
 . . . . . . . . . . . . o o o o o o o . . . . . . . . . . . . 
 . . . . . . o . o o o o o o o o o o o o o o o . o . . . . . . 
 . . . . . . o . o o o o o o o o o o o o o o o . o . . . . . . 
 . . . . . . o o o o o o o o o o o o o o o o o o o . . . . . . 
 . . o o o o o o o o o o o o o o o o o o o o o o o o o o o . . 
 . . . o o o o o o o o o o o o o o o o o o o o o o o o o . . . 
 . . . . o o o o o o o o o o o o o o o o o o o o o o o . . . . 
 . . o o o o o o o o o o o o o o o o o o o o o o o o o o o . . 
 . . . o o o o o o o o o o o o o o o o o o o o o o o o o . . . 
 . . o o o o o o o o o o o o o o o o o o o o o o o o o o o . . 
 o . o o o o o o o o o o o o o o o o o o o o o o o o o o o . o 
 o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 
 o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 
 o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 
 o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 
 o . o o o o o o o o o o o o o o o o o o o o o o o o o o o . o 
 . . o o o o o o o o o o o o o o o o o o o o o o o o o o o . . 
 . . . o o o o o o o o o o o o o o o o o o o o o o o o o . . . 
 . . o . o o o o o o o o o o o o o o o o o o o o o o o . o . . 
 . . . . o o o o o o o o o o o o o o o o o o o o o o o . . . . 
 . . . . o o o o o o o o o o o o o o o o o o o o o o o . . . . 
 . . . . o o o o o o o o o o o . o o o o o o o o o o o . . . . 
 . . . . o . . . o o o o o o . . . o o o o o o . . . o . . . . 
 . . . . . . . . o . . o o . . . . . o o . . o . . . . . . . . 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Lasso

define mandelbrotBailout => 16
define mandelbrotMaxIterations => 1000

define mandelbrotIterate(x, y) => {
	local(cr = #y - 0.5,
		ci = #x, 
		zi = 0.0, 
		zr = 0.0, 
		i = 0, 
		temp, zr2, zi2)

	{
		++#i;
		#temp = #zr * #zi
		#zr2 = #zr * #zr
		#zi2 = #zi * #zi
				
		#zi2 + #zr2 > mandelbrotBailout?
			return #i
		#i > mandelbrotMaxIterations?
			return 0

		#zr = #zr2 - #zi2 + #cr
		#zi = #temp + #temp + #ci
		
		currentCapture->restart
	}()
}

define mandelbrotTest() => {
	local(x, y = -39.0)
	{
		stdout('\n')
		#x = -39.0
		{
			mandelbrotIterate(#x / 40.0, #y / 40.0) == 0?
				stdout('*')
				| stdout(' ');
			++#x
			#x <= 39.0?
				currentCapture->restart
		}();
		++#y
		
		#y <= 39.0?
			currentCapture->restart
	}()
	stdout('\n')
}

mandelbrotTest
Output:

                                       *                                       
                                       *                                       
                                       *                                       
                                       *                                       
                                       *                                       
                                      ***                                      
                                     *****                                     
                                     *****                                     
                                      ***                                      
                                       *                                       
                                   *********                                   
                                 *************                                 
                                ***************                                
                             *********************                             
                             *********************                             
                              *******************                              
                              *******************                              
                              *******************                              
                              *******************                              
                            ***********************                            
                              *******************                              
                              *******************                              
                             *********************                             
                              *******************                              
                              *******************                              
                               *****************                               
                                ***************                                
                                 *************                                 
                                   *********                                   
                                       *                                       
                                ***************                                
                            ***********************                            
                         * ************************* *                         
                         *****************************                         
                      * ******************************* *                      
                       *********************************                       
                      ***********************************                      
                    ***************************************                    
               *** ***************************************** ***               
               *************************************************               
                ***********************************************                
                 *********************************************                 
                 *********************************************                 
                ***********************************************                
                ***********************************************                
              ***************************************************              
               *************************************************               
               *************************************************               
              ***************************************************              
              ***************************************************              
         *    ***************************************************    *         
       *****  ***************************************************  *****       
       ****** *************************************************** ******       
      ******* *************************************************** *******      
    ***********************************************************************    
    ********* *************************************************** *********    
       ****** *************************************************** ******       
       *****  ***************************************************  *****       
              ***************************************************              
              ***************************************************              
              ***************************************************              
              ***************************************************              
               *************************************************               
               *************************************************               
              ***************************************************              
                ***********************************************                
                ***********************************************                
                  *******************************************                  
                   *****************************************                   
                 *********************************************                 
                **** ****************** ****************** ****                
                 ***  ****************   ****************  ***                 
                  *    **************     **************    *                  
                         ***********       ***********                         
                         **  *****           *****  **                         
                          *   *                 *   *                          

LIL

From the source distribution. Produces a PBM, not shown here.

#
# A mandelbrot generator that outputs a PBM file. This can be used to measure
# performance differences between LIL versions and measure performance
# bottlenecks (although keep in mind that LIL is not supposed to be a fast
# language, but a small one which depends on C for the slow parts - in a real
# program where for some reason mandelbrots are required, the code below would
# be written in C). The code is based on the mandelbrot test for the Computer
# Language Benchmarks Game at http://shootout.alioth.debian.org/
#
# In my current computer (Intel Core2Quad Q9550 @ 2.83GHz) running x86 Linux
# the results are (using the default 256x256 size):
#
#  2m3.634s  - commit 1c41cdf89f4c1e039c9b3520c5229817bc6274d0 (Jan 10 2011)
#
# To test call
#
#  time ./lil mandelbrot.lil > mandelbrot.pbm
#
# with an optimized version of lil (compiled with CFLAGS=-O3 make).
#

set width [expr $argv]
if not $width { set width 256 }
set height $width
set bit_num 0
set byte_acc 0
set iter 50
set limit 2.0

write "P4\n${width} ${height}\n"

for {set y 0} {$y < $height} {inc y} {
   for {set x 0} {$x < $width} {inc x} {
       set Zr 0.0 Zi 0.0 Tr 0.0 Ti 0.0
       set Cr [expr 2.0 * $x / $width - 1.5]
       set Ci [expr 2.0 * $y / $height - 1.0]
       for {set i 0} {$i < $iter && $Tr + $Ti <= $limit * $limit} {inc i} {
           set Zi [expr 2.0 * $Zr * $Zi + $Ci]
           set Zr [expr $Tr - $Ti + $Cr]
           set Tr [expr $Zr * $Zr]
           set Ti [expr $Zi * $Zi]
       }

       set byte_acc [expr $byte_acc << 1]
       if [expr $Tr + $Ti <= $limit * $limit] {
           set byte_acc [expr $byte_acc | 1]
       }

       inc bit_num

       if [expr $bit_num == 8] {
           writechar $byte_acc
           set byte_acc 0
           set bit_num 0
       } {if [expr $x == $width - 1] {
           set byte_acc [expr 8 - $width % 8]
           writechar $byte_acc
           set byte_acc 0
           set bit_num 0
       }}
   }
}

Works with: UCB Logo
to mandelbrot :left :bottom :side :size
  cs setpensize [1 1]
  make "inc :side/:size
  make "zr :left
  repeat :size [
    make "zr :zr + :inc
    make "zi :bottom
    pu
    setxy repcount - :size/2  minus :size/2
    pd
    repeat :size [
      make "zi :zi + :inc
      setpencolor count.color calc :zr :zi
      fd 1 ] ]
end

to count.color :count
  ;op (list :count :count :count)
  if :count > 256 [op 0]	; black
  if :count > 128 [op 7]	; white
  if :count >  64 [op 5]	; magenta
  if :count >  32 [op 6]	; yellow
  if :count >  16 [op 4]	; red
  if :count >   8 [op 2]	; green
  if :count >   4 [op 1]	; blue
  op 3				; cyan
end

to calc :zr :zi [:count 0] [:az 0] [:bz 0]
  if :az*:az + :bz*:bz > 4 [op :count]
  if :count > 256 [op :count]
  op (calc :zr :zi (:count + 1) (:zr + :az*:az - :bz*:bz) (:zi + 2*:az*:bz))
end

mandelbrot -2 -1.25 2.5 400

Lua

Graphical

Needs LÖVE 2D Engine
Zoom in: drag the mouse; zoom out: right click

local maxIterations = 250
local minX, maxX, minY, maxY = -2.5, 2.5, -2.5, 2.5
local miX, mxX, miY, mxY
function remap( x, t1, t2, s1, s2 )
    local f = ( x - t1 ) / ( t2 - t1 )
    local g = f * ( s2 - s1 ) + s1
    return g;
end
function drawMandelbrot()
    local pts, a, as, za, b, bs, zb, cnt, clr = {}
    for j = 0, hei - 1 do
        for i = 0, wid - 1 do
            a = remap( i, 0, wid, minX, maxX )
            b = remap( j, 0, hei, minY, maxY )
            cnt = 0; za = a; zb = b
            while( cnt < maxIterations ) do
                as = a * a - b * b; bs = 2 * a * b
                a = za + as; b = zb + bs
                if math.abs( a ) + math.abs( b ) > 16 then break end
                cnt = cnt + 1
            end
            if cnt == maxIterations then clr = 0
            else clr = remap( cnt, 0, maxIterations, 0, 255 )
            end
            pts[1] = { i, j, clr, clr, 0, 255 }
            love.graphics.points( pts )
        end
    end
end
function startFractal()
    love.graphics.setCanvas( canvas ); love.graphics.clear()
    love.graphics.setColor( 255, 255, 255 )
    drawMandelbrot(); love.graphics.setCanvas()
end
function love.load()
    wid, hei = love.graphics.getWidth(), love.graphics.getHeight()
    canvas = love.graphics.newCanvas( wid, hei )
    startFractal()
end
function love.mousepressed( x, y, button, istouch )
    if button ==  1 then
        startDrag = true; miX = x; miY = y
    else
        minX = -2.5; maxX = 2.5; minY = minX; maxY = maxX
        startFractal()
        startDrag = false
    end
end
function love.mousereleased( x, y, button, istouch )
    if startDrag then
        local l
        if x > miX then mxX = x
        else l = x; mxX = miX; miX = l
        end
        if y > miY then mxY = y
        else l = y; mxY = miY; miY = l
        end
        miX = remap( miX, 0, wid, minX, maxX ) 
        mxX = remap( mxX, 0, wid, minX, maxX )
        miY = remap( miY, 0, hei, minY, maxY ) 
        mxY = remap( mxY, 0, hei, minY, maxY )
        minX = miX; maxX = mxX; minY = miY; maxY = mxY
        startFractal()
    end
end
function love.draw()
    love.graphics.draw( canvas )
end

ASCII

-- Mandelbrot set in Lua 6/15/2020 db
local charmap = { [0]=" ", ".", ":", "-", "=", "+", "*", "#", "%", "@" }
for y = -1.3, 1.3, 0.1 do
  for x = -2.1, 1.1, 0.04 do
    local zi, zr, i = 0, 0, 0
    while i < 100 do
      if (zi*zi+zr*zr >= 4) then break end
      zr, zi, i = zr*zr-zi*zi+x, 2*zr*zi+y, i+1
    end
    io.write(charmap[i%10])
  end
  print()
end
Output:
...............::::::::::::::::::---------------::::::::::::::::::::::::::::::::
.............:::::::::::---------------------------------:::::::::::::::::::::::
...........::::::::---------------------======+#@#++=====-----::::::::::::::::::
..........::::::--------------------=======+++**@+@.@*+=====-----:::::::::::::::
........:::::--------------------========++++*#@@#=:%#*++=====------::::::::::::
.......:::--------------------========+++***#%:     .:#*+++++===-------:::::::::
......:::------------------=======+++#%@%%%@@ :#    %.@@%#***%*+==------::::::::
.....::-----------------====++++++**# =  =%             %-.*+=#%+==-------::::::
.....:--------------==+++++++++****%:.*+                     *%*++==-------:::::
....:--------=====+*#=%##########%%.**                        .@ +===-------::::
....---========++++*#@:=*:-@+ .@@ :=                          @ #*===--------:::
...--=======+++++*##%.=:        @+.                           @##+====--------::
...=======****##% .-=%                                        *#*+====--------::
...@.::   :: %                                              :@#*++====--------::
...=======****##% .-=%                                        *#*+====--------::
...--=======+++++*##%.=:        @+.                           @##+====--------::
....---========++++*#@:=*:-@+ .@@ :=                          @ #*===--------:::
....:--------=====+*#=%##########%%.**                        .@ +===-------::::
.....:--------------==+++++++++****%:.*+                     *%*++==-------:::::
.....::-----------------====++++++**# =  =%             %-.*+=#%+==-------::::::
......:::------------------=======+++#%@%%%@@ :#    %.@@%#***%*+==------::::::::
.......:::--------------------========+++***#%:     .:#*+++++===-------:::::::::
........:::::--------------------========++++*#@@#=:%#*++=====------::::::::::::
..........::::::--------------------=======+++**@+@.@*+=====-----:::::::::::::::
...........::::::::---------------------======+#@#++=====-----::::::::::::::::::
.............:::::::::::---------------------------------:::::::::::::::::::::::
...............::::::::::::::::::---------------::::::::::::::::::::::::::::::::

ASCII (obfuscated)

Produces an 80x25 ASCII Mandelbrot set, using only two lines of code. The result isn't very high quality because there's only so many iterations you can cram into two lines of 80 columns. And this code cheats, because it starts the iteration count at -15 instead of 0, to avoid the need for an excessively long character lookup table.

for y=-12,12 do l=""for x=-2,1,3/80 do a,b,n=0,0,-15 while n<9 and a*a+b*b<1e12
do a,b,n=a*a-b*b+x,2*a*b+y/8,n+1 end l=l..(".,:;=$%# "):sub(n,n)end print(l)end
Output:
............................................,,,,,,,,............................
.................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,...................
.........................,,,,,,,,,,,,,,,,,,,,,,::::,,,,,,,,,,,,,,,..............
...................,,,,,,,,,,,,,,,,,,,,,::::::;=$=;;::::::,,,,,,,,,,,,..........
..............,,,,,,,,,,,,,,,,,,,,:::::::::;;;==% :#=;;:::::,,,,,,,,,,,.......
.........,,,,,,,,,,,,,,,,,,,,:::::::::;;;;;==$%;;  ,##==;;;::::::,,,,,,,,,.....
.....,,,,,,,,,,,,,,,,,:::::::::::;;;;====$$$%#:       %$$===;;;;::::,,,,,,,,...
..,,,,,,,,,,,,,,::::::::::::;;;;;;==$     ,               .#% #=;:::,,,,,,,,,.
,,,,,,,,,,,,::::::;;;;;;;;;;=====$$#:.                         $=;;::::,,,,,,,,
,,,,,,,,:::::::;;;=%:%%%%%=%%%%%%#                            $  $;;:::,,,,,,,,
,,,,:::::::;;;;===$%#:         ,..                              :,=;;::::,,,,,,,
::::;;;;;;====$#  ..#                                           ;$=;;::::,,,,,,,
                                                             ; %$=;;;::::,,,,,,,
::::;;;;;;====$#  ..#                                           ;$=;;::::,,,,,,,
,,,,:::::::;;;;===$%#:         ,..                              :,=;;::::,,,,,,,
,,,,,,,,:::::::;;;=%:%%%%%=%%%%%%#                            $  $;;:::,,,,,,,,
,,,,,,,,,,,,::::::;;;;;;;;;;=====$$#:.                         $=;;::::,,,,,,,,
..,,,,,,,,,,,,,,::::::::::::;;;;;;==$     ,               .#% #=;:::,,,,,,,,,.
.....,,,,,,,,,,,,,,,,,:::::::::::;;;;====$$$%#:       %$$===;;;;::::,,,,,,,,...
.........,,,,,,,,,,,,,,,,,,,,:::::::::;;;;;==$%;;  ,##==;;;::::::,,,,,,,,,.....
..............,,,,,,,,,,,,,,,,,,,,:::::::::;;;==% :#=;;:::::,,,,,,,,,,,.......
...................,,,,,,,,,,,,,,,,,,,,,::::::;=$=;;::::::,,,,,,,,,,,,..........
.........................,,,,,,,,,,,,,,,,,,,,,,::::,,,,,,,,,,,,,,,..............
.................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,...................
............................................,,,,,,,,............................

M2000 Interpreter

Console is a bitmap so we can plot on it. A subroutine plot different size of pixels so we get Mandelbrot image at final same size for 32X26 for a big pixel of 16x16 pixels to 512x416 for a 1:1 pixel. Iterations for each pixel set to 25. Module can get left top corner as twips, and the size factor from 1 to 16 (size of output is 512x416 pixels for any factor).

Module Mandelbrot(x=0&,y=0&,z=1&) {
      If z<1  then z=1
      If z>16 then z=16
      Const iXmax=32*z
      Const iYmax=26*z
      Def single Cx, Cy, CxMin=-2.05, CxMax=0.85, CyMin=-1.2,  CyMax=1.2
      Const PixelWidth=(CxMax-CxMin)/iXmax, iXm=(iXmax-1)*PixelWidth
      Const PixelHeight=(CyMax-CyMin)/iYmax,Ph2=PixelHeight/2
      Const Iteration=25
      Const EscRadious=2.5, ER2=EscRadious**2
      Def single preview
      preview=iXmax*twipsX*(z/16)
      Def long yp, xp, dx, dy, dx1, dy1
      Let dx=twipsx*(16/z), dx1=dx-1
      Let dy=twipsy*(16/z), dy1=dy-1
      yp=y
      For iY=0 to (iYmax-1)*PixelHeight step PixelHeight {
            Cy=CyMin+iY
            xp=x
            if abs(Cy)<Ph2 Then Cy=0
            For iX=0 to iXm Step PixelWidth {
                  Let  Cx=CxMin+iX,Zx=0,Zy=0,Zx2=0,Zy2=0
                  For It=Iteration to 1 {Let Zy=2*Zx*Zy+Cy,Zx=Zx2-Zy2+Cx,Zx2=Zx**2,Zy2=Zy**2 :if Zx2+Zy2>ER2 Then exit
                  }
                  if it>13 then {it-=13} else.if it=0 then SetPixel(xp,yp,0): xp+=dx : continue
                  it*=10:SetPixel(xp,yp,color(it, it,255)) :xp+=dx
            } : yp+=dy
      }
      Sub SetPixel()
            move number, number: fill  dx1, dy1, number
      End Sub
}
Cls 1,0
sz=(1,2,4,8,16)
i=each(sz)
While i {
      Mandelbrot 250*twipsx,100*twipsy, array(i)
}

Version 2 without Subroutine. Also there is a screen refresh every 2 seconds.

Module Mandelbrot(x=0&,y=0&,z=1&) {
      If z<1  then z=1
      If z>16 then z=16
      Const iXmax=32*z
      Const iYmax=26*z
      Def single Cx, Cy, CxMin=-2.05, CxMax=0.85, CyMin=-1.2,  CyMax=1.2
      Const PixelWidth=(CxMax-CxMin)/iXmax, iXm=(iXmax-1)*PixelWidth
      Const PixelHeight=(CyMax-CyMin)/iYmax,Ph2=PixelHeight/2
      Const Iteration=25
      Const EscRadious=2.5, ER2=EscRadious**2
      Def single preview
      preview=iXmax*twipsX*(z/16)
      Def long yp, xp, dx, dy, dx1, dy1
      Let dx=twipsx*(16/z), dx1=dx-1
      Let dy=twipsy*(16/z), dy1=dy-1
      yp=y
      Refresh 2000
      For iY=0 to (iYmax-1)*PixelHeight step PixelHeight {
            Cy=CyMin+iY
            xp=x
            if abs(Cy)<Ph2 Then Cy=0
            move xp, yp
            For iX=0 to iXm Step PixelWidth {
                  Let  Cx=CxMin+iX,Zx=0,Zy=0,Zx2=0,Zy2=0
                  For It=Iteration to 1 {Let Zy=2*Zx*Zy+Cy,Zx=Zx2-Zy2+Cx,Zx2=Zx**2,Zy2=Zy**2 :if Zx2+Zy2>ER2 Then exit
                  }
                  if it>13 then {it-=13} else.if it=0 then fill  dx1, dy1, 0: Step 0,-dy1: continue
                  it*=10:fill  dx1, dy1, color(it, it,255): Step 0,-dy1
            } : yp+=dy
      }

}
Cls 1,0
sz=(1,2,4,8,16)
i=each(sz)
While i {
      Mandelbrot 250*twipsx,100*twipsy, array(i)
}

M4

Works with: GNU m4 version 1.4.19
Works with: OpenBSD m4

The following m4 code is not optimized very well, but it works. It is actually output from a program I call vmc, which translates output from the code generator task to different languages. The Mandelbrot set algorithm from the test set for that task. The vmc program itself is written in ATS, and the m4 it generates should run in any POSIX-compliant m4 (if not others as well). For very old m4 implementations, one might need to use an option such as -S 1000 to set the stack size larger than the default.

There are two data structures employed:

  • A FORTH-like data stack, an example of which would be 789:456:123:stack-bottom
  • A list of variables, such as var0:123:var1:456:var2:789:

There are macros to do calculations with the stack. There are also macros to fetch and store the values of variables, which are referenced by name.

One might enjoy even manually writing m4 code using such structures. However, the big mutual recursion that is the core of the program probably is not how one would write code manually.

(None of the above involves m4's notorious trickery with commas.)

divert(-1)
changecom
define(`newline',`
')
define(`leftquote',`[')
define(`rightquote',`]')
changequote(`[',`]')
define([print_char],
[ifelse(
$1,0,[*],
$1,1,[*],
$1,2,[*],
$1,3,[*],
$1,4,[*],
$1,5,[*],
$1,6,[*],
$1,7,[*],
$1,8,[*],
$1,9,[*],
$1,10,[newline],
$1,11,[*],
$1,12,[*],
$1,13,[*],
$1,14,[*],
$1,15,[*],
$1,16,[*],
$1,17,[*],
$1,18,[*],
$1,19,[*],
$1,20,[*],
$1,21,[*],
$1,22,[*],
$1,23,[*],
$1,24,[*],
$1,25,[*],
$1,26,[*],
$1,27,[*],
$1,28,[*],
$1,29,[*],
$1,30,[*],
$1,31,[*],
$1,32,[ ],
$1,33,[!],
$1,34,["],
$1,35,[#],
$1,36,[$],
$1,37,[%],
$1,38,[&],
$1,39,['],
$1,40,[(],
$1,41,[)],
$1,42,[*],
$1,43,[+],
$1,44,[,],
$1,45,[-],
$1,46,[.],
$1,47,[/],
$1,48,[0],
$1,49,[1],
$1,50,[2],
$1,51,[3],
$1,52,[4],
$1,53,[5],
$1,54,[6],
$1,55,[7],
$1,56,[8],
$1,57,[9],
$1,58,[:],
$1,59,[;],
$1,60,[<],
$1,61,[=],
$1,62,[>],
$1,63,[?],
$1,64,[@],
$1,65,[A],
$1,66,[B],
$1,67,[C],
$1,68,[D],
$1,69,[E],
$1,70,[F],
$1,71,[G],
$1,72,[H],
$1,73,[I],
$1,74,[J],
$1,75,[K],
$1,76,[L],
$1,77,[M],
$1,78,[N],
$1,79,[O],
$1,80,[P],
$1,81,[Q],
$1,82,[R],
$1,83,[S],
$1,84,[T],
$1,85,[U],
$1,86,[V],
$1,87,[W],
$1,88,[X],
$1,89,[Y],
$1,90,[Z],
$1,91,[changequote([`],['])leftquote`'changequote(`[',`]')],
$1,92,[\],
$1,93,[rightquote],
$1,94,[^],
$1,95,[_],
$1,96,[`],
$1,97,[a],
$1,98,[b],
$1,99,[c],
$1,100,[d],
$1,101,[e],
$1,102,[f],
$1,103,[g],
$1,104,[h],
$1,105,[i],
$1,106,[j],
$1,107,[k],
$1,108,[l],
$1,109,[m],
$1,110,[n],
$1,111,[o],
$1,112,[p],
$1,113,[q],
$1,114,[r],
$1,115,[s],
$1,116,[t],
$1,117,[u],
$1,118,[v],
$1,119,[w],
$1,120,[x],
$1,121,[y],
$1,122,[z],
$1,123,[{],
$1,124,[|],
$1,125,[}],
$1,126,[~],
[*])])
define([stack_1st],[substr([$1],0,index([$1],[:]))])
define([stack_2nd],[stack_1st(stack_drop([$1]))])
define([stack_drop],[substr([$1],eval(index([$1],[:]) [+ 1]))])
define([stack_drop2],[stack_drop(stack_drop([$1]))])
define([stack_not],[eval(stack_1st([$1]) [== 0]):stack_drop([$1])])
define([stack_neg],[eval([-] stack_1st([$1])):stack_drop([$1])])
define([stack_and],[eval(stack_2nd([$1] [!= 0]) [&&] stack_1st([$1] [!= 0])):stack_drop2([$1])])
define([stack_or],[eval(stack_2nd([$1] [!= 0]) [||] stack_1st([$1] [!= 0])):stack_drop2([$1])])
define([stack_lt],[eval(stack_2nd([$1]) [<] stack_1st([$1])):stack_drop2([$1])])
define([stack_le],[eval(stack_2nd([$1]) [<=] stack_1st([$1])):stack_drop2([$1])])
define([stack_gt],[eval(stack_2nd([$1]) [>] stack_1st([$1])):stack_drop2([$1])])
define([stack_ge],[eval(stack_2nd([$1]) [>=] stack_1st([$1])):stack_drop2([$1])])
define([stack_eq],[eval(stack_2nd([$1]) [==] stack_1st([$1])):stack_drop2([$1])])
define([stack_ne],[eval(stack_2nd([$1]) [!=] stack_1st([$1])):stack_drop2([$1])])
define([stack_add],[eval(stack_2nd([$1]) [+] stack_1st([$1])):stack_drop2([$1])])
define([stack_sub],[eval(stack_2nd([$1]) [-] stack_1st([$1])):stack_drop2([$1])])
define([stack_mul],[eval(stack_2nd([$1]) [*] stack_1st([$1])):stack_drop2([$1])])
define([stack_div],[eval(stack_2nd([$1]) [/] stack_1st([$1])):stack_drop2([$1])])
define([stack_mod],[eval(stack_2nd([$1]) [%] stack_1st([$1])):stack_drop2([$1])])
define([prtc_1st],[print_char(stack_1st([$1]))])
define([prti_1st],[stack_1st([$1])])
define([prts_1st],[print_string(stack_1st([$1]))])
define([store],[define([_tmp1],index([$2],[$1:]))[]substr([$2],0,_tmp1)[$1:$3]define([_tmp2],substr([$2],eval(_tmp1 + len([$1]) [+ 1])))substr(_tmp2,index(_tmp2,[:]))])
define([fetch],[define([_tmp],substr([$2],eval(index([$2],[$1:]) [+] len([$1]) [+ 1])))[]substr(_tmp,0,index(_tmp,[:]))])
define([initial_vars],[var0:0:var1:0:var2:0:var3:0:var4:0:var5:0:var6:0:var7:0:var8:0:var9:0:var10:0:var11:0:var12:0:var13:0:var14:0:])
define([kont0],[kont5([420:$1],[$2])])
define([kont5],[kont6(stack_neg([$1]),[$2])])
define([kont6],[kont11(stack_drop([$1]),store([var0],[$2],stack_1st([$1])))])
define([kont11],[kont16([300:$1],[$2])])
define([kont16],[kont21(stack_drop([$1]),store([var1],[$2],stack_1st([$1])))])
define([kont21],[kont26([300:$1],[$2])])
define([kont26],[kont31(stack_drop([$1]),store([var2],[$2],stack_1st([$1])))])
define([kont31],[kont36([300:$1],[$2])])
define([kont36],[kont37(stack_neg([$1]),[$2])])
define([kont37],[kont42(stack_drop([$1]),store([var3],[$2],stack_1st([$1])))])
define([kont42],[kont47([7:$1],[$2])])
define([kont47],[kont52(stack_drop([$1]),store([var4],[$2],stack_1st([$1])))])
define([kont52],[kont57([15:$1],[$2])])
define([kont57],[kont62(stack_drop([$1]),store([var5],[$2],stack_1st([$1])))])
define([kont62],[kont67([200:$1],[$2])])
define([kont67],[kont72(stack_drop([$1]),store([var6],[$2],stack_1st([$1])))])
define([kont72],[kont77(fetch([var2],[$2])[:$1],[$2])])
define([kont77],[kont82(stack_drop([$1]),store([var7],[$2],stack_1st([$1])))])
define([kont82],[kont87(fetch([var7],[$2])[:$1],[$2])])
define([kont87],[kont92(fetch([var3],[$2])[:$1],[$2])])
define([kont92],[kont93(stack_gt([$1]),[$2])])
define([kont93],[ifelse(eval(stack_1st([$1]) [== 0]),1,[kont423(stack_drop([$1]),[$2])],[kont98(stack_drop([$1]),[$2])])])
define([kont98],[kont103(fetch([var0],[$2])[:$1],[$2])])
define([kont103],[kont108(stack_drop([$1]),store([var8],[$2],stack_1st([$1])))])
define([kont108],[kont113(fetch([var8],[$2])[:$1],[$2])])
define([kont113],[kont118(fetch([var1],[$2])[:$1],[$2])])
define([kont118],[kont119(stack_lt([$1]),[$2])])
define([kont119],[ifelse(eval(stack_1st([$1]) [== 0]),1,[kont396(stack_drop([$1]),[$2])],[kont124(stack_drop([$1]),[$2])])])
define([kont124],[kont129([0:$1],[$2])])
define([kont129],[kont134(stack_drop([$1]),store([var9],[$2],stack_1st([$1])))])
define([kont134],[kont139([0:$1],[$2])])
define([kont139],[kont144(stack_drop([$1]),store([var10],[$2],stack_1st([$1])))])
define([kont144],[kont149([32:$1],[$2])])
define([kont149],[kont154(stack_drop([$1]),store([var11],[$2],stack_1st([$1])))])
define([kont154],[kont159([0:$1],[$2])])
define([kont159],[kont164(stack_drop([$1]),store([var12],[$2],stack_1st([$1])))])
define([kont164],[kont169(fetch([var12],[$2])[:$1],[$2])])
define([kont169],[kont174(fetch([var6],[$2])[:$1],[$2])])
define([kont174],[kont175(stack_lt([$1]),[$2])])
define([kont175],[ifelse(eval(stack_1st([$1]) [== 0]),1,[kont369(stack_drop([$1]),[$2])],[kont180(stack_drop([$1]),[$2])])])
define([kont180],[kont185(fetch([var10],[$2])[:$1],[$2])])
define([kont185],[kont190(fetch([var10],[$2])[:$1],[$2])])
define([kont190],[kont191(stack_mul([$1]),[$2])])
define([kont191],[kont196([200:$1],[$2])])
define([kont196],[kont197(stack_div([$1]),[$2])])
define([kont197],[kont202(stack_drop([$1]),store([var13],[$2],stack_1st([$1])))])
define([kont202],[kont207(fetch([var9],[$2])[:$1],[$2])])
define([kont207],[kont212(fetch([var9],[$2])[:$1],[$2])])
define([kont212],[kont213(stack_mul([$1]),[$2])])
define([kont213],[kont218([200:$1],[$2])])
define([kont218],[kont219(stack_div([$1]),[$2])])
define([kont219],[kont224(stack_drop([$1]),store([var14],[$2],stack_1st([$1])))])
define([kont224],[kont229(fetch([var13],[$2])[:$1],[$2])])
define([kont229],[kont234(fetch([var14],[$2])[:$1],[$2])])
define([kont234],[kont235(stack_add([$1]),[$2])])
define([kont235],[kont240([800:$1],[$2])])
define([kont240],[kont241(stack_gt([$1]),[$2])])
define([kont241],[ifelse(eval(stack_1st([$1]) [== 0]),1,[kont298(stack_drop([$1]),[$2])],[kont246(stack_drop([$1]),[$2])])])
define([kont246],[kont251([48:$1],[$2])])
define([kont251],[kont256(fetch([var12],[$2])[:$1],[$2])])
define([kont256],[kont257(stack_add([$1]),[$2])])
define([kont257],[kont262(stack_drop([$1]),store([var11],[$2],stack_1st([$1])))])
define([kont262],[kont267(fetch([var12],[$2])[:$1],[$2])])
define([kont267],[kont272([9:$1],[$2])])
define([kont272],[kont273(stack_gt([$1]),[$2])])
define([kont273],[ifelse(eval(stack_1st([$1]) [== 0]),1,[kont288(stack_drop([$1]),[$2])],[kont278(stack_drop([$1]),[$2])])])
define([kont278],[kont283([64:$1],[$2])])
define([kont283],[kont288(stack_drop([$1]),store([var11],[$2],stack_1st([$1])))])
define([kont288],[kont293(fetch([var6],[$2])[:$1],[$2])])
define([kont293],[kont298(stack_drop([$1]),store([var12],[$2],stack_1st([$1])))])
define([kont298],[kont303(fetch([var10],[$2])[:$1],[$2])])
define([kont303],[kont308(fetch([var9],[$2])[:$1],[$2])])
define([kont308],[kont309(stack_mul([$1]),[$2])])
define([kont309],[kont314([100:$1],[$2])])
define([kont314],[kont315(stack_div([$1]),[$2])])
define([kont315],[kont320(fetch([var7],[$2])[:$1],[$2])])
define([kont320],[kont321(stack_add([$1]),[$2])])
define([kont321],[kont326(stack_drop([$1]),store([var9],[$2],stack_1st([$1])))])
define([kont326],[kont331(fetch([var13],[$2])[:$1],[$2])])
define([kont331],[kont336(fetch([var14],[$2])[:$1],[$2])])
define([kont336],[kont337(stack_sub([$1]),[$2])])
define([kont337],[kont342(fetch([var8],[$2])[:$1],[$2])])
define([kont342],[kont343(stack_add([$1]),[$2])])
define([kont343],[kont348(stack_drop([$1]),store([var10],[$2],stack_1st([$1])))])
define([kont348],[kont353(fetch([var12],[$2])[:$1],[$2])])
define([kont353],[kont358([1:$1],[$2])])
define([kont358],[kont359(stack_add([$1]),[$2])])
define([kont359],[kont364(stack_drop([$1]),store([var12],[$2],stack_1st([$1])))])
define([kont364],[kont164([$1],[$2])])
define([kont369],[kont374(fetch([var11],[$2])[:$1],[$2])])
define([kont374],[prtc_1st([$1])[]kont375(stack_drop([$1]),[$2])])
define([kont375],[kont380(fetch([var8],[$2])[:$1],[$2])])
define([kont380],[kont385(fetch([var4],[$2])[:$1],[$2])])
define([kont385],[kont386(stack_add([$1]),[$2])])
define([kont386],[kont391(stack_drop([$1]),store([var8],[$2],stack_1st([$1])))])
define([kont391],[kont108([$1],[$2])])
define([kont396],[kont401([10:$1],[$2])])
define([kont401],[prtc_1st([$1])[]kont402(stack_drop([$1]),[$2])])
define([kont402],[kont407(fetch([var7],[$2])[:$1],[$2])])
define([kont407],[kont412(fetch([var5],[$2])[:$1],[$2])])
define([kont412],[kont413(stack_sub([$1]),[$2])])
define([kont413],[kont418(stack_drop([$1]),store([var7],[$2],stack_1st([$1])))])
define([kont418],[kont82([$1],[$2])])
define([kont423],[])
divert[]dnl
kont0([stack-bottom],initial_vars)[]dnl
Output:
$ m4 mandel.m4
1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333222222222222222222222222222222222222222
1111111111111222222222233333333333333333333333344444456655544443333332222222222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
11111111111222222333333333333333333333334444444445555679@@@@7654444443333333222222222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98755544444433333332222222222222222222222222
1111111122223333333333333333333333344444444445556668@@@    @@@76555544444333333322222222222222222222222
1111111222233333333333333333333344444444455566667778@@      @987666555544433333333222222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@    @@@@@@877779@5443333333322222222222222222222
1111112233333333333333333334444455555556679@   @@@               @@@@@@ 8544333333333222222222222222222
1111122333333333333333334445555555556666789@@@                        @86554433333333322222222222222222
1111123333333333333444456666555556666778@@ @                         @@87655443333333332222222222222222
111123333333344444455568@887789@8777788@@@                            @@@@65444333333332222222222222222
111133334444444455555668@@@@@@@@@@@@99@@@                              @@765444333333333222222222222222
111133444444445555556778@@@         @@@@                                @855444333333333222222222222222
11124444444455555668@99@@             @                                 @655444433333333322222222222222
11134555556666677789@@                                                @86655444433333333322222222222222
111                                                                 @@876555444433333333322222222222222
11134555556666677789@@                                                @86655444433333333322222222222222
11124444444455555668@99@@             @                                 @655444433333333322222222222222
111133444444445555556778@@@         @@@@                                @855444333333333222222222222222
111133334444444455555668@@@@@@@@@@@@99@@@                              @@765444333333333222222222222222
111123333333344444455568@887789@8777788@@@                            @@@@65444333333332222222222222222
1111123333333333333444456666555556666778@@ @                         @@87655443333333332222222222222222
1111122333333333333333334445555555556666789@@@                        @86554433333333322222222222222222
1111112233333333333333333334444455555556679@   @@@               @@@@@@ 8544333333333222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@    @@@@@@877779@5443333333322222222222222222222
1111111222233333333333333333333344444444455566667778@@      @987666555544433333333222222222222222222222
1111111122223333333333333333333333344444444445556668@@@    @@@76555544444333333322222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98755544444433333332222222222222222222222222
11111111111222222333333333333333333333334444444445555679@@@@7654444443333333222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
1111111111111222222222233333333333333333333333344444456655544443333332222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333222222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211

The entry for ALGOL W also is based on Rosetta Code's "compiler" task suite.

Maple

ImageTools:-Embed(Fractals[EscapeTime]:-Mandelbrot(500, -2.0-1.35*I, .7+1.35*I, output = layer1));

Mathematica / Wolfram Language

The implementation could be better. But this is a start...

eTime[c_, maxIter_Integer: 100] := Length@NestWhileList[#^2 + c &, 0, Abs@# <= 2 &, 1, maxIter] - 1

DistributeDefinitions[eTime];
mesh = ParallelTable[eTime[x + I*y, 1000], {y, 1.2, -1.2, -0.01}, {x, -1.72, 1, 0.01}];
ReliefPlot[mesh, Frame -> False]

Faster version:

cf = With[{
      mandel = Block[{z = #, c = #}, 
        Catch@Do[If[Abs[z] > 2, Throw@i]; z = z^2 + c, {i, 100}]] &
    },
   Compile[{},Table[mandel[y + x I], {x, -1, 1, 0.005}, {y, -2, 0.5, 0.005}]]
  ];
ArrayPlot[cf[]]

Built-in function:

MandelbrotSetPlot[]

Mathmap

filter mandelbrot (gradient coloration)
   c=ri:(xy/xy:[X,X]*1.5-xy:[0.5,0]);
   z=ri:[0,0]; # initial value z0 = 0 
   # iteration of z
   iter=0;
   while abs(z)<2 && iter<31
   do
       z=z*z+c;  # z(n+1) = fc(zn)
       iter=iter+1
   end;
   coloration(iter/32) # color of pixel
end

MATLAB

This solution uses the escape time algorithm to determine the coloring of the coordinates on the complex plane. The code can be reduced to a single line via vectorization after the Escape Time Algorithm function definition, but the code becomes unnecessarily obfuscated. Also, this code uses a lot of memory. You will need a computer with a lot of memory to compute the set with high resolution.

function [theSet,realAxis,imaginaryAxis] = mandelbrotSet(start,gridSpacing,last,maxIteration)

    %Define the escape time algorithm
    function escapeTime = escapeTimeAlgorithm(z0)
        
        escapeTime = 0;
        z = 0;
        
        while( (abs(z)<=2) && (escapeTime < maxIteration) )
            z = (z + z0)^2;            
            escapeTime = escapeTime + 1;
        end
                
    end
    
    %Define the imaginary axis
    imaginaryAxis = (imag(start):imag(gridSpacing):imag(last));
    
    %Define the real axis
    realAxis = (real(start):real(gridSpacing):real(last));
    
    %Construct the complex plane from the real and imaginary axes
    complexPlane = meshgrid(realAxis,imaginaryAxis) + meshgrid(imaginaryAxis(end:-1:1),realAxis)'.*i;
    
    %Apply the escape time algorithm to each point in the complex plane 
    theSet = arrayfun(@escapeTimeAlgorithm, complexPlane);
    

    %Draw the set
    pcolor(realAxis,imaginaryAxis,theSet);
    shading flat;
    
end

To use this function you must specify the:

  1. lower left hand corner of the complex plane from which to start the image,
  2. the grid spacing in both the imaginary and real directions,
  3. the upper right hand corner of the complex plane at which to end the image and
  4. the maximum iterations for the escape time algorithm.

For example:

  1. Lower Left Corner: -2.05-1.2i
  2. Grid Spacing: 0.004+0.0004i
  3. Upper Right Corner: 0.45+1.2i
  4. Maximum Iterations: 500

Sample usage:

mandelbrotSet(-2.05-1.2i,0.004+0.0004i,0.45+1.2i,500);

Maxima

Using autoloded package plotdf

mandelbrot ([iterations, 30], [x, -2.4, 0.75], [y, -1.2, 1.2],
            [grid,320,320])$
File:MandelbrotMaxima.png

Metapost

prologues:=3;
outputtemplate:="%j-%c.svg";
outputformat:="svg";


def mandelbrot(expr maxX, maxY) =
  max_iteration := 500;

  color col[];
  for i := 0 upto max_iteration:
    t := i / max_iteration;
    col[i] = (t,t,t);
  endfor;
  

  for px := 0 upto maxX:
    for py := 0 upto maxY:
      xz := px * 3.5 / maxX - 2.5;  % (-2.5,1)
      yz := py * 2 / maxY - 1;      % (-1,1)

      x := 0;
      y := 0;

      iteration := 0;

      forever: exitunless ((x*x + y*y < 4) and (iteration < max_iteration));
        xtemp := x*x - y*y + xz;
        y := 2*x*y + yz;
        x := xtemp;
        iteration := iteration + 1;
      endfor;

      draw (px,py) withpen pencircle withcolor col[iteration];

    endfor;
  endfor;
enddef;


beginfig(1);
  mandelbrot(200, 150);
endfig;

end

Sample usage:

mpost -numbersystem="double" mandelbrot.mp

MiniScript

Works with: Mini Micro
ZOOM = 100
MAX_ITER = 40
gfx.clear color.black
for y in range(0,200)
	for x in range(0,300)
		zx = 0
		zy = 0
		cx = (x - 200) / ZOOM
		cy = (y - 100) / ZOOM
		for iter in range(MAX_ITER)
			if zx*zx + zy*zy > 4 then break
			tmp = zx * zx - zy * zy + cx
			zy = 2 * zx * zy + cy
			zx = tmp
		end for
		if iter then
			gfx.setPixel x, y, rgb(255-iter*6, 0, iter*6)
		end if
	end for
end for
Output:

Modula-3

MODULE Mandelbrot EXPORTS Main;

IMPORT Wr, Stdio, Fmt, Word;

CONST m = 50;
      limit2 = 4.0;

TYPE UByte = BITS 8 FOR [0..16_FF];

VAR width := 200;
    height := 200;
    bitnum: CARDINAL := 0;
    byteacc: UByte := 0;
    isOverLimit: BOOLEAN;
    Zr, Zi, Cr, Ci, Tr, Ti: REAL;

BEGIN
  
  Wr.PutText(Stdio.stdout, "P4\n" & Fmt.Int(width) & " " & Fmt.Int(height) & "\n");

  FOR y := 0 TO height - 1 DO
    FOR x := 0 TO width - 1 DO
      Zr := 0.0; Zi := 0.0;
      Cr := 2.0 * FLOAT(x) / FLOAT(width) - 1.5;
      Ci := 2.0 * FLOAT(y) / FLOAT(height) - 1.0;
      
      FOR i := 1 TO m + 1 DO
        Tr := Zr*Zr - Zi*Zi + Cr;
        Ti := 2.0*Zr*Zi + Ci;
        Zr := Tr; Zi := Ti;
        isOverLimit := Zr*Zr + Zi*Zi > limit2;
        IF isOverLimit THEN EXIT; END;
      END;
      
      IF isOverLimit THEN
        byteacc := Word.Xor(Word.LeftShift(byteacc, 1), 16_00);
      ELSE
        byteacc := Word.Xor(Word.LeftShift(byteacc, 1), 16_01);
      END;

      INC(bitnum);
      
      IF bitnum = 8 THEN
        Wr.PutChar(Stdio.stdout, VAL(byteacc, CHAR));
        byteacc := 0;
        bitnum := 0;
      ELSIF x = width - 1 THEN
        byteacc := Word.LeftShift(byteacc, 8 - (width MOD 8));
        Wr.PutChar(Stdio.stdout, VAL(byteacc, CHAR));
        byteacc := 0;
        bitnum := 0
      END;
      Wr.Flush(Stdio.stdout);
    END;
  END;
END Mandelbrot.

MySQL

See http://arbitraryscrawl.blogspot.co.uk/2012/06/fractsql.html for an explanation.

-- Table to contain all the data points
CREATE TABLE points (
  c_re DOUBLE,
  c_im DOUBLE,
  z_re DOUBLE DEFAULT 0,
  z_im DOUBLE DEFAULT 0,
  znew_re DOUBLE DEFAULT 0,
  znew_im DOUBLE DEFAULT 0,
  steps INT DEFAULT 0,
  active CHAR DEFAULT 1
);

DELIMITER |

-- Iterate over all the points in the table 'points'
CREATE PROCEDURE itrt (IN n INT)
BEGIN
  label: LOOP
    UPDATE points
      SET
        znew_re=POWER(z_re,2)-POWER(z_im,2)+c_re,
        znew_im=2*z_re*z_im+c_im,
        steps=steps+1
      WHERE active=1;
    UPDATE points SET
        z_re=znew_re,
        z_im=znew_im,
        active=IF(POWER(z_re,2)+POWER(z_im,2)>4,0,1)
      WHERE active=1;
    SET n = n - 1;
    IF n > 0 THEN
      ITERATE label;
    END IF;
    LEAVE label;
  END LOOP label;
END|

-- Populate the table 'points'
CREATE PROCEDURE populate (
  r_min DOUBLE,
  r_max DOUBLE,
  r_step DOUBLE,
  i_min DOUBLE,
  i_max DOUBLE,
  i_step DOUBLE)
BEGIN
  DELETE FROM points;
  SET @rl = r_min;
  SET @a = 0;
  rloop: LOOP
    SET @im = i_min;
    SET @b = 0;
    iloop: LOOP
      INSERT INTO points (c_re, c_im)
        VALUES (@rl, @im);
      SET @b=@b+1;
      SET @im=i_min + @b * i_step;
      IF @im < i_max THEN
        ITERATE iloop;
      END IF;
      LEAVE iloop;
    END LOOP iloop;
      SET @a=@a+1;
    SET @rl=r_min + @a * r_step;
    IF @rl < r_max THEN
      ITERATE rloop;
    END IF;
    LEAVE rloop;
  END LOOP rloop;
END|

DELIMITER ;

-- Choose size and resolution of graph
--             R_min, R_max, R_step, I_min, I_max, I_step
CALL populate( -2.5,  1.5,   0.005,  -2,    2,     0.005 );

-- Calculate 50 iterations
CALL itrt( 50 );

-- Create the image (/tmp/image.ppm)
-- Note, MySQL will not over-write an existing file and you may need
-- administrator access to delete or move it
SELECT @xmax:=COUNT(c_re) INTO @xmax FROM points GROUP BY c_im LIMIT 1;
SELECT @ymax:=COUNT(c_im) INTO @ymax FROM points GROUP BY c_re LIMIT 1;
SET group_concat_max_len=11*@xmax*@ymax;
SELECT
  'P3', @xmax, @ymax, 200,
  GROUP_CONCAT(
    CONCAT(
      IF( active=1, 0, 55+MOD(steps, 200) ), ' ',
      IF( active=1, 0, 55+MOD(POWER(steps,3), 200) ), ' ',
      IF( active=1, 0, 55+MOD(POWER(steps,2), 200) ) )
    ORDER BY c_im ASC, c_re ASC SEPARATOR ' ' )
    INTO OUTFILE '/tmp/image.ppm'
  FROM points;

Nim

Textual version

Translation of: Python
import complex

proc inMandelbrotSet(c: Complex, maxEscapeIterations = 50): bool =
  result = true; var z: Complex
  for i in 0..maxEscapeIterations:
    z = z * z + c
    if abs2(z) > 4: return false

iterator steps(start, step: float, numPixels: int): float =
  for i in 0..numPixels:
    yield start + i.float * step

proc mandelbrotImage(yStart, yStep, xStart, xStep: float, height, width: int): string =
  for y in steps(yStart, yStep, height):
    for x in steps(xStart, xStep, width):
      result.add(if complex(x, y).inMandelbrotSet: '*'
                 else: ' ')
    result.add('\n')

echo mandelbrotImage(1.0, -0.05, -2.0, 0.0315, 40, 80)
Output:
                                                           **                    
                                                         ******                  
                                                       ********                  
                                                         ******                  
                                                      ******** **   *            
                                              ***   *****************            
                                              ************************  ***      
                                              ****************************       
                                           ******************************        
                                            ******************************       
                                         ************************************    
                                *         **********************************     
                           ** ***** *     **********************************     
                           ***********   ************************************    
                         ************** ************************************     
                         ***************************************************     
                     *****************************************************       
************************************************************************         
                     *****************************************************       
                         ***************************************************     
                         ************** ************************************     
                           ***********   ************************************    
                           ** ***** *     **********************************     
                                *         **********************************     
                                         ************************************    
                                            ******************************       
                                           ******************************        
                                              ****************************       
                                              ************************  ***      
                                              ***   *****************            
                                                      ******** **   *            
                                                         ******                  
                                                       ********                  
                                                         ******                  
                                                           **                    

Graphical version

Translation of: Julia
Library: imageman
import math, complex, lenientops
import imageman

const
  W = 800
  H = 600
  Zoom = 0.5
  MoveX = -0.5
  MoveY = 0.0
  MaxIter = 30

func hsvToRgb(h, s, v: float): array[3, float] =
  let c = v * s
  let x = c * (1 - abs(((h / 60) mod 2) - 1))
  let m = v - c
  let (r, g, b) = if h < 60: (c, x, 0.0)
                  elif h < 120: (x, c, 0.0)
                  elif h < 180: (0.0, c, x)
                  elif h < 240: (0.0, x, c)
                  elif x < 300: (x, 0.0, c)
                  else: (c, 0.0, x)
  result = [r + m, g + m, b + m]


var img = initImage[ColorRGBF64](W, H)
for x in 1..W:
  for y in 1..H:
    var i = MaxIter - 1
    let c = complex((2 * x - W) / (W * Zoom) + MoveX, (2 * y - H) / (H * Zoom) + MoveY)
    var z = c
    while abs(z) < 2 and i > 0:
      z = z * z + c
      dec i
    let color = hsvToRgb(i / MaxIter * 360, 1, i / MaxIter)
    img[x - 1, y - 1] = ColorRGBF64(color)

img.savePNG("mandelbrot.png", compression = 9)

ObjectIcon

A simple interactive graphics program that can dump PNG images. An escape-time algorithm is used to set the opacity of black on white.

You can run it with oiscript the-file-name-you-gave-it.icn. Or you can compile it to an executable intermediate code with oit the-file-name-you-gave-it.icn and then run ./the-file-name-you-gave-it

# -*- ObjectIcon -*-

import graphics
import ipl.graphics
import io
import util(Math)

procedure main ()
  local w
  local width, height
  local xcenter, ycenter, pixels_per_unit, max_iter
  local zoom_ratio

  write ("q or Q       : quit")
  write ("left press   : recenter")
  write ("+            : zoom in")
  write ("-            : zoom in")
  write ("2 .. 9       : set zoom ratio")
  write ("o or O       : restore original")
  write ("p or P       : dump to a PNG")

  width := 400
  height := 400

  pixels_per_unit := 150
  max_iter := 200
  zoom_ratio := 2
  xcenter := -0.75
  ycenter := 0.0

  w := Window().
    set_size(width, height).
    set_resize(&yes).
    set_bg("white").
    set_canvas("normal") | stop(&why)

  event_loop (w, xcenter, ycenter, pixels_per_unit, max_iter,
              zoom_ratio)
end

procedure event_loop (w, xcenter, ycenter, pixels_per_unit,
                      max_iter, zoom_ratio)
  local event
  local xy
  local png_number, png_name
  local redraw
  local width, height
  local xleft, ytop
  local i, j
  local cx, cy, step
  local iter, color

  png_number := 1

  redraw := &yes
  repeat
  {
    if \redraw then
    {
      w.erase_area()

      step := 1.0 / pixels_per_unit

      width := w.get_width()
      height := w.get_height()

      xleft := xcenter - (width / (2.0 * pixels_per_unit))
      ytop := ycenter + (height / (2.0 * pixels_per_unit))

      cx := xleft
      cy := ytop

      j := 0
      i := 0

      redraw := &no
    }

    if j ~= height then
    {
      iter := count_mandelbrot_iterations (cx, cy, max_iter)
      color := map_iterations_to_color (max_iter, iter)
      w.set_fg (color)
      w.draw_point (i, j)
      i +:= 1;  cx +:= step
      if i = width then
      {
        i := 0;   cx := xleft
        j +:= 1;  cy -:= step
      }
    }

    if *w.pending() ~= 0 then
    {
      event := w.event()
      case event[1] of
      {
        QuitEvents():
          exit()

        Mouse.LEFT_PRESS:
        {
          xy := window_coords_to_point (w, event[2], event[3],
                                        xcenter, ycenter,
                                        pixels_per_unit)
          xcenter := xy[1]
          ycenter := xy[2]
          redraw := &yes
        }

        "+":
        {
          pixels_per_unit := zoom_ratio * pixels_per_unit
          redraw := &yes
        }

        "-":
        {
          pixels_per_unit :=
            max (1, (1.0 / zoom_ratio) * pixels_per_unit)
          redraw := &yes
        }

        !"23456789":
          zoom_ratio := integer(event[1])

        !"oO":
        {
          pixels_per_unit := 150
          max_iter := 200
          zoom_ratio := 2
          xcenter := -0.75
          ycenter := 0.0
          redraw := &yes
        }

        !"pP":
        {
          png_name := "mandelbrot-image-" || png_number || ".png"
          png_number +:= 1
          w.get_pixels().to_file(png_name)
          write ("Wrote ", png_name)
        }

        Window.RESIZE:
          redraw := &yes
      }

      WDelay(w, 100)
    }
  }
end

procedure count_mandelbrot_iterations (cx, cy, max_iter)
  local x, y, xsquared, ysquared, iter, tmp

  x := 0
  y := 0
  iter := 0
  until (iter = max_iter |
         4 < (xsquared := x * x) + (ysquared := y * y)) do
  {
    tmp := xsquared - ysquared + cx
    y := (2 * x * y) + cy
    x := tmp
    iter +:= 1
  }
  return iter
end

procedure map_iterations_to_color (max_iter, iter)
  return "black " ||
    integer((Math.log (iter) * 100.0) / Math.log (max_iter)) ||
    "%"
end

procedure window_coords_to_point (w, xcoord, ycoord,
                                  xcenter, ycenter,
                                  pixels_per_unit)
  local x, y

  x := xcenter +
    (((2.0 * xcoord) - w.get_width()) / (2.0 * pixels_per_unit))
  y := ycenter +
    ((w.get_height() - (2.0 * ycoord)) / (2.0 * pixels_per_unit))

  return [x, y]
end
Output:

An example of a dumped PNG:

A sample of seahorse valley from the Object Icon program.

OCaml

#load "graphics.cma";;

let mandelbrot xMin xMax yMin yMax xPixels yPixels maxIter =
  let rec mandelbrotIterator z c n =
    if (Complex.norm z) > 2.0 then false else
      match n with
      | 0 -> true
      | n -> let z' = Complex.add (Complex.mul z z) c in
             mandelbrotIterator z' c (n-1) in
  Graphics.open_graph
    (" "^(string_of_int xPixels)^"x"^(string_of_int yPixels));
  let dx = (xMax -. xMin) /. (float_of_int xPixels) 
  and dy = (yMax -. yMin) /. (float_of_int yPixels) in
  for xi = 0 to xPixels - 1 do
    for yi = 0 to yPixels - 1 do
      let c = {Complex.re = xMin +. (dx *. float_of_int xi);
               Complex.im = yMin +. (dy *. float_of_int yi)} in
      if (mandelbrotIterator Complex.zero c maxIter) then
        (Graphics.set_color Graphics.white;
         Graphics.plot xi yi )
      else
        (Graphics.set_color Graphics.black;
         Graphics.plot xi yi )
    done
  done;;
 
mandelbrot (-1.5) 0.5 (-1.0) 1.0 500 500 200;;

Octave

This code runs rather slowly and produces coloured Mandelbrot set by accident (output image).

#! /usr/bin/octave -qf
global width = 200;
global height = 200;
maxiter = 100;

z0 = 0;
global cmax = 1 + i;
global cmin = -2 - i;

function cs = pscale(c)
  global cmax;
  global cmin;
  global width;
  global height;
  persistent px = (real(cmax-cmin))/width;
  persistent py = (imag(cmax-cmin))/height;
  cs = real(cmin) + px*real(c) + i*(imag(cmin) + py*imag(c));
endfunction

ms = zeros(width, height);
for x = 0:width-1
  for y = 0:height-1
    z0 = 0;
    c = pscale(x+y*i);
    for ic = 1:maxiter
      z1 = z0^2 + c;
      if ( abs(z1) > 2 ) break; endif
      z0 = z1;
    endfor
    ms(x+1, y+1) = ic/maxiter;
  endfor
endfor

saveimage("mandel.ppm", round(ms .* 255).', "ppm");

A bit faster than the above implementation

function z = mandelbrot()
    % to view the image call "image(mandelbrot())"
    width = 500; height = 500;
    z = zeros(width, height);
    c = zeros(width, height);

    xi = 1;
    for x = linspace(-2, 2, width)
        yi = 1;
        for y = linspace(-2, 2, height)
            c(yi, xi) = x+y*i; yi += 1;
        end
        xi += 1;
    end

    for iter = 1:50
        z = z.*z + c;
    end

    z = abs(z);
end

Ol

(define x-size 59)
(define y-size 21)
(define min-im -1)
(define max-im 1)
(define min-re -2)
(define max-re 1)

(define step-x (/ (- max-re min-re) x-size))
(define step-y (/ (- max-im min-im) y-size))

(for-each (lambda (y)
      (let ((im (+ min-im (* step-y y))))
         (for-each (lambda (x)
            (let*((re (+ min-re (* step-x x)))
                  (zr (inexact re))
                  (zi (inexact im)))
               (let loop ((n 0) (zi zi) (zr zr))
                  (let ((a (* zr zr))
                        (b (* zi zi)))
                     (cond
                        ((> (+ a b) 4)
                           (display (string (- 62 n))))
                        ((= n 30)
                           (display (string (- 62 n))))
                        (else
                           (loop (+ n 1) (+ (* 2 zr zi) im) (- (+ a re) b))))))))
            (iota x-size))
         (print)))
   (iota y-size))

Output:

>>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<==========
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<=======
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<======
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<====
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<===
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<==
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<=
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<
><;;;;;;::::9875&      .3                       *9;;;<<<<<<
>;;;;;;::997564'        '                       8:;;;<<<<<<
>::988897735/                                 &89:;;;<<<<<<
>::988897735/                                 &89:;;;<<<<<<
>;;;;;;::997564'        '                       8:;;;<<<<<<
><;;;;;;::::9875&      .3                       *9;;;<<<<<<
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<=
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<==
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<===
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<====
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<=======

OpenEdge/Progress

DEFINE VARIABLE print_str AS CHAR NO-UNDO INIT ''.
DEFINE VARIABLE X1 AS DECIMAL NO-UNDO INIT 50.
DEFINE VARIABLE Y1 AS DECIMAL NO-UNDO INIT 21.
DEFINE VARIABLE X AS DECIMAL NO-UNDO.
DEFINE VARIABLE Y AS DECIMAL NO-UNDO.
DEFINE VARIABLE N AS DECIMAL NO-UNDO.
DEFINE VARIABLE I3 AS DECIMAL NO-UNDO.
DEFINE VARIABLE R3 AS DECIMAL NO-UNDO.
DEFINE VARIABLE Z1 AS DECIMAL NO-UNDO.
DEFINE VARIABLE Z2 AS DECIMAL NO-UNDO.
DEFINE VARIABLE A AS DECIMAL NO-UNDO.
DEFINE VARIABLE B AS DECIMAL NO-UNDO.
DEFINE VARIABLE I1 AS DECIMAL NO-UNDO INIT -1.0.
DEFINE VARIABLE I2 AS DECIMAL NO-UNDO INIT 1.0.
DEFINE VARIABLE R1 AS DECIMAL NO-UNDO INIT -2.0.
DEFINE VARIABLE R2 AS DECIMAL NO-UNDO INIT 1.0.
DEFINE VARIABLE S1 AS DECIMAL NO-UNDO.
DEFINE VARIABLE S2 AS DECIMAL NO-UNDO.


S1 = (R2 - R1) / X1.
S2 = (I2 - I1) / Y1.
DO Y = 0 TO Y1 - 1:
  I3 = I1 + S2 * Y.
  DO X = 0 TO X1 - 1:
    R3 = R1 + S1 * X.
    Z1 = R3.
    Z2 = I3.
    DO N = 0 TO 29:
      A = Z1 * Z1.
      B = Z2 * Z2.
      IF A + B > 4.0 THEN
        LEAVE.
      Z2 = 2 * Z1 * Z2 + I3.
      Z1 = A - B + R3.
    END.
    print_str = print_str + CHR(62 - N).
  END.
  print_str = print_str + '~n'.
END.

OUTPUT TO "C:\Temp\out.txt".
MESSAGE print_str.
OUTPUT CLOSE.
Example :

PARI/GP

Define function mandelbrot():

mandelbrot() = 
{
  forstep(y=-1, 1, 0.05, 
    forstep(x=-2, 0.5, 0.0315,
      print1(((c)->my(z=c);for(i=1,20,z=z*z+c;if(abs(z)>2,return(" ")));"#")(x+y*I)));
    print());
}
Output:
gp > mandelbrot()
                                                                                
                                                                                
                                                            #                   
                                                        #  ###  #               
                                                        ########                
                                                       #########                
                                                         ######                 
                                             ##    ## ############  #           
                                              ### ###################      #    
                                              #############################     
                                              ############################      
                                          ################################      
                                           ################################     
                                         #################################### # 
                          #     #        ###################################    
                          ###########    ###################################    
                           ###########   #####################################  
                         ############## ####################################    
                        ####################################################    
                     ######################################################     
#########################################################################       
                     ######################################################     
                        ####################################################    
                         ############## ####################################    
                           ###########   #####################################  
                          ###########    ###################################    
                          #     #        ###################################    
                                         #################################### # 
                                           ################################     
                                          ################################      
                                              ############################      
                                              #############################     
                                              ### ###################      #    
                                             ##    ## ############  #           
                                                         ######                 
                                                       #########                
                                                        ########                
                                                        #  ###  #               
                                                            #                   
                                                                                
                                                                                

Pascal

Translation of: C
program mandelbrot;
 
  {$IFDEF FPC}
      {$MODE DELPHI}  
  {$ENDIF}

const
   ixmax = 800;
   iymax = 800;
   cxmin = -2.5;
   cxmax =  1.5;
   cymin = -2.0;
   cymax =  2.0;
   maxcolorcomponentvalue = 255;
   maxiteration = 200;
   escaperadius = 2;
 
type
   colortype = record
      red   : byte;
      green : byte;
      blue  : byte;
   end;
 
var
   ix, iy      : integer;
   cx, cy      : real;
   pixelwidth  : real = (cxmax - cxmin) / ixmax;
   pixelheight : real = (cymax - cymin) / iymax;
   filename    : string = 'new1.ppm';
   comment     : string = '# ';
   outfile     : textfile;
   color       : colortype;
   zx, zy      : real;
   zx2, zy2    : real;
   iteration   : integer;
   er2         : real = (escaperadius * escaperadius);
 
begin
   {$I-}
   assign(outfile, filename);
   rewrite(outfile);
   if ioresult <> 0 then
   begin
      {$IFDEF FPC}
         writeln(stderr, 'Unable to open output file: ', filename);
      {$ELSE}
         writeln('ERROR: Unable to open output file: ', filename);
      {$ENDIF}      
      exit;
   end;
 
   writeln(outfile, 'P6');
   writeln(outfile, ' ', comment);
   writeln(outfile, ' ', ixmax);
   writeln(outfile, ' ', iymax);
   writeln(outfile, ' ', maxcolorcomponentvalue);
 
   for iy := 1 to iymax do
   begin
      cy := cymin + (iy - 1)*pixelheight;
      if abs(cy) < pixelheight / 2 then cy := 0.0;
      for ix := 1 to ixmax do
      begin
         cx := cxmin + (ix - 1)*pixelwidth;
         zx := 0.0;
         zy := 0.0;
         zx2 := zx*zx;
         zy2 := zy*zy;
         iteration := 0;
         while (iteration < maxiteration) and (zx2 + zy2 < er2) do
         begin
            zy := 2*zx*zy + cy;
            zx := zx2 - zy2 + cx;
            zx2 := zx*zx;
            zy2 := zy*zy;
            iteration := iteration + 1;
         end;
         if iteration = maxiteration then
         begin
            color.red   := 0;
            color.green := 0;
            color.blue  := 0;
         end
         else
         begin
            color.red   := 255;
            color.green := 255;
            color.blue  := 255;
         end;
         write(outfile, chr(color.red), chr(color.green), chr(color.blue));
      end;
   end;
 
   close(outfile);
end.

Peri

###sysinclude standard.uh
###sysinclude str.uh
###sysinclude system.uh
###sysinclude X.uh
$ff0000 sto szin
300 sto maxiter
maxypixel sto YRES
maxxpixel sto XRES
myscreen "Mandelbrot" @YRES @XRES graphic
#g
@YRES 2 / (#d) sto y2
@YRES 2 / (#d) sto x2
@XRES i: {{
@YRES {{
{{}}§i #g !(#d) 480. - @x2 - @x2 /
sto xx
{{}}   #g !(#d) @y2 - @y2 /
sto yy
zero#d xa zero#d ya zero iter

#d
ciklus:
@xa dup* @ya dup* - @xx +
@xa 2. * @ya * @yy + sto ya
sto xa ++()#g iter
@xa dup* @ya dup* + 4. > @iter @maxiter >=#g |#g then §ciklusvége
goto §ciklus
ciklusvége:
@iter @maxiter ==#g {
myscreen {{}} {{}}§i @szin setpixel
}{
myscreen {{}} {{}}§i @iter 64 *#g setpixel
}
}}
}}
myscreen 10000 key?
vége: myscreen inv graphic
//."A lenyomott billentyű: " kprintnl
end
{ „xx” }
{ „x2” }
{ „yy” }
{ „y2” }
{ „xa” }
{ „ya” }
{ „iter” }
{ „maxiter” }
{ „szin” }
{ „YRES” }
{ „XRES” }
{ „myscreen” }
Output:

Perl

translation / optimization of the ruby solution

use Math::Complex;

sub mandelbrot {
    my ($z, $c) = @_[0,0];
    for (1 .. 20) {
        $z = $z * $z + $c;
        return $_ if abs $z > 2;
    }
}

for (my $y = 1; $y >= -1; $y -= 0.05) {
    for (my $x = -2; $x <= 0.5; $x += 0.0315)
        {print mandelbrot($x + $y * i) ? ' ' : '#'}
    print "\n"
}

Phix

Ascii

This is included in the distribution (with some extra validation) as demo\mandle.exw

--
-- Mandlebrot set in ascii art demo.
-- 
constant b=" .:,;!/>)|&IH%*#"
atom r, i, c, C, z, Z, t, k
    for y=30 to 0 by -1 do
        C = y*0.1-1.5
        puts(1,'\n')
        for x=0 to 74 do
            c = x*0.04-2
            z = 0
            Z = 0
            r = c
            i = C
            k = 0
            while k<112 do
                t = z*z-Z*Z+r
                Z = 2*z*Z+i
                z = t
                if z*z+Z*Z>10 then exit end if
                k += 1
            end while
            puts(1,b[remainder(k,16)+1])
        end for
    end for
Graphical

This is included in the distribution as demo\arwendemo\mandel.exw

include arwen.ew
include ..\arwen\dib256.ew

constant HelpText = "Left-click drag with the mouse to move the image.\n"&
                    " (the image is currently only redrawn on mouseup).\n"&
                    "Right-click-drag with the mouse to select a region to zoom in to.\n"&
                    "Use the mousewheel to zoom in and out (nb: can be slow).\n"&
                    "Press F2 to select iterations, higher==more detail but slower.\n"&
                    "Resize the window as you please, but note that going fullscreen, \n"&
                    "especially at high iteration, may mean a quite long draw time.\n"&
                    "Press Escape to close the window."

procedure Help()
    void = messageBox("Mandelbrot Set",HelpText,MB_OK)
end procedure

integer cWidth = 520    -- client area width
integer cHeight = 480   -- client area height

constant Main = create(Window, "Mandelbrot Set", 0, 0, 50, 50, cWidth+16, cHeight+38, 0),
         mainHwnd = getHwnd(Main),
         mainDC = getPrivateDC(Main),

         mIter = create(Menu, "", 0, 0, 0,0,0,0,0),
         iterHwnd = getHwnd(mIter),
         mIter50 = create(MenuItem,"50 (fast, low detail)",     0, mIter, 0,0,0,0,0),
         mIter100 = create(MenuItem,"100 (default)",            0, mIter, 0,0,0,0,0),
         mIter500 = create(MenuItem,"500",                      0, mIter, 0,0,0,0,0),
         mIter1000 = create(MenuItem,"1000 (slow, high detail)",0, mIter, 0,0,0,0,0),
         m50to1000 = {mIter50,mIter100,mIter500,mIter1000},
         i50to1000 = {     50,     100,     500,     1000}
        
integer mainDib = 0

constant whitePen = c_func(xCreatePen, {0,1,BrightWhite})
constant NULL_BRUSH = 5,
         NullBrushID = c_func(xGetStockObject,{NULL_BRUSH})

atom t0
integer iter
atom x0, y0     -- top-left coords to draw
atom scale      -- controls width/zoom

procedure init()
    x0 = -2
    y0 = -1.25
    scale = 2.5/cHeight
    iter = 100
    void = c_func(xSelectObject,{mainDC,whitePen})
    void = c_func(xSelectObject,{mainDC,NullBrushID})
end procedure
init()

function in_set(atom x, atom y)
atom u,t
    if x>-0.75 then
        u = x-0.25
        t = u*u+y*y
        return ((2*t+u)*(2*t+u)>t)
    else
        return ((x+1)*(x+1)+y*y)>0.0625
    end if
end function

function pixel_colour(atom x0, atom y0, integer iter)
integer count = 1
atom x = 0, y = 0
    while (count<=iter) and (x*x+y*y<4) do
        count += 1
        {x,y} = {x*x-y*y+x0,2*x*y+y0}
    end while
    if count<=iter  then return count end if
    return 0
end function

procedure mandel(atom x0, atom y0, atom scale)
atom x,y
integer c   
    t0 = time()
    y = y0
    for yi=1 to cHeight do
        x = x0
        for xi=1 to cWidth do
            c = 0   -- default to black
            if in_set(x,y) then
                c = pixel_colour(x,y,iter)
            end if
            setDibPixel(mainDib, xi, yi, c)
            x += scale
        end for
        y += scale
    end for
end procedure

integer firsttime = 1
integer drawBox = 0
integer drawTime = 0

procedure newDib()
sequence pal

    if mainDib!=0 then
        {} = deleteDib(mainDib)
    end if
    mainDib = createDib(cWidth, cHeight)
    pal = repeat({0,0,0},256)
    for i=2 to 256 do
        pal[i][1] = i*5
        pal[i][2] = 0
        pal[i][3] = i*10
    end for
    setDibPalette(mainDib, 1, pal)
    mandel(x0,y0,scale)
    drawTime = 2
end procedure

procedure reDraw()
    setText(Main,"Please Wait...")
    mandel(x0,y0,scale)
    drawTime = 2
    repaintWindow(Main,False)
end procedure

procedure zoom(integer z)
    while z do
        if z>0 then
            scale /= 1.1
            z -= 1
        else
            scale *= 1.1
            z += 1
        end if
    end while
    reDraw()
end procedure

integer dx=0,dy=0   -- mouse down coords
integer mx=0,my=0   -- mouse move/up coords

function mainHandler(integer id, integer msg, atom wParam, object lParam)
integer x, y    -- scratch vars
atom scale10

    if msg=WM_SIZE then -- (also activate/firsttime)
        {{},{},x,y} = getClientRect(Main)
        if firsttime or cWidth!=x or cHeight!=y then
            scale *= cWidth/x
            {cWidth, cHeight} = {x,y}
            newDib()
            firsttime = 0
        end if
    elsif msg=WM_PAINT then
        copyDib(mainDC, 0, 0, mainDib)
        if drawBox then
            void = c_func(xRectangle, {mainDC, dx, dy, mx, my})
        end if
        if drawTime then
            if drawTime=2 then
                setText(Main,sprintf("Mandelbrot Set [generated in %gs]",time()-t0))
            else
                setText(Main,"Mandelbrot Set")
            end if
            drawTime -= 1
        end if
    elsif msg=WM_CHAR then
        if wParam=VK_ESCAPE then
            closeWindow(Main)
        elsif wParam='+' then zoom(+1)
        elsif wParam='-' then zoom(-1)
        end if
    elsif msg=WM_LBUTTONDOWN
       or msg=WM_RBUTTONDOWN then
        {dx,dy} = lParam
    elsif msg=WM_MOUSEMOVE then
        if and_bits(wParam,MK_LBUTTON) then
            {mx,my} = lParam
            -- minus dx,dy (see WM_LBUTTONUP)
            -- DEV maybe a timer to redraw, but probably too slow...
            --  (this is where we need a background worker thread,
            --   ideally one we can direct to abandon what it is
            --   currently doing and start work on new x,y instead)
        elsif and_bits(wParam,MK_RBUTTON) then
            {mx,my} = lParam
            drawBox = 1
            repaintWindow(Main,False)
        end if
    elsif msg=WM_MOUSEWHEEL then
        wParam = floor(wParam/#10000)
        if wParam>=#8000 then   -- sign bit set
            wParam-=#10000
        end if
        wParam = floor(wParam/120)  -- (gives +/-1, usually)
        zoom(wParam)
    elsif msg=WM_LBUTTONUP then
        {mx,my} = lParam
        drawBox = 0
        x0 += (dx-mx)*scale
        y0 += (dy-my)*scale
        reDraw()
    elsif msg=WM_RBUTTONUP then
        {mx,my} = lParam
        drawBox = 0
        if mx!=dx and my!=dy then
            x0 += min(mx,dx)*scale
            y0 += min(my,dy)*scale
            scale *= (abs(mx-dx))/cHeight
            reDraw()
        end if
    elsif msg=WM_KEYDOWN then
        if wParam=VK_F1 then
            Help()
        elsif wParam=VK_F2 then
            {x,y} = getWindowRect(Main)
            void = c_func(xTrackPopupMenu, {iterHwnd,TPM_LEFTALIGN,x+20,y+40,0,mainHwnd,NULL})
        elsif find(wParam,{VK_UP,VK_DOWN,VK_LEFT,VK_RIGHT}) then
            drawBox = 0
            scale10 = scale*10
            if wParam=VK_UP then
                y0 += scale10
            elsif wParam=VK_DOWN then
                y0 -= scale10
            elsif wParam=VK_LEFT then
                x0 += scale10
            elsif wParam=VK_RIGHT then
                x0 -= scale10
            end if
            reDraw()
        end if
    elsif msg=WM_COMMAND then
        id = find(id,m50to1000)
        if id!=0 then
            iter = i50to1000[id]
            reDraw()
        end if
    end if
    return 0
end function
setHandler({Main,mIter50,mIter100,mIter500,mIter1000}, routine_id("mainHandler"))

WinMain(Main,SW_NORMAL)
void = deleteDib(0)

PHP

Works with: PHP version 5.3.5
Sample output
$min_x=-2;
$max_x=1;
$min_y=-1;
$max_y=1;

$dim_x=400;
$dim_y=300;

$im = @imagecreate($dim_x, $dim_y)
  or die("Cannot Initialize new GD image stream");
header("Content-Type: image/png");
$black_color = imagecolorallocate($im, 0, 0, 0);
$white_color = imagecolorallocate($im, 255, 255, 255);

for($y=0;$y<=$dim_y;$y++) {
  for($x=0;$x<=$dim_x;$x++) {
    $c1=$min_x+($max_x-$min_x)/$dim_x*$x;
    $c2=$min_y+($max_y-$min_y)/$dim_y*$y;

    $z1=0;
    $z2=0;

    for($i=0;$i<100;$i++) {
      $new1=$z1*$z1-$z2*$z2+$c1;
      $new2=2*$z1*$z2+$c2;
      $z1=$new1;
      $z2=$new2;
      if($z1*$z1+$z2*$z2>=4) {
        break;
      }
    }
    if($i<100) {
      imagesetpixel ($im, $x, $y, $white_color);
    }
  }
}

imagepng($im);
imagedestroy($im);

Picat

Translation of: Unicon

Picat has not support for fancy graphics so it's plain 0/1 ASCII. Also, there's no built-in support for complex numbers.

go => 

   Width = 90,
   Height = 50,
   Limit = 50,
   foreach(Y in 1..Height)
      P="",
      foreach (X in 1..Width) 
         Z=complex(0,0),
         C=complex(2.5*X/Width-2.0,2.0*Y/Height-1.0),
         J = 0,
         while (J < Limit, c_abs(Z)<2.0) 
            Z := c_add(c_mul(Z,Z),C),
            J := J + 1
         end,
         if J == Limit then
             P := P ++ "#"
         else 
             P := P ++ "."
         end
      end,
      printf("%s\n", P)
  end,
  nl.

% Operations on complex numbers
complex(R,I) = [R,I].
c_add(X,Y) = complex(X[1]+Y[1],X[2]+Y[2]).
c_mul(X,Y) = complex(X[1]*Y[1]-X[2]*Y[2],X[1]*Y[2]+X[2]*Y[1]).
c_abs(X) = sqrt(X[1]*X[1]+X[2]*X[2]).
Output:
..........................................................................................
..........................................................................................
...................................................................##.....................
..................................................................##......................
...............................................................########...................
..............................................................#########...................
...............................................................#######....................
................................................................######....................
..........................................................#.#.############................
...................................................###..#####################.............
...................................................###########################..####......
.....................................................##############################.......
..................................................###############################.........
..............................................#.###################################.......
................................................####################################......
................................................####################################.#....
...............................................#######################################....
...............................#...##.........#######################################.....
.............................##########......#########################################....
..............................############...#########################################....
...........................################..#########################################....
...........................#################.########################################.....
...........................#################.#######################################......
.......................############################################################.......
#################################################################################.........
.......................############################################################.......
...........................#################.#######################################......
...........................#################.########################################.....
...........................################..#########################################....
..............................############...#########################################....
.............................##########......#########################################....
...............................#...##.........#######################################.....
...............................................#######################################....
................................................####################################.#....
................................................####################################......
..............................................#.###################################.......
..................................................###############################.........
.....................................................##############################.......
...................................................###########################..####......
...................................................###..#####################.............
..........................................................#.#.############................
................................................................######....................
...............................................................#######....................
..............................................................#########...................
...............................................................########...................
..................................................................##......................
...................................................................##.....................
..........................................................................................
..........................................................................................
.......................................................................#..................

PicoLisp

(scl 6)

(let Ppm (make (do 300 (link (need 400))))
   (for (Y . Row) Ppm
      (for (X . @) Row
         (let (ZX 0  ZY 0  CX (*/ (- X 250) 1.0 150)  CY (*/ (- Y 150) 1.0 150)  C 570)
            (while (and (> 4.0 (+ (*/ ZX ZX 1.0) (*/ ZY ZY 1.0))) (gt0 C))
               (let Tmp (- (*/ ZX ZX 1.0) (*/ ZY ZY 1.0) (- CX))
                  (setq
                     ZY (+ (*/ 2 ZX ZY 1.0) CY)
                     ZX Tmp ) )
               (dec 'C) )
            (set (nth Ppm Y X) (list 0 C C)) ) ) )
   (out "img.ppm"
      (prinl "P6")
      (prinl 400 " " 300)
      (prinl 255)
      (for Y Ppm (for X Y (apply wr X))) ) )

PostScript

%!PS-Adobe-2.0
%%BoundingBox: 0 0 300 200
%%EndComments
/origstate save def
/ld {load def} bind def
/m /moveto ld /g /setgray ld
/dot { currentpoint 1 0 360 arc fill } bind def
%%EndProlog
% param
/maxiter 200 def
% complex manipulation
/complex { 2 array astore } def
/real { 0 get } def
/imag { 1 get } def
/cmul { /a exch def /b exch def
    a real b real mul
    a imag b imag mul sub
    a real b imag mul
    a imag b real mul add
    2 array astore
} def
/cadd { aload pop 3 -1 roll aload pop
    3 -1 roll add
    3 1 roll add exch 2 array astore
} def
/cconj { aload pop neg 2 array astore } def
/cabs2 { dup cconj cmul 0 get} def
% mandel
200 100 translate
-200 1 100 { /x exch def
  -100 1 100 { /y exch def
    /z0 0.0 0.0 complex def
    0 1 maxiter { /iter exch def
	x 100 div y 100 div complex
	z0 z0 cmul
	cadd dup /z0 exch def
	cabs2 4 gt {exit} if
    } for
    iter maxiter div g
    x y m dot
  } for
} for
%
showpage
origstate restore
%%EOF

PowerShell

$x = $y = $i = $j = $r = -16
$colors = [Enum]::GetValues([System.ConsoleColor])

while(($y++) -lt 15)
{
    for($x=0; ($x++) -lt 84; Write-Host " " -BackgroundColor ($colors[$k -band 15]) -NoNewline)
    {
        $i = $k = $r = 0

        do
        {
            $j = $r * $r - $i * $i -2 + $x / 25
            $i = 2 * $r * $i + $y / 10
            $r = $j
        }
        while (($j * $j + $i * $i) -lt 11 -band ($k++) -lt 111)
    }

    Write-Host
}

Processing

Click on an area to zoom in. Choose areas with multiple colors for interesting zooming.

double x, y, zr, zi, zr2, zi2, cr, ci, n;
double zmx1, zmx2, zmy1, zmy2, f, di, dj;
double fn1, fn2, fn3, re, gr, bl, xt, yt, i, j;
 
void setup() {
  size(500, 500);
  di = 0;
  dj = 0;
  f = 10;
  fn1 = random(20); 
  fn2 = random(20); 
  fn3 = random(20);
  zmx1 = int(width / 4);
  zmx2 = 2;
  zmy1 = int(height / 4);
  zmy2 = 2;
}
 
void draw() {
  if (i <= width) i++;
  x =  (i +  di)/ zmx1 - zmx2;
  for ( j = 0; j <= height; j++) {
    y = zmy2 - (j + dj) / zmy1;
    zr = 0;
    zi = 0;
    zr2 = 0; 
    zi2 = 0; 
    cr = x;   
    ci = y;  
    n = 1;
    while (n < 200 && (zr2 + zi2) < 4) {
      zi2 = zi * zi;
      zr2 = zr * zr;
      zi = 2 * zi * zr + ci;
      zr = zr2 - zi2 + cr;
      n++;
    }  
    re = (n * fn1) % 255;
    gr = (n * fn2) % 255;
    bl = (n * fn3) % 255;
    stroke((float)re, (float)gr, (float)bl); 
    point((float)i, (float)j);
  }
}
 
void mousePressed() {
  background(200); 
  xt = mouseX;
  yt = mouseY;
  di = di + xt - float(width / 2);
  dj = dj + yt - float(height / 2);
  zmx1 = zmx1 * f;
  zmx2 = zmx2 * (1 / f);
  zmy1 = zmy1 * f;
  zmy2 = zmy2 * (1 / f);
  di = di * f;
  dj = dj * f;
  i = 0;
  j = 0;
}
The sketch can be run online :
here.

Processing Python mode

Click on an area to zoom in. Choose areas with multiple colors for interesting zooming.

i = di = dj = 0
fn1, fn2, fn3 = random(20), random(20), random(20)
f = 10
    
def setup():
    global zmx1, zmx2, zmy1, zmy2
    size(500, 500)
    zmx1 = int(width / 4)
    zmx2 = 2
    zmy1 = int(height / 4)
    zmy2 = 2


def draw():
    global i

    if i <= width:
        i += 1
    x = float(i + di) / zmx1 - zmx2
    for j in range(height + 1):
        y = zmy2 - float(j + dj) / zmy1
        zr = zi = zr2 = zi2 = 0
        cr, ci = x, y
        n = 1
        while n < 200 and (zr2 + zi2) < 4:
            zi2 = zi * zi
            zr2 = zr * zr
            zi = 2 * zi * zr + ci
            zr = zr2 - zi2 + cr
            n += 1

        re = (n * fn1) % 255
        gr = (n * fn2) % 255
        bl = (n * fn3) % 255
        stroke(re, gr, bl)
        point(i, j)


def mousePressed():
    global zmx1, zmx2, zmy1, zmy2, di, dj
    global i, j
    background(200)
    xt, yt = mouseX, mouseY
    di = di + xt - width / 2.
    dj = dj + yt - height / 2.
    zmx1 = zmx1 * f
    zmx2 = zmx2 * (1. / f)
    zmy1 = zmy1 * f
    zmy2 = zmy2 * (1. / f)
    di, dj = di * f, dj * f
    i = j = 0

Prolog

SWI-Prolog has a graphic interface XPCE :

:- use_module(library(pce)).

mandelbrot :-
    new(D, window('Mandelbrot Set')),
    send(D, size, size(700, 650)),
    new(Img, image(@nil, width := 700, height := 650, kind := pixmap)),

    forall(between(0,699, I),
           (   forall(between(0,649, J),
              (   get_RGB(I, J, R, G, B),
                  R1 is (R * 256) mod 65536,
                  G1 is (G * 256) mod 65536,
                  B1 is (B * 256) mod 65536,
                  send(Img, pixel(I, J, colour(@default, R1, G1, B1))))))),
    new(Bmp, bitmap(Img)),
    send(D, display, Bmp, point(0,0)),
    send(D, open).

get_RGB(X, Y, R, G, B) :-
    CX is (X - 350) / 150,
    CY is (Y - 325) / 150,
    Iter = 570,
    compute_RGB(CX, CY, 0, 0, Iter, It),
    IterF is It \/ It << 15,
    R is IterF >> 16,
    Iter1 is IterF - R << 16,
    G is Iter1 >> 8,
    B  is Iter1 - G << 8.

compute_RGB(CX, CY, ZX, ZY, Iter, IterF) :-
    ZX * ZX + ZY * ZY < 4,
    Iter > 0,
    !,
    Tmp is  ZX * ZX - ZY * ZY + CX,
    ZY1 is 2 * ZX * ZY + CY,
    Iter1 is Iter - 1,
    compute_RGB(CX, CY, Tmp, ZY1, Iter1, IterF).

compute_RGB(_CX, _CY, _ZX, _ZY, Iter, Iter).
Example :


Python

Translation of the ruby solution

# Python 3.0+ and 2.5+
try:
    from functools import reduce
except:
    pass


def mandelbrot(a):
    return reduce(lambda z, _: z * z + a, range(50), 0)

def step(start, step, iterations):
    return (start + (i * step) for i in range(iterations))

rows = (("*" if abs(mandelbrot(complex(x, y))) < 2 else " "
        for x in step(-2.0, .0315, 80))
        for y in step(1, -.05, 41))

print("\n".join("".join(row) for row in rows))

A more "Pythonic" version of the code:

import math

def mandelbrot(z , c , n=40):
    if abs(z) > 1000:
        return float("nan")
    elif n > 0:
        return mandelbrot(z ** 2 + c, c, n - 1) 
    else:
        return z ** 2 + c

print("\n".join(["".join(["#" if not math.isnan(mandelbrot(0, x + 1j * y).real) else " "
                 for x in [a * 0.02 for a in range(-80, 30)]]) 
                 for y in [a * 0.05 for a in range(-20, 20)]])
     )

Finally, we can also use Matplotlib to visualize the Mandelbrot set with Python:

Library: matplotlib
Library: NumPy
from pylab import *
from numpy import NaN

def m(a):
	z = 0
	for n in range(1, 100):
		z = z**2 + a
		if abs(z) > 2:
			return n
	return NaN

X = arange(-2, .5, .002)
Y = arange(-1,  1, .002)
Z = zeros((len(Y), len(X)))

for iy, y in enumerate(Y):
	print (iy, "of", len(Y))
	for ix, x in enumerate(X):
		Z[iy,ix] = m(x + 1j * y)

imshow(Z, cmap = plt.cm.prism, interpolation = 'none', extent = (X.min(), X.max(), Y.min(), Y.max()))
xlabel("Re(c)")
ylabel("Im(c)")
savefig("mandelbrot_python.svg")
show()

Another Numpy version using masks to avoid (explicit) nested loops. Runs about 16x faster for the same resolution.

import matplotlib.pyplot as plt
import numpy as np

npts = 300
max_iter = 100

X = np.linspace(-2, 1, 2 * npts)
Y = np.linspace(-1, 1, npts)

#broadcast X to a square array
C = X[:, None] + 1J * Y
#initial value is always zero
Z = np.zeros_like(C)

exit_times = max_iter * np.ones(C.shape, np.int32)
mask = exit_times > 0

for k in range(max_iter):
    Z[mask] = Z[mask] * Z[mask] + C[mask]
    mask, old_mask = abs(Z) < 2, mask
    #use XOR to detect the area which has changed 
    exit_times[mask ^ old_mask] = k

plt.imshow(exit_times.T,
           cmap=plt.cm.prism,
           extent=(X.min(), X.max(), Y.min(), Y.max()))
plt.show()

Normal Map Effect, Mercator Projection and Deep Zoom Images

Normalization, Distance Estimation and Boundary Detection

The Mandelbrot set is printed with smooth colors. The e^(-|z|)-smoothing, normalized iteration count and exterior distance estimation algorithms are used with NumPy and complex matrices (see Javier Barrallo & Damien M. Jones: Coloring Algorithms for Dynamical Systems in the Complex Plane and Arnaud Chéritat: Boundary detection methods via distance estimators). Partial antialiasing is used for boundary detection.

import numpy as np
import matplotlib.pyplot as plt

d, h = 800, 500  # pixel density (= image width) and image height
n, r = 200, 500  # number of iterations and escape radius (r > 2)

x = np.linspace(0, 2, num=d+1)
y = np.linspace(0, 2 * h / d, num=h+1)

A, B = np.meshgrid(x - 1, y - h / d)
C = 2.0 * (A + B * 1j) - 0.5

Z, dZ = np.zeros_like(C), np.zeros_like(C)
D, S, T = np.zeros(C.shape), np.zeros(C.shape), np.zeros(C.shape)

for k in range(n):
    M = abs(Z) < r
    S[M], T[M] = S[M] + np.exp(- abs(Z[M])), T[M] + 1
    Z[M], dZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1

plt.imshow(S ** 0.1, cmap=plt.cm.twilight_shifted, origin="lower")
plt.savefig("Mandelbrot_set_1.png", dpi=200)

N = abs(Z) >= r  # normalized iteration count
T[N] = T[N] - np.log2(np.log(np.abs(Z[N])) / np.log(r))

plt.imshow(T ** 0.1, cmap=plt.cm.twilight_shifted, origin="lower")
plt.savefig("Mandelbrot_set_2.png", dpi=200)

N = abs(Z) > 2  # exterior distance estimation
D[N] = np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N])

plt.imshow(D ** 0.1, cmap=plt.cm.twilight_shifted, origin="lower")
plt.savefig("Mandelbrot_set_3.png", dpi=200)

N, thickness = D > 0, 0.01  # boundary detection
D[N] = np.maximum(1 - D[N] / thickness, 0)

plt.imshow(D ** 2.0, cmap=plt.cm.binary, origin="lower")
plt.savefig("Mandelbrot_set_4.png", dpi=200)

Normal Map Effect and Stripe Average Coloring

The Mandelbrot set is represented using Normal Maps and Stripe Average Coloring by Jussi Härkönen (cf. Arnaud Chéritat: Normal map effect). Note that the second derivative (ddZ) grows very fast, so the second method can only be used for small iteration numbers (n <= 400). See also the picture in section Mixing it all and Julia Stripes on Shadertoy. To get a stripe pattern similar to that of Arnaud Chéritat, one can increase the density of the stripes, use cos instead of sin, and set the colormap to binary.

import numpy as np
import matplotlib.pyplot as plt

d, h = 800, 500  # pixel density (= image width) and image height
n, r = 200, 500  # number of iterations and escape radius (r > 2)

direction, height = 45.0, 1.5  # direction and height of the light
density, intensity = 4.0, 0.5  # density and intensity of the stripes

x = np.linspace(0, 2, num=d+1)
y = np.linspace(0, 2 * h / d, num=h+1)

A, B = np.meshgrid(x - 1, y - h / d)
C = (2.0 + 1.0j) * (A + B * 1j) - 0.5

Z, dZ, ddZ = np.zeros_like(C), np.zeros_like(C), np.zeros_like(C)
D, S, T = np.zeros(C.shape), np.zeros(C.shape), np.zeros(C.shape)

for k in range(n):
    M = abs(Z) < r
    S[M], T[M] = S[M] + np.sin(density * np.angle(Z[M])), T[M] + 1
    Z[M], dZ[M], ddZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1, 2 * (dZ[M] ** 2 + Z[M] * ddZ[M])

N = abs(Z) >= r  # basic normal map effect and stripe average coloring (potential function)
P, Q = S[N] / T[N], (S[N] + np.sin(density * np.angle(Z[N]))) / (T[N] + 1)
U, V = Z[N] / dZ[N], 1 + (np.log2(np.log(np.abs(Z[N])) / np.log(r)) * (P - Q) + Q) * intensity
U, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j)  # unit normal vectors and light vector
D[N] = np.maximum((U.real * v.real + U.imag * v.imag + V * height) / (1 + height), 0)

plt.imshow(D ** 1.0, cmap=plt.cm.bone, origin="lower")
plt.savefig("Mandelbrot_normal_map_1.png", dpi=200)

N = abs(Z) > 2  # advanced normal map effect using higher derivatives (distance estimation)
U = Z[N] * dZ[N] * ((1 + np.log(abs(Z[N]))) * np.conj(dZ[N] ** 2) - np.log(abs(Z[N])) * np.conj(Z[N] * ddZ[N]))
U, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j)  # unit normal vectors and light vector
D[N] = np.maximum((U.real * v.real + U.imag * v.imag + height) / (1 + height), 0)

plt.imshow(D ** 1.0, cmap=plt.cm.afmhot, origin="lower")
plt.savefig("Mandelbrot_normal_map_2.png", dpi=200)

Mercator Mandelbrot Maps and Zoom Images

A small change in the code above creates Mercator maps of the Mandelbrot set (see David Madore: Mandelbrot set images and videos and Anders Sandberg: Mercator Mandelbrot Maps). The maximum magnification is about , which is also the maximum for 64-bit arithmetic. Note that Anders Sandberg uses a different scaling. He uses instead of , so his images appear somewhat compressed in comparison (but not much, because ). With the same pixel density and the same maximum magnification, the difference in height between the maps is only about 10 percent. By misusing a scatter plot, it is possible to create zoom images of the Mandelbrot set. See also Mandelbrot sequence new on Wikimedia for a zoom animation to the given coordinates.

import numpy as np
import matplotlib.pyplot as plt

d, h = 200, 1200  # pixel density (= image width) and image height
n, r = 8000, 10000  # number of iterations and escape radius (r > 2)

a = -.743643887037158704752191506114774  # https://mathr.co.uk/web/m-location-analysis.html
b = 0.131825904205311970493132056385139  # try: a, b, n = -1.748764520194788535, 3e-13, 800

x = np.linspace(0, 2, num=d+1)
y = np.linspace(0, 2 * h / d, num=h+1)

A, B = np.meshgrid(x * np.pi, y * np.pi)
C = 8.0 * np.exp((A + B * 1j) * 1j) + (a + b * 1j)

Z, dZ = np.zeros_like(C), np.zeros_like(C)
D = np.zeros(C.shape)

for k in range(n):
    M = Z.real ** 2 + Z.imag ** 2 < r ** 2
    Z[M], dZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1

N = abs(Z) > 2  # exterior distance estimation
D[N] = np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N])

plt.imshow(D.T ** 0.05, cmap=plt.cm.nipy_spectral, origin="lower")
plt.savefig("Mercator_Mandelbrot_map.png", dpi=200)

X, Y = C.real, C.imag  # zoom images (adjust circle size 100 and zoom level 20 as needed)
R, c, z = 100 * (2 / d) * np.pi * np.exp(- B), min(d, h) + 1, max(0, h - d) // 20

fig, ax = plt.subplots(2, 2, figsize=(12, 12))
ax[0,0].scatter(X[1*z:1*z+c,0:d], Y[1*z:1*z+c,0:d], s=R[0:c,0:d]**2, c=D[1*z:1*z+c,0:d]**.5, cmap=plt.cm.nipy_spectral)
ax[0,1].scatter(X[2*z:2*z+c,0:d], Y[2*z:2*z+c,0:d], s=R[0:c,0:d]**2, c=D[2*z:2*z+c,0:d]**.4, cmap=plt.cm.nipy_spectral)
ax[1,0].scatter(X[3*z:3*z+c,0:d], Y[3*z:3*z+c,0:d], s=R[0:c,0:d]**2, c=D[3*z:3*z+c,0:d]**.3, cmap=plt.cm.nipy_spectral)
ax[1,1].scatter(X[4*z:4*z+c,0:d], Y[4*z:4*z+c,0:d], s=R[0:c,0:d]**2, c=D[4*z:4*z+c,0:d]**.2, cmap=plt.cm.nipy_spectral)
plt.savefig("Mercator_Mandelbrot_zoom.png", dpi=100)

Perturbation Theory and Deep Mercator Maps

For deep zoom images it is sufficient to calculate a single point with high accuracy. A good approximation can then be found for all other points by means of a perturbation calculation with standard accuracy. Rebasing is used to reduce glitches. See Perturbation theory (Wikipedia) and Avoiding loss of precision (Fractalshades) for details. See also the image Deeper Mercator Mandelbrot by Anders Sandberg.

import numpy as np
import matplotlib.pyplot as plt

import decimal as dc  # decimal floating point arithmetic with arbitrary precision
dc.getcontext().prec = 80  # set precision to 80 digits (about 256 bits)

d, h = 50, 1000  # pixel density (= image width) and image height
n, r = 80000, 100000  # number of iterations and escape radius (r > 2)

a = dc.Decimal("-1.256827152259138864846434197797294538253477389787308085590211144291")
b = dc.Decimal(".37933802890364143684096784819544060002129071484943239316486643285025")

S = np.zeros(n+1, dtype=np.complex128)
u, v = dc.Decimal(0), dc.Decimal(0)

for k in range(n+1):
    S[k] = float(u) + float(v) * 1j
    if u ** 2 + v ** 2 < r ** 2:
        u, v = u ** 2 - v ** 2 + a, 2 * u * v + b
    else:
        print("The reference sequence diverges within %s iterations." % k)
        break

x = np.linspace(0, 2, num=d+1, dtype=np.float64)
y = np.linspace(0, 2 * h / d, num=h+1, dtype=np.float64)

A, B = np.meshgrid(x * np.pi, y * np.pi)
C = 8.0 * np.exp((A + B * 1j) * 1j)

E, Z, dZ = np.zeros_like(C), np.zeros_like(C), np.zeros_like(C)
D, I, J = np.zeros(C.shape), np.zeros(C.shape, dtype=np.int64), np.zeros(C.shape, dtype=np.int64)

for k in range(n):
    Z2 = Z.real ** 2 + Z.imag ** 2
    M, R = Z2 < r ** 2, Z2 < E.real ** 2 + E.imag ** 2
    E[R], I[R] = Z[R], J[R]  # rebase when z is closer to zero
    E[M], I[M] = (2 * S[I[M]] + E[M]) * E[M] + C[M], I[M] + 1
    Z[M], dZ[M] = S[I[M]] + E[M], 2 * Z[M] * dZ[M] + 1

N = abs(Z) > 2  # exterior distance estimation
D[N] = np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N])

plt.imshow(D.T ** 0.015, cmap=plt.cm.nipy_spectral, origin="lower")
plt.savefig("Mercator_Mandelbrot_deep_map.png", dpi=200)

You can only rebase to the beginning of the reference sequence. If you want to change from current reference point to reference point , the difference must be calculated. With this subtraction, however, the entire precision is lost due to catastrophic cancellation. Only at the first reference point there is no cancellation because . Therefore, the rebasing condition can also be written as or as . This keeps the differences to the reference sequence as small as possible: rebasing occurs when the distance to reference point is smaller than the distance to the current reference point .

Python - "One liner"

print(
'\n'.join(
    ''.join(
        ' *'[(z:=0, c:=x/50+y/50j, [z:=z*z+c for _ in range(99)], abs(z))[-1]<2]
        for x in range(-100,25)
    )
    for y in range(-50,50)
))

Python - "Functional"

Based on the "One liner" approach.

from functools import reduce

def mandelbrot(x, y, c): return ' *'[abs(reduce(lambda z, _: z*z + c, range(99), 0)) < 2]

print('\n'.join(''.join(mandelbrot(x, y, x/50 + y/50j) for x in range(-100, 25)) for y in range(-50, 50)))

q

/adapted from https://www.linkedin.com/pulse/want-work-k-1010data-michal-wallace
q)s:{(.[-]x*x),2*prd x}            / complex square (x is R,Im pair)
q)m:{floor sqrt sum x*x}           / magnitude (distance from origin)
q)d: 120 60                        / dimensions of the picture
q)t: -88 -30                       / camera translation
q)f: reciprocal 40 20              / scale factor

q)c: (,/:\:) . f * t + til each d  / complex plane near mandelbrot set
q)z: d # enlist 0 0                / 3d array of zeroes in same shape
q)mb: c+ (s'')@					   / mandelbrot: s(z) + c
q)r: 1 _ 8 mb\z                    / collect 8 times

q)o: " 12345678"@ sum 2<m'''[r]    / "color" by how soon point "escapes"

q)-1 "\n"sv flip o;                / transpose and print the output
555555555555555555555556666666666666665555555555555555555555555555555555555555555555555555555555555666666666666666666666
555555555555555555556666666666666555555555555555555555555555555555555555555555555555555555555555555555556666666666666666
555555555555555556666666666666555555555555555555555555555555555555555555555555555555555555555555555555555556666666666666
555555555555555666666666665555555555555555555555555555555555555555555556666666666666666666555555555555555555555666666666
555555555555666666666666555555555555555555555555555555555555555556666666666666666666666666666665555555555555555556666666
555555555566666666666555555555555555555555555555555555555555566666666555555555555555555555566666665555555555555555556666
555555556666666666655555555555555555555555555555555555556666666655555555555555555555555555555555666665555555555555555566
555555666666666655555555555555555555555555555555555566666666555555555555555554444444444555555555555666665555555555555555
55556666666666555555555555555555555555555555555566666666555555555555555555444432  13344444555555555555666655555555555555
556666666666655555555555555555555555555555555666666665555555555555555554444443321  1222234445555555555556666655555555555
666666666665555555555555555555555555555556666666665555555555555555555444444433321        3344455555555555566666555555555
666666666555555555555555555555555555556666666665555555555555555555544444443332211       22334444455555555555666655555555
666666665555555555555555555555555566666666665555555555555555555544444444333321          12233444444555555555566666555555
6666665555555555555555555555555666666666665555555555555555555444444443333322              123334444444555555555666655555
6666655555555555555555555555666666666665555555555555555554444444433333332221               22333344444445555555566666555
666655555555555555555555566666666666555555555555555554444444443333322222211                11223333333444455555556666655
666555555555555555555556666666666555555555555555544444444444332111   111                      11222222 23444555555666665
665555555555555555556666666666555555555555555444444444444333321                                   11    2334455555566666
655555555555555555666666665555555555555544444444444444433333221                                          134445555556666
555555555555555566666665555555555555544444444444444433333332211                                          234444555555666
555555555555556666655555555555555444444444444333333333332221                                            1233444555555566
55555555555566665555555555555544444332233333333333322222211                                             1223344455555566
5555555555666555555555555554444443331  1122222111122222111                                                 2344455555556
5555555566655555555555555444444433321                1                                                      344455555556
5555555666555555555555544444444333221                                                                     12334455555555
5555566655555555555554444444433332221                                                                      2344445555555
555566655555555555444444443333322111                                                                      12344445555555
5556665555555554444443333333221                                                                           23344445555555
556666555544444443333333322221                                                                           233344445555555
55666555444333322 122111111                                                                            12233444445555555
55666555                                                                                               12233444445555555
55666555444333322 122111111                                                                            12233444445555555
556666555544444443333333322221                                                                           233344445555555
5556665555555554444443333333221                                                                           23344445555555
555566655555555555444444443333322111                                                                      12344445555555
5555566655555555555554444444433332221                                                                      2344445555555
5555555666555555555555544444444333221                                                                     12334455555555
5555555566655555555555555444444433321                1                                                      344455555556
5555555555666555555555555554444443331  1122222111122222111                                                 2344455555556
55555555555566665555555555555544444332233333333333322222211                                             1223344455555566
555555555555556666655555555555555444444444444333333333332221                                            1233444555555566
555555555555555566666665555555555555544444444444444433333332211                                          234444555555666
655555555555555555666666665555555555555544444444444444433333221                                          134445555556666
665555555555555555556666666666555555555555555444444444444333321                                   11    2334455555566666
666555555555555555555556666666666555555555555555544444444444332111   111                      11222222 23444555555666665
666655555555555555555555566666666666555555555555555554444444443333322222211                11223333333444455555556666655
6666655555555555555555555555666666666665555555555555555554444444433333332221               22333344444445555555566666555
6666665555555555555555555555555666666666665555555555555555555444444443333322              123334444444555555555666655555
666666665555555555555555555555555566666666665555555555555555555544444444333321          12233444444555555555566666555555
666666666555555555555555555555555555556666666665555555555555555555544444443332211       22334444455555555555666655555555
666666666665555555555555555555555555555556666666665555555555555555555444444433321        3344455555555555566666555555555
556666666666655555555555555555555555555555555666666665555555555555555554444443321  1222234445555555555556666655555555555
55556666666666555555555555555555555555555555555566666666555555555555555555444432  13344444555555555555666655555555555555
555555666666666655555555555555555555555555555555555566666666555555555555555554444444444555555555555666665555555555555555
555555556666666666655555555555555555555555555555555555556666666655555555555555555555555555555555666665555555555555555566
555555555566666666666555555555555555555555555555555555555555566666666555555555555555555555566666665555555555555555556666
555555555555666666666666555555555555555555555555555555555555555556666666666666666666666666666665555555555555555556666666
555555555555555666666666665555555555555555555555555555555555555555555556666666666666666666555555555555555555555666666666
555555555555555556666666666666555555555555555555555555555555555555555555555555555555555555555555555555555556666666666666
555555555555555555556666666666666555555555555555555555555555555555555555555555555555555555555555555555556666666666666666

R

iterate.until.escape <- function(z, c, trans, cond, max=50, response=dwell) {
  #we iterate all active points in the same array operation,
  #and keeping track of which points are still iterating.
  active <- seq_along(z)
  dwell <- z
  dwell[] <- 0
  for (i in 1:max) {
    z[active] <- trans(z[active], c[active]);
    survived <- cond(z[active])
    dwell[active[!survived]] <- i
    active <- active[survived]
    if (length(active) == 0) break
  }
  eval(substitute(response))
}

re = seq(-2, 1, len=500)
im = seq(-1.5, 1.5, len=500)
c <- outer(re, im, function(x,y) complex(real=x, imaginary=y))
x <- iterate.until.escape(array(0, dim(c)), c,
                          function(z,c)z^2+c, function(z)abs(z) <= 2,
                          max=100)
image(x)

Mandelbrot Set with R Animation

Modified Mandelbrot set animation by Jarek Tuszynski, PhD. (see: Wikipedia: R (programming_language) and R Tricks: Mandelbrot Set with R Animation)

#install.packages("caTools") # install external package (if missing)
library(caTools)             # external package providing write.gif function
jet.colors <- colorRampPalette(c("red", "blue", "#007FFF", "cyan", "#7FFF7F",
                                 "yellow", "#FF7F00", "red", "#7F0000"))
dx <- 800                    # define width
dy <- 600                    # define height
C  <- complex(real = rep(seq(-2.5, 1.5, length.out = dx), each = dy),
              imag = rep(seq(-1.5, 1.5, length.out = dy), dx))
C <- matrix(C, dy, dx)       # reshape as square matrix of complex numbers
Z <- 0                       # initialize Z to zero
X <- array(0, c(dy, dx, 20)) # initialize output 3D array
for (k in 1:20) {            # loop with 20 iterations
  Z <- Z^2 + C               # the central difference equation
  X[, , k] <- exp(-abs(Z))   # capture results
}
write.gif(X, "Mandelbrot.gif", col = jet.colors, delay = 100)

Racket

#lang racket

(require racket/draw)

(define (iterations a z i)
  (define z′ (+ (* z z) a))
  (if (or (= i 255) (> (magnitude z′) 2))
      i
      (iterations a z′ (add1 i))))

(define (iter->color i)
  (if (= i 255)
      (make-object color% "black")
      (make-object color% (* 5 (modulo i 15)) (* 32 (modulo i 7)) (* 8 (modulo i 31)))))

(define (mandelbrot width height)
  (define target (make-bitmap width height))
  (define dc (new bitmap-dc% [bitmap target]))
  (for* ([x width] [y height])
    (define real-x (- (* 3.0 (/ x width)) 2.25))
    (define real-y (- (* 2.5 (/ y height)) 1.25))
    (send dc set-pen (iter->color (iterations (make-rectangular real-x real-y) 0 0)) 1 'solid)
    (send dc draw-point x y))
  (send target save-file "mandelbrot.png" 'png))

(mandelbrot 300 200)

Raku

(formerly Perl 6)

Works with: rakudo version 2023.08-3-g2f8234c22

Using the hyper statement prefix for concurrency, the code below produces a graymap to standard output.

File:Mandelbrot-raku.jpg
constant MAX-ITERATIONS = 64;
my $width = +(@*ARGS[0] // 800);
my $height = $width + $width %% 2;
say "P2";
say "$width $height";
say MAX-ITERATIONS;

sub cut(Range $r, UInt $n where $n > 1 --> Seq) {
    $r.min, * + ($r.max - $r.min) / ($n - 1) ... $r.max
}

my @re = cut(-2 .. 1/2, $width);
my @im = cut( 0 .. 5/4, 1 + ($height div 2)) X* 1i;
 
sub mandelbrot(Complex $z is copy, Complex $c --> Int) {
    for 1 .. MAX-ITERATIONS {
        $z = $z*$z + $c;
        return $_ if $z.abs > 2;
    }
    return 0;
}
 
my @lines = hyper for @im X+ @re {
  mandelbrot(0i, $_);
}.rotor($width);

.put for @lines[1..*].reverse;
.put for @lines;


REXX

version 1

Translation of: AWK

This REXX version doesn't depend on the ASCII sequence of glyphs;   an internal character string was used that mimics a part of the ASCII glyph sequence.

/*REXX program  generates and displays a Mandelbrot set as an ASCII art character image.*/
@ = '>=<;:9876543210/.-,+*)(''&%$#"!'            /*the characters used in the display.  */
Xsize = 59;  minRE = -2;  maxRE = +1;     stepX = (maxRE-minRE) / Xsize
Ysize = 21;  minIM = -1;  maxIM = +1;     stepY = (maxIM-minIM) / Ysize

  do y=0  for ysize;      im=minIM + stepY*y
  $=
        do x=0  for Xsize;   re=minRE + stepX*x;    zr=re;    zi=im

            do n=0  for 30;  a=zr**2;   b=zi**2;    if a+b>4  then leave
            zi=zr*zi*2 + im;            zr=a-b+re
            end   /*n*/

        $=$ || substr(@, n+1, 1)                 /*append number (as a char) to $ string*/
        end       /*x*/
  say $                                          /*display a line of  character  output.*/
  end             /*y*/                          /*stick a fork in it,  we're all done. */

output   using the internal defaults:

>>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<==========
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<=======
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<======
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<====
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<===
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<==
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<=
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<
><;;;;;;::::9875&      .3                       *9;;;<<<<<<
>;;;;;;::997564'        '                       8:;;;<<<<<<
>::988897735/                                 &89:;;;<<<<<<
>::988897735/                                 &89:;;;<<<<<<
>;;;;;;::997564'        '                       8:;;;<<<<<<
><;;;;;;::::9875&      .3                       *9;;;<<<<<<
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<=
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<==
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<===
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<====
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<=======

version 2

This REXX version uses glyphs that are "darker" (with a white background) around the output's peripheral.

/*REXX program  generates and displays a Mandelbrot set as an ASCII art character image.*/
@ = '█▓▒░@9876543210=.-,+*)(·&%$#"!'             /*the characters used in the display.  */
Xsize = 59;  minRE = -2;  maxRE = +1;     stepX = (maxRE-minRE) / Xsize
Ysize = 21;  minIM = -1;  maxIM = +1;     stepY = (maxIM-minIM) / Ysize

  do y=0  for ysize;      im=minIM + stepY*y
  $=
        do x=0  for Xsize;   re=minRE + stepX*x;    zr=re;    zi=im

            do n=0  for 30;  a=zr**2;   b=zi**2;    if a+b>4  then leave
            zi=zr*zi*2 + im;            zr=a-b+re
            end   /*n*/

        $=$ || substr(@, n+1, 1)                 /*append number (as a char) to $ string*/
        end       /*x*/
  say $                                          /*display a line of  character  output.*/
  end             /*y*/                          /*stick a fork in it,  we're all done. */

output   using the internal defaults:

██████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@@@96032@░░░░▒▒▒▒▓▓▓▓▓▓▓▓▓▓
█████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@@873*079@@░░░░▒▒▒▒▒▓▓▓▓▓▓▓
████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@9974    (.9@@@@░░▒▒▒▒▒▓▓▓▓▓▓
███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@98888764     5789999@░░▒▒▒▒▒▓▓▓▓
██▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░@@@@996. &2           45335@░▒▒▒▒▒▒▓▓▓
██▓▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@999752                 *79@░▒▒▒▒▒▒▓▓
█▓▒▒▒▒▒▒▒▒░░░@599999999886                    %78@░░▒▒▒▒▒▒▓
█▒▒▒▒░░░░░@@@972456-567763                      +9░░▒▒▒▒▒▒▒
█▒░░░░░░@@@@9875&      .3                       *9░░░▒▒▒▒▒▒
█░░░░░░@@997564·        ·                       8@░░░▒▒▒▒▒▒
█@@988897735=                                 &89@░░░▒▒▒▒▒▒
█@@988897735=                                 &89@░░░▒▒▒▒▒▒
█░░░░░░@@997564·        ·                       8@░░░▒▒▒▒▒▒
█▒░░░░░░@@@@9875&      .3                       *9░░░▒▒▒▒▒▒
█▒▒▒▒░░░░░@@@972456-567763                      +9░░▒▒▒▒▒▒▒
█▓▒▒▒▒▒▒▒▒░░░@599999999886                    %78@░░▒▒▒▒▒▒▓
██▓▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@999752                 *79@░▒▒▒▒▒▒▓▓
██▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░@@@@996. &2           45335@░▒▒▒▒▒▒▓▓▓
███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@98888764     5789999@░░▒▒▒▒▒▓▓▓▓
████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@9974    (.9@@@@░░▒▒▒▒▒▓▓▓▓▓▓
█████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@@873*079@@░░░░▒▒▒▒▒▓▓▓▓▓▓▓

version 3

This REXX version produces a larger output   (it uses the full width of the terminal screen (less one),   and the height is one-half of the width.

/*REXX program  generates and displays a Mandelbrot set as an ASCII art character image.*/
@ = '█▓▒░@9876543210=.-,+*)(·&%$#"!'             /*the characters used in the display.  */
parse arg Xsize Ysize .                          /*obtain optional arguments from the CL*/
if Xsize==''  then Xsize=linesize() - 1          /*X:  the (usable) linesize  (minus 1).*/
if Ysize==''  then Ysize=Xsize%2 + (Xsize//2==1) /*Y:  half the linesize (make it even).*/
minRE = -2;     maxRE = +1;       stepX = (maxRE-minRE) / Xsize
minIM = -1;     maxIM = +1;       stepY = (maxIM-minIM) / Ysize

  do y=0  for ysize;      im=minIM + stepY*y
  $=
        do x=0  for Xsize;   re=minRE + stepX*x;    zr=re;    zi=im

            do n=0  for 30;  a=zr**2;   b=zi**2;    if a+b>4  then leave
            zi=zr*zi*2 + im;            zr=a-b+re
            end   /*n*/

        $=$ || substr(@, n+1, 1)                 /*append number (as a char) to $ string*/
        end       /*x*/
  say $                                          /*display a line of  character  output.*/
  end             /*y*/                          /*stick a fork in it,  we're all done. */

output   using the internal defaults:

████████▓▓▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░@@@@985164(9@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓▓▓▓
███████▓▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@@@98763=5799@░░░░░░▒▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓▓
███████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@@98763.-2789@@@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓
██████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@@985 2.  1448@@@@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓
█████▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@999874      *=79@@@@@░░░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓▓
█████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@999998873       17899@@@@@░░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓
████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@98888888764      #4678899999@@░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓
████▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@@@9343,665 322=     =215357888709@░░▒▒▒▒▒▒▒▒▓▓▓▓▓
███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@@@@@9986  + 32               ,56554)79@░▒▒▒▒▒▒▒▒▒▓▓▓▓
███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░@@@@@@@999863   +                  2· ",59@░░▒▒▒▒▒▒▒▒▓▓▓▓
███▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@@@@@9998763                      $   379@@░▒▒▒▒▒▒▒▒▒▓▓▓
██▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@@@@@999986.2 $                        +689@@░░▒▒▒▒▒▒▒▒▒▓▓
██▓▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@689999@@@99999887                             05789@░░▒▒▒▒▒▒▒▒▒▓▓
██▒▒▒▒▒▒▒▒▒▒░░░░░@@9717888877888888763.                            2558@░░░▒▒▒▒▒▒▒▒▒▓
█▓▒▒▒▒▒▒░░░░░░░@@@996)566761467777762                                 4@░░░▒▒▒▒▒▒▒▒▒▓
█▓▒▒▒▒░░░░░░░░@@@@99763 & 42&..366651·                              .68@░░░░▒▒▒▒▒▒▒▒▓
█▒▒▒░░░░░░░░@@@@@@98864*  )   $  343                                259@░░░░▒▒▒▒▒▒▒▒▒
█▒▒░░░░░░░░@@@@@@988753.          11                                 #9@░░░░▒▒▒▒▒▒▒▒▒
█▒░░░░░░░░@@@@@9877650             -                                289@░░░░▒▒▒▒▒▒▒▒▒
█░░░░░░░░@9999887%413+             %                               &69@@░░░░▒▒▒▒▒▒▒▒▒
█░@@@@@89999888763 % (                                             389@@░░░░▒▒▒▒▒▒▒▒▒
█@@99872676676422                                                 5789@@░░░░▒▒▒▒▒▒▒▒▒
█@@99872676676422                                                 5789@@░░░░▒▒▒▒▒▒▒▒▒
█░@@@@@89999888763 % (                                             389@@░░░░▒▒▒▒▒▒▒▒▒
█░░░░░░░░@9999887%413+             %                               &69@@░░░░▒▒▒▒▒▒▒▒▒
█▒░░░░░░░░@@@@@9877650             -                                289@░░░░▒▒▒▒▒▒▒▒▒
█▒▒░░░░░░░░@@@@@@988753.          11                                 #9@░░░░▒▒▒▒▒▒▒▒▒
█▒▒▒░░░░░░░░@@@@@@98864*  )   $  343                                259@░░░░▒▒▒▒▒▒▒▒▒
█▓▒▒▒▒░░░░░░░░@@@@99763 & 42&..366651·                              .68@░░░░▒▒▒▒▒▒▒▒▓
█▓▒▒▒▒▒▒░░░░░░░@@@996)566761467777762                                 4@░░░▒▒▒▒▒▒▒▒▒▓
██▒▒▒▒▒▒▒▒▒▒░░░░░@@9717888877888888763.                            2558@░░░▒▒▒▒▒▒▒▒▒▓
██▓▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@689999@@@99999887                             05789@░░▒▒▒▒▒▒▒▒▒▓▓
██▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@@@@@999986.2 $                        +689@@░░▒▒▒▒▒▒▒▒▒▓▓
███▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@@@@@9998763                      $   379@@░▒▒▒▒▒▒▒▒▒▓▓▓
███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░@@@@@@@999863   +                  2· ",59@░░▒▒▒▒▒▒▒▒▓▓▓▓
███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@@@@@9986  + 32               ,56554)79@░▒▒▒▒▒▒▒▒▒▓▓▓▓
████▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@@@9343,665 322=     =215357888709@░░▒▒▒▒▒▒▒▒▓▓▓▓▓
████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@98888888764      #4678899999@@░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓
█████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@999998873       17899@@@@@░░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓
█████▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@999874      *=79@@@@@░░░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓▓
██████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@@985 2.  1448@@@@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓
███████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@@98763.-2789@@@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓
███████▓▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@@@98763=5799@░░░░░░▒▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓▓

This REXX program makes use of   linesize   REXX program (or BIF) which is used to determine the screen width (or linesize) of the terminal (console).

The   LINESIZE.REX   REXX program is included here   ──►   LINESIZE.REX.

Ring

load "guilib.ring"

new qapp 
        {
        win1 = new qwidget() {
               setwindowtitle("Mandelbrot set")
               setgeometry(100,100,500,500)
               label1 = new qlabel(win1) {
                        setgeometry(10,10,400,400)
                        settext("")
               }
               new qpushbutton(win1) {
                   setgeometry(200,400,100,30)
                   settext("draw")
                   setclickevent("draw()")
               }
               show()
         }
         exec()
         }

func draw
        p1 = new qpicture()
             color = new qcolor() {
             setrgb(0,0,255,255)
        }
        pen = new qpen() {
              setcolor(color)
              setwidth(1)
        }
        new qpainter() {
            begin(p1)
            setpen(pen)

        x1=300 y1=250
        i1=-1 i2=1 r1=-2 r2=1
        s1=(r2-r1)/x1 s2=(i2-i1)/y1
        for y=0 to y1
            i3=i1+s2*y
            for x=0 to x1
                r3=r1+s1*x z1=r3 z2=i3
                for n=0 to 30
                    a=z1*z1 b=z2*z2
                    if a+b>4 exit ok
                       z2=2*z1*z2+i3 z1=a-b+r3
                next
                if n != 31 drawpoint(x,y) ok
            next 
        next

        endpaint()
        }
        label1 { setpicture(p1) show() }

Output:

Ruby

Text only, prints an 80-char by 41-line depiction. Found here.

require 'complex'

def mandelbrot(a)
  Array.new(50).inject(0) { |z,c| z*z + a }
end

(1.0).step(-1,-0.05) do |y|
  (-2.0).step(0.5,0.0315) do |x|
    print mandelbrot(Complex(x,y)).abs < 2 ? '*' : ' '
  end
  puts
end
Translation of: Tcl

Uses Raster graphics operations/Ruby

# frozen_string_literal: true

require_relative 'raster_graphics'

class RGBColour
  def self.mandel_colour(i)
    self.new( 16*(i % 15), 32*(i % 7), 8*(i % 31) )
  end
end

class Pixmap
  def self.mandelbrot(width, height)
    mandel = Pixmap.new(width,height)
    pb = ProgressBar.new(width) if $DEBUG
    width.times do |x|
      height.times do |y|
        x_ish = Float(x - width*11/15) / (width/3)
        y_ish = Float(y - height/2) / (height*3/10)
        mandel[x,y] = RGBColour.mandel_colour(mandel_iters(x_ish, y_ish))
      end
      pb.update(x) if $DEBUG
    end
    pb.close if $DEBUG
    mandel
  end

  def self.mandel_iters(cx,cy)
    x = y = 0.0
    count = 0
    while Math.hypot(x,y) < 2 and count < 255
      x, y = (x**2 - y**2 + cx), (2*x*y + cy)
      count += 1
    end
    count
  end
end

Pixmap.mandelbrot(300,300).save('mandel.ppm')
Library: RubyGems
Library: JRubyArt

JRubyArt is a port of processing to ruby

# frozen_string_literal: true

def setup
  sketch_title 'Mandelbrot'
  load_pixels
  no_loop
end

def draw
  grid(900, 600) do |x, y|
    const = Complex(
      map1d(x, (0...900), (-3..1.5)), map1d(y, (0...600), (-1.5..1.5))
    )
    pixels[x + y * 900] = color(
      constrained_map(mandel(const, 20), (5..20), (255..0))
    )
  end
  update_pixels
end

def mandel(z, max)
  score = 0
  const = z
  while score < max
    # z = z^2 + c
    z *= z
    z += const
    break if z.abs > 2

    score += 1
  end
  score
end

def settings
  size(900, 600)
end

Rust

Dependencies: image, num-complex

extern crate image;
extern crate num_complex;

use num_complex::Complex;

fn main() {
    let max_iterations = 256u16;
    let img_side = 800u32;
    let cxmin = -2f32;
    let cxmax = 1f32;
    let cymin = -1.5f32;
    let cymax = 1.5f32;
    let scalex = (cxmax - cxmin) / img_side as f32;
    let scaley = (cymax - cymin) / img_side as f32;

    // Create a new ImgBuf
    let mut imgbuf = image::ImageBuffer::new(img_side, img_side);

    // Calculate for each pixel
    for (x, y, pixel) in imgbuf.enumerate_pixels_mut() {
        let cx = cxmin + x as f32 * scalex;
        let cy = cymin + y as f32 * scaley;

        let c = Complex::new(cx, cy);
        let mut z = Complex::new(0f32, 0f32);

        let mut i = 0;
        for t in 0..max_iterations {
            if z.norm() > 2.0 {
                break;
            }
            z = z * z + c;
            i = t;
        }

        *pixel = image::Luma([i as u8]);
    }

    // Save image
    imgbuf.save("fractal.png").unwrap();
}

Sass/SCSS

$canvasWidth: 200;
$canvasHeight: 200;
$iterations: 20;
$xCorner: -2;
$yCorner: -1.5;
$zoom: 3;
$data: ()!global;
@mixin plot ($x,$y,$count){
  $index: ($y * $canvasWidth + $x) * 4;
  $r: $count * -12 + 255;
  $g: $count * -12 + 255;
  $b: $count * -12 + 255;
  $data: append($data, $x + px $y + px 0 rgb($r,$g,$b), comma)!global;
}

@for $x from 1 to $canvasWidth {
    @for $y from 1 to $canvasHeight {
      $count: 0;
      $size: 0;
      $cx: $xCorner + (($x * $zoom) / $canvasWidth);
      $cy: $yCorner + (($y * $zoom) / $canvasHeight);

      $zx: 0;
      $zy: 0;

      @while $count < $iterations and $size <= 4  {
        $count: $count + 1;
        $temp:  ($zx * $zx) - ($zy * $zy);
        $zy:  (2 * $zx * $zy) + $cy;
        $zx:  $temp + $cx;
        $size:  ($zx * $zx) + ($zy * $zy);
      }

      @include plot($x, $y, $count); 
    }
}
.set {
  height: 1px;
  width: 1px;
  position: absolute;
  top: 50%;
  left: 50%;
  transform: translate($canvasWidth*0.5px, $canvasWidth*0.5px);
  box-shadow: $data;
}

Scala

Works with: Scala version 2.8

Uses RgbBitmap from Basic Bitmap Storage task and Complex number class from this programming task.

import org.rosettacode.ArithmeticComplex._
import java.awt.Color

object Mandelbrot
{
   def generate(width:Int =600, height:Int =400)={
      val bm=new RgbBitmap(width, height)

      val maxIter=1000
      val xMin = -2.0
      val xMax =  1.0
      val yMin = -1.0
      val yMax =  1.0

      val cx=(xMax-xMin)/width
      val cy=(yMax-yMin)/height

      for(y <- 0 until bm.height; x <- 0 until bm.width){
         val c=Complex(xMin+x*cx, yMin+y*cy)
         val iter=itMandel(c, maxIter, 4)
         bm.setPixel(x, y, getColor(iter, maxIter))
      }
      bm
   }

   def itMandel(c:Complex, imax:Int, bailout:Int):Int={
      var z=Complex()
      for(i <- 0 until imax){
         z=z*z+c;
         if(z.abs > bailout) return i
      }
      imax;
   }

   def getColor(iter:Int, max:Int):Color={
      if (iter==max) return Color.BLACK

      var c=3*math.log(iter)/math.log(max-1.0)
      if(c<1) new Color((255*c).toInt, 0, 0)
      else if(c<2) new Color(255, (255*(c-1)).toInt, 0)
      else new Color(255, 255, (255*(c-2)).toInt)
   }
}

Read–eval–print loop

import scala.swing._
import javax.swing.ImageIcon
val imgMandel=Mandelbrot.generate()
val mainframe=new MainFrame(){title="Test"; visible=true
   contents=new Label(){icon=new ImageIcon(imgMandel.image)}
}

Scheme

A simple implementation for many Scheme implementations

This implementation writes an image of the Mandelbrot set to a plain pgm file. The set itself is drawn in white, while the exterior is drawn in black.

(define x-centre -0.5)
(define y-centre 0.0)
(define width 4.0)
(define i-max 800)
(define j-max 600)
(define n 100)
(define r-max 2.0)
(define file "out.pgm")
(define colour-max 255)
(define pixel-size (/ width i-max))
(define x-offset (- x-centre (* 0.5 pixel-size (+ i-max 1))))
(define y-offset (+ y-centre (* 0.5 pixel-size (+ j-max 1))))

(define (inside? z)
  (define (*inside? z-0 z n)
    (and (< (magnitude z) r-max)
         (or (= n 0)
             (*inside? z-0 (+ (* z z) z-0) (- n 1)))))
  (*inside? z 0 n))

(define (boolean->integer b)
  (if b colour-max 0))

(define (pixel i j)
  (boolean->integer
    (inside?
      (make-rectangular (+ x-offset (* pixel-size i))
                        (- y-offset (* pixel-size j))))))

(define (plot)
  (with-output-to-file file
    (lambda ()
      (begin (display "P2") (newline)
             (display i-max) (newline)
             (display j-max) (newline)
             (display colour-max) (newline)
             (do ((j 1 (+ j 1))) ((> j j-max))
                 (do ((i 1 (+ i 1))) ((> i i-max))
                     (begin (display (pixel i j)) (newline))))))))

(plot)

An interactive program for CHICKEN Scheme

Translation of: ObjectIcon
Works with: CHICKEN Scheme version 5.3.0

You will need several CHICKEN "eggs", which can be deduced from the imports.

Compile with (for example) csc -O3 mandelbrot_task_CHICKEN.scm.

;; A program written for CHICKEN Scheme version 5.3.0 and various
;; eggs.

(import (r7rs))
(import (scheme base))
(import (scheme case-lambda))
(import (scheme inexact))

(import (prefix sdl2 "sdl2:"))
(import (prefix imlib2 "imlib2:"))

(import (format))
(import (matchable))
(import (simple-exceptions))

(define sdl2-subsystems-used '(events video))

;; ------------------------------
;; Basics for using the sdl2 egg:
(sdl2:set-main-ready!)
(sdl2:init! sdl2-subsystems-used)
(on-exit sdl2:quit!)
(current-exception-handler
 (let ((original-handler (current-exception-handler)))
   (lambda (exception)
     (sdl2:quit!)
     (original-handler exception))))
;; ------------------------------

(define-record-type <mandel-params>
  (%%make-mandel-params)
  mandel-params?
  (window ref-window set-window!)
  (xcenter ref-xcenter set-xcenter!)
  (ycenter ref-ycenter set-ycenter!)
  (pixels-per-unit ref-pixels-per-unit set-pixels-per-unit!)
  (pixels-per-event-check ref-pixels-per-event-check
                          set-pixels-per-event-check!)
  (max-escape-time ref-max-escape-time set-max-escape-time!))

(define initial-width                   400)
(define initial-height                  400)
(define initial-xcenter                -3/4)
(define initial-ycenter                 0)
(define initial-pixels-per-unit         150)
(define initial-pixels-per-event-check  1000)
(define initial-max-escape-time         1000)

(define (make-mandel-params window)
  (let ((params (%%make-mandel-params)))
    (set-window! params window)
    (set-xcenter! params initial-xcenter)
    (set-ycenter! params initial-ycenter)
    (set-pixels-per-unit! params initial-pixels-per-unit)
    (set-pixels-per-event-check! params
                                 initial-pixels-per-event-check)
    (set-max-escape-time! params initial-max-escape-time)
    params))

(define window (sdl2:create-window! "mandelbrot set task"
                                    'centered 'centered
                                    initial-width initial-height
                                    '()))
(define params (make-mandel-params window))

(define empty-color (sdl2:make-color 200 200 200))

(define (clear-mandel!)
  (sdl2:fill-rect! (sdl2:window-surface (ref-window params))
                   #f empty-color)
  (sdl2:update-window-surface! window))

(define drawing? #t)
(define redraw? #f)

(define (draw-mandel! event-checker)
  (clear-mandel!)
  (let repeat ()
    (let*-values
        (((window) (ref-window params))
         ((width height) (sdl2:window-size window)))
      (let* ((xcenter (ref-xcenter params))
             (ycenter (ref-ycenter params))
             (pixels-per-unit (ref-pixels-per-unit params))
             (pixels-per-event-check
              (ref-pixels-per-event-check params))
             (max-escape-time (ref-max-escape-time params))
             (step (/ 1.0 pixels-per-unit))
             (xleft (- xcenter (/ width (* 2.0 pixels-per-unit))))
             (ytop (+ ycenter (/ height (* 2.0 pixels-per-unit))))
             (pixel-count 0))
        (do ((j 0 (+ j 1))
             (cy ytop (- cy step)))
            ((= j height))
          (do ((i 0 (+ i 1))
               (cx xleft (+ cx step)))
              ((= i width))
            (let* ((color (compute-color-by-escape-time-algorithm
                           cx cy max-escape-time)))
              (sdl2:surface-set! (sdl2:window-surface window)
                                 i j color)
              (if (= pixel-count pixels-per-event-check)
                  (let ((event-checker (call/cc event-checker)))
                    (cond (redraw?
                           (set! redraw? #f)
                           (clear-mandel!)
                           (repeat)))
                    (set! pixel-count 0))
                  (set! pixel-count (+ pixel-count 1)))))
          ;; Display a row.
          (sdl2:update-window-surface! window))))
    (set! drawing? #f)
    (repeat)))  

(define (compute-color-by-escape-time-algorithm
         cx cy max-escape-time)
  (escape-time->color (compute-escape-time cx cy max-escape-time)
                      max-escape-time))

(define (compute-escape-time cx cy max-escape-time)
  (let loop ((x 0.0)
             (y 0.0)
             (iter 0))
    (if (= iter max-escape-time)
        iter
        (let ((xsquared (* x x))
              (ysquared (* y y)))
          (if (< 4 (+ xsquared ysquared))
              iter
              (let ((x (+ cx (- xsquared ysquared)))
                    (y (+ cy (* (+ x x) y))))
                (loop x y (+ iter 1))))))))

(define (escape-time->color escape-time max-escape-time)
  ;; This is a very naive and ad hoc algorithm for choosing colors,
  ;; but hopefully will suffice for the task. With this algorithm, at
  ;; least one can zoom in and see some of the fractal-like structures
  ;; out on the filaments.
  (let* ((initial-ppu initial-pixels-per-unit)
         (ppu (ref-pixels-per-unit params))
         (fraction (* (/ (log escape-time) (log max-escape-time))))
         (fraction (if (= fraction 1.0)
                       fraction
                       (* fraction
                          (/ (log initial-ppu)
                             (log (max initial-ppu (* 0.05 ppu)))))))
         (value (- 255 (min 255 (exact-rounded (* fraction 255))))))
    (sdl2:make-color value value value)))

(define (exact-rounded x)
  (exact (round x)))

(define (event-loop)
  (define event (sdl2:make-event))
  (define painter draw-mandel!)
  (define zoom-ratio 2)

  (define (recenter! xcoord ycoord)
    (let*-values
        (((window) (ref-window params))
         ((width height) (sdl2:window-size window))
         ((ppu) (ref-pixels-per-unit params)))
      (set-xcenter! params
                    (+ (ref-xcenter params)
                       (/ (- (* 2.0 xcoord) width) (* 2.0 ppu))))
      (set-ycenter! params
                    (+ (ref-ycenter params)
                       (/ (- height (* 2.0 ycoord)) (* 2.0 ppu))))))

  (define (zoom-in!)
    (let* ((ppu (ref-pixels-per-unit params))
           (ppu (* ppu zoom-ratio)))
      (set-pixels-per-unit! params ppu)))

  (define (zoom-out!)
    (let* ((ppu (ref-pixels-per-unit params))
           (ppu (* (/ 1.0 zoom-ratio) ppu)))
      (set-pixels-per-unit! params (max 1 ppu))))

  (define (restore-original-settings!)
    (set-xcenter! params initial-xcenter)
    (set-ycenter! params initial-ycenter)
    (set-pixels-per-unit! params initial-pixels-per-unit)
    (set-pixels-per-event-check!
     params initial-pixels-per-event-check)
    (set-max-escape-time! params initial-max-escape-time)
    (set! zoom-ratio 2))

  (define dump-image!            ; Really this should put up a dialog.
    (let ((dump-number 1))
      (lambda ()
        (let*-values
            (((window) (ref-window params))
             ((width height) (sdl2:window-size window))
             ((surface) (sdl2:window-surface window)))
          (let ((filename (string-append "mandelbrot-image-"
                                         (number->string dump-number)
                                         ".png"))
                (img (imlib2:image-create width height)))
            (do ((j 0 (+ j 1)))
                ((= j height))
              (do ((i 0 (+ i 1)))
                  ((= i width))
                (let-values
                    (((r g b a) (sdl2:color->values
                                 (sdl2:surface-ref surface i j))))
                  (imlib2:image-draw-pixel
                   img (imlib2:color/rgba r g b a) i j))))
            (imlib2:image-alpha-set! img #f)
            (imlib2:image-save img filename)
            (format #t "~a written~%" filename)
            (set! dump-number (+ dump-number 1)))))))
    
  (let loop ()
    (when redraw?
      (set! drawing? #t))
    (when drawing?
      (set! painter (call/cc painter)))
    (set! redraw? #f)
    (if (not (sdl2:poll-event! event))
        (loop)
        (begin
          (match (sdl2:event-type event)
            ('quit)                     ; Quit by leaving the loop.
            ('window
             (match (sdl2:window-event-event event)
               ;; It should be possible to resize the window, but I
               ;; have not yet figured out how to do this with SDL2
               ;; and not crash sometimes.
               ((or 'exposed 'restored)
                (sdl2:update-window-surface! (ref-window params))
                (loop))
               (_ (loop))))
            ('mouse-button-down
             (recenter! (sdl2:mouse-button-event-x event)
                        (sdl2:mouse-button-event-y event))
             (set! redraw? #t)
             (loop))
            ('key-down
             (match (sdl2:keyboard-event-sym event)
               ('q 'quit-by-leaving-the-loop)
               ((or 'plus 'kp-plus)
                (zoom-in!)
                (set! redraw? #t)
                (loop))
               ((or 'minus 'kp-minus)
                (zoom-out!)
                (set! redraw? #t)
                (loop))
               ((or 'n-2 'kp-2)
                (set! zoom-ratio 2)
                (loop))
               ((or 'n-3 'kp-3)
                (set! zoom-ratio 3)
                (loop))
               ((or 'n-4 'kp-4)
                (set! zoom-ratio 4)
                (loop))
               ((or 'n-5 'kp-5)
                (set! zoom-ratio 5)
                (loop))
               ((or 'n-6 'kp-6)
                (set! zoom-ratio 6)
                (loop))
               ((or 'n-7 'kp-7)
                (set! zoom-ratio 7)
                (loop))
               ((or 'n-8 'kp-8)
                (set! zoom-ratio 8)
                (loop))
               ((or 'n-9 'kp-9)
                (set! zoom-ratio 9)
                (loop))
               ('o
                (restore-original-settings!)
                (set! redraw? #t)
                (loop))
               ('p
                (dump-image!)
                (loop))
               (some-key-in-which-we-are-not-interested
                (loop))))
            (some-event-in-which-we-are-not-interested
             (loop)))))))

;; At the least this legend should go in a window, but printing it to
;; the terminal will, hopefully, suffice for the task.
(format #t "~%~8tACTIONS~%")
(format #t "~8t-------~%")
(define fmt "~2t~a~15t: ~a~%")
(format #t fmt "Q key" "quit")
(format #t fmt "mouse button" "recenter")
(format #t fmt "+ key" "zoom in")
(format #t fmt "- key" "zoom in")
(format #t fmt "2 .. 9 key" "set zoom ratio")
(format #t fmt "O key" "restore original")
(format #t fmt "P key" "dump to a PNG")
(format #t "~%")

(event-loop)
Output:

An example of a PNG dumped by the program while it was zoomed in:

A zoomed-in picture of a part of the Mandelbrot set.

Scratch

Seed7

$ include "seed7_05.s7i";
  include "float.s7i";
  include "complex.s7i";
  include "draw.s7i";
  include "keybd.s7i";

# Display the Mandelbrot set, that are points z[0] in the complex plane
# for which the sequence z[n+1] := z[n] ** 2 + z[0] (n >= 0) is bounded.
# Since this program is computing intensive it should be compiled with
# hi comp -O2 mandelbr

const integer: pix is 200;
const integer: max_iter is 256;

var array color: colorTable is max_iter times black;

const func integer: iterate (in complex: z0) is func
  result
    var integer: iter is 1;
  local
    var complex: z is complex.value;
  begin
    z := z0;
    while sqrAbs(z) < 4.0 and  # not diverged
        iter < max_iter do     # not converged
      z *:= z;
      z +:= z0;
      incr(iter);
    end while;
  end func;

const proc: displayMandelbrotSet (in complex: center, in float: zoom) is func
  local
    var integer: x is 0;
    var integer: y is 0;
    var complex: z0 is complex.value;
  begin
    for x range -pix to pix do
      for y range -pix to pix do
        z0 := center + complex(flt(x) * zoom, flt(y) * zoom);
        point(x + pix, y + pix, colorTable[iterate(z0)]);
      end for;    
    end for;
  end func;

const proc: main is func
  local
    const integer: num_pix is 2 * pix + 1;
    var integer: col is 0;
  begin
    screen(num_pix, num_pix);
    clear(curr_win, black);
    KEYBOARD := GRAPH_KEYBOARD;
    for col range 1 to pred(max_iter) do
      colorTable[col] := color(65535 - (col * 5003) mod 65535,
                                       (col * 257)  mod 65535,
                                       (col * 2609) mod 65535);
    end for;
    displayMandelbrotSet(complex(-0.75, 0.0), 1.3 / flt(pix));
    DRAW_FLUSH;
    readln(KEYBOARD);
  end func;


Original source: [1]

SenseTalk

put 0 into oReal # Real origin
put 0 into oImag # Imaginary origin
put 0.5 into mag # Magnification

put oReal - .8 / mag into leftReal
put oImag + .5 / mag into topImag
put 1 / 200 / mag into inc

put [
	(0,255,255),	# aqua	
	(0,0,255), # blue 
	(255,0,255), # fuchsia
	(128,128,128), # gray	
	(0,128,0), # green
	(0,255,0), # lime	
	(128,0,0), # maroon
	(0,0,128), # navy	
	(128,128,0), # olive
	(128,0,128), # purple
	(255,0,0), # red
	(192,192,192), # silver
	(0,128,128), # teal
	(255,255,255), # white
	(255,255,0) #	yellow
] into colors

put "mandelbrot.ppm" into myFile

open file myFile for writing
write "P3" & return to file myFile # PPM file magic number
write "320 200" & return to file myFile # Width and height
write "255" & return to file myFile # Max value in color channels

put topImag into cImag
repeat with each item in 1 .. 200
	put leftReal into cReal
	repeat with each item in 1 .. 320
		put 0 into zReal
		put 0 into zImag
		put 0 into count
		put 0 into size
		repeat at least once until size > 2 or count = 100
			put zReal squared + zImag squared * -1 into newZreal
			put zReal * zImag + zReal * zImag into newZimag
			put newZreal + cReal into zReal
			put newZimag + cImag into zImag
			put sqrt(zReal squared + zImag squared) into size
			add 1 to count
		end repeat
		if size > 2 then # Outside the set - colorize
			put item count mod 15 + 1 of colors into color
			write color joined by " " to file myFile
			write return to file myFile
		else # Inside the set - black
			write "0 0 0" & return to file myFile
		end if
		add inc to cReal
	end repeat
	subtract inc from cImag
end repeat

close file myFile

SequenceL

SequenceL Code for Computing and Coloring:

import <Utilities/Complex.sl>;
import <Utilities/Sequence.sl>;
import <Utilities/Math.sl>;

COLOR_STRUCT ::= (R: int(0), G: int(0), B: int(0));
rgb(r(0), g(0), b(0)) := (R: r, G: g, B: b);

RESULT_STRUCT ::= (FinalValue: Complex(0), Iterations: int(0));
makeResult(val(0), iters(0)) := (FinalValue: val, Iterations: iters);

zSquaredOperation(startingNum(0), currentNum(0)) :=
    complexAdd(startingNum, complexMultiply(currentNum, currentNum));

zSquared(minX(0), maxX(0), resolutionX(0), minY(0), maxY(0), resolutionY(0), maxMagnitude(0), maxIters(0))[Y,X] := 
    let
        stepX := (maxX - minX) / resolutionX;
        stepY := (maxY - minY) / resolutionY;
        
        currentX := X * stepX + minX;
        currentY := Y * stepY + minY;
        
    in 
        operateUntil(zSquaredOperation, makeComplex(currentX, currentY), makeComplex(currentX, currentY), maxMagnitude, 0, maxIters)
    foreach Y within 0 ... (resolutionY - 1),
            X within 0 ... (resolutionX - 1);

operateUntil(operation(0), startingNum(0), currentNum(0), maxMagnitude(0), currentIters(0), maxIters(0)) :=
    let
        operated := operation(startingNum, currentNum);
    in
        makeResult(currentNum, maxIters) when currentIters >= maxIters
    else
        makeResult(currentNum, currentIters) when complexMagnitude(currentNum) >= maxMagnitude
    else
        operateUntil(operation, startingNum, operated, maxMagnitude, currentIters + 1, maxIters);

//region Smooth Coloring

COLOR_COUNT := size(colorSelections);

colorRange := range(0, 255, 1);

colors := 
    let
        first[i] := rgb(0, 0, i) foreach i within colorRange;
        second[i] := rgb(i, i, 255) foreach i within colorRange;
        third[i] := rgb(255, 255, i) foreach i within reverse(colorRange);
        fourth[i] := rgb(255, i, 0) foreach i within reverse(colorRange);
        fifth[i] := rgb(i, 0, 0) foreach i within reverse(colorRange);

        red[i] :=   rgb(i, 0, 0) foreach i within colorRange;
        redR[i] :=  rgb(i, 0, 0) foreach i within reverse(colorRange);
        green[i] := rgb(0, i, 0) foreach i within colorRange;
        greenR[i] :=rgb(0, i, 0) foreach i within reverse(colorRange);
        blue[i] :=  rgb(0, 0, i) foreach i within colorRange;
        blueR[i] := rgb(0, 0, i) foreach i within reverse(colorRange);

    in
        //red ++ redR ++ green ++ greenR ++ blue ++ blueR;  
        first ++ second ++ third ++ fourth ++ fifth;
        //first ++ fourth;

colorSelections := range(1, size(colors), 30);

getSmoothColorings(zSquaredResult(2), maxIters(0))[Y,X] :=
    let
        current := zSquaredResult[Y,X];
        
        zn := complexMagnitude(current.FinalValue);
        nu := ln(ln(zn) / ln(2)) / ln(2);
        
        result := abs(current.Iterations + 1 - nu);
        
        index := floor(result);
        rem := result - index;
                
        color1 := colorSelections[(index mod COLOR_COUNT) + 1];
        color2 := colorSelections[((index + 1) mod COLOR_COUNT) + 1];
    in
        rgb(0, 0, 0) when current.Iterations = maxIters
    else
        colors[color1] when color2 < color1
    else
        colors[floor(linearInterpolate(color1, color2, rem))];
        
linearInterpolate(v0(0), v1(0), t(0)) := (1 - t) * v0 + t * v1;

//endregion

C++ Driver Code:

Library: CImg
#include "SL_Generated.h"
#include "../../../ThirdParty/CImg/CImg.h"

using namespace std;
using namespace cimg_library;

int main(int argc, char ** argv)
{
    int cores = 0;

    Sequence<Sequence<_sl_RESULT_STRUCT> > computeResult;
    Sequence<Sequence<_sl_COLOR_STRUCT> > colorResult;

    sl_init(cores);

    int maxIters = 1000;
    int imageWidth = 1920;
    int imageHeight = 1200;
    double maxMag = 256;

    double xmin = -2.5;
    double xmax = 1.0;
    double ymin = -1.0;
    double ymax = 1.0;

    CImg<unsigned char> visu(imageWidth, imageHeight, 1, 3);
    CImgDisplay draw_disp(visu, "Mandelbrot Fractal in SequenceL");

    bool redraw = true;

    SLTimer t;

    double computeTime;
    double colorTime;
    double renderTime;
    
    while(!draw_disp.is_closed())
    {
        if(redraw)
        {
            redraw = false;
            
            t.start();
            sl_zSquared(xmin, xmax, imageWidth, ymin, ymax, imageHeight, maxMag, maxIters, cores, computeResult);
            t.stop();
            computeTime = t.getTime();

            t.start();
            sl_getSmoothColorings(computeResult, maxIters, cores, colorResult);
            t.stop();
            colorTime = t.getTime();

            t.start();

            visu.fill(0);
            for(int i = 1; i <= colorResult.size(); i++)
            {
                for(int j = 1; j <= colorResult[i].size(); j++)
                {
                    visu(j-1,i-1,0,0) = colorResult[i][j].R;
                    visu(j-1,i-1,0,1) = colorResult[i][j].G;
                    visu(j-1,i-1,0,2) = colorResult[i][j].B;
                }
            }
            visu.display(draw_disp);

            t.stop();

            renderTime = t.getTime();

            draw_disp.set_title("X:[%f, %f] Y:[%f, %f] | Mandelbrot Fractal in SequenceL | Compute Time: %f | Color Time: %f | Render Time: %f | Total FPS: %f", xmin, xmax, ymin, ymax, cores, computeTime, colorTime, renderTime, 1 / (computeTime + colorTime + renderTime));
        }
        
        draw_disp.wait();

        double xdiff = (xmax - xmin);
        double ydiff = (ymax - ymin);

        double xcenter = ((1.0 * draw_disp.mouse_x()) / imageWidth) * xdiff + xmin;
        double ycenter = ((1.0 * draw_disp.mouse_y()) / imageHeight) * ydiff + ymin;

        if(draw_disp.button()&1)
        {
            redraw = true;
            xmin = xcenter - (xdiff / 4);
            xmax = xcenter + (xdiff / 4);
            ymin = ycenter - (ydiff / 4);
            ymax = ycenter + (ydiff / 4);
        }
        else if(draw_disp.button()&2)
        {
            redraw = true;
            xmin = xcenter - xdiff;
            xmax = xcenter + xdiff;
            ymin = ycenter - ydiff;
            ymax = ycenter + ydiff;
        }
    }

    sl_done();

    return 0;
}
Output:

Output Screenshot

Sidef

func mandelbrot(z) {
    var c = z
    {   z = (z*z + c)
        z.abs > 2 && return true
    } * 20
    return false
}
 
for y range(1, -1, -0.05) {
    for x in range(-2, 0.5, 0.0315) {
        print(mandelbrot(x + y.i) ? ' ' : '#')
    }
    print "\n"
}


Simula

Translation of: Scheme
BEGIN
    REAL XCENTRE, YCENTRE, WIDTH, RMAX, XOFFSET, YOFFSET, PIXELSIZE;
    INTEGER N, IMAX, JMAX, COLOURMAX;
    TEXT FILENAME;

    CLASS COMPLEX(RE,IM); REAL RE,IM;;

    REF(COMPLEX) PROCEDURE ADD(A,B); REF(COMPLEX) A,B;
        ADD :- NEW COMPLEX(A.RE + B.RE, A.IM + B.IM);

    REF(COMPLEX) PROCEDURE SUB(A,B); REF(COMPLEX) A,B;
        SUB :- NEW COMPLEX(A.RE - B.RE, A.IM - B.IM);

    REF(COMPLEX) PROCEDURE MUL(A,B); REF(COMPLEX) A,B;
        MUL :- NEW COMPLEX(A.RE * B.RE - A.IM * B.IM,
                           A.RE * B.IM + A.IM * B.RE);

    REF(COMPLEX) PROCEDURE DIV(A,B); REF(COMPLEX) A,B;
    BEGIN
        REAL TMP;
        TMP := B.RE * B.RE + B.IM * B.IM;
        DIV :- NEW COMPLEX((A.RE * B.RE + A.IM * B.IM) / TMP,
                           (A.IM * B.RE - A.RE * B.IM) / TMP);
    END DIV;
 
    REF(COMPLEX) PROCEDURE RECTANGULAR(RE,IM); REAL RE,IM;
        RECTANGULAR :- NEW COMPLEX(RE,IM);

    REAL PROCEDURE MAGNITUDE(CX); REF(COMPLEX) CX;
        MAGNITUDE := SQRT(CX.RE**2 + CX.IM**2);

    BOOLEAN PROCEDURE INSIDEP(Z); REF(COMPLEX) Z;
    BEGIN
        BOOLEAN PROCEDURE INSIDE(Z0,Z,N); REAL N; REF(COMPLEX) Z,Z0;
            INSIDE := MAGNITUDE(Z) < RMAX
                AND THEN N = 0 OR ELSE INSIDE(Z0, ADD(Z0,MUL(Z,Z)), N-1);
        INSIDEP := INSIDE(Z, NEW COMPLEX(0,0), N);
    END INSIDEP;

    INTEGER PROCEDURE BOOL2INT(B); BOOLEAN B;
        BOOL2INT := IF B THEN COLOURMAX ELSE 0;
 
    INTEGER PROCEDURE PIXEL(I,J); INTEGER I,J;
        PIXEL := BOOL2INT(INSIDEP(RECTANGULAR(XOFFSET + PIXELSIZE * I,
                                              YOFFSET - PIXELSIZE * J)));
    PROCEDURE PLOT;
    BEGIN
       REF (OUTFILE) OUTF;
       INTEGER J,I;
       OUTF :- NEW OUTFILE(FILENAME);
       OUTF.OPEN(BLANKS(132));
       OUTF.OUTTEXT("P2");        OUTF.OUTIMAGE;
       OUTF.OUTINT(IMAX,0);       OUTF.OUTIMAGE;
       OUTF.OUTINT(JMAX,0);       OUTF.OUTIMAGE;
       OUTF.OUTINT(COLOURMAX,0);  OUTF.OUTIMAGE;
       FOR J := 1 STEP 1 UNTIL JMAX DO
       BEGIN
           FOR I := 1 STEP 1 UNTIL IMAX DO
           BEGIN
               OUTF.OUTINT(PIXEL(I,J),0);
               OUTF.OUTIMAGE;
           END;
       END;
       OUTF.CLOSE;
    END PLOT;
 
    XCENTRE := -0.5;
    YCENTRE := 0.0;
    WIDTH := 4.0;
    IMAX := 800;
    JMAX := 600;
    N := 100;
    RMAX := 2.0;
    FILENAME :- "out.pgm";
    COLOURMAX := 255;
    PIXELSIZE := WIDTH / IMAX;
    XOFFSET := XCENTRE - (0.5 * PIXELSIZE * (IMAX + 1));
    YOFFSET := YCENTRE + (0.5 * PIXELSIZE * (JMAX + 1));

    OUTTEXT("OUTPUT WILL BE WRITTEN TO ");
    OUTTEXT(FILENAME);
    OUTIMAGE;

    PLOT;
END;

Spin

Works with: BST/BSTC
Works with: FastSpin/FlexSpin
Works with: HomeSpun
Works with: OpenSpin
con
  _clkmode = xtal1+pll16x
  _clkfreq = 80_000_000

  xmin=-8601    ' int(-2.1*4096)
  xmax=2867     ' int( 0.7*4096)

  ymin=-4915    ' int(-1.2*4096)
  ymax=4915     ' int( 1.2*4096)

  maxiter=25

obj
  ser : "FullDuplexSerial"

pub main | c,cx,cy,dx,dy,x,y,x2,y2,iter

  ser.start(31, 30, 0, 115200)

  dx:=(xmax-xmin)/79
  dy:=(ymax-ymin)/24

  cy:=ymin
  repeat while cy=<ymax
    cx:=xmin
    repeat while cx=<xmax
      x:=0
      y:=0
      x2:=0
      y2:=0
      iter:=0
      repeat while iter=<maxiter and x2+y2=<16384
        y:=((x*y)~>11)+cy
        x:=x2-y2+cx
        iter+=1
        x2:=(x*x)~>12
        y2:=(y*y)~>12
      cx+=dx
      ser.tx(iter+32)
    cy+=dy
    ser.str(string(13,10))

  waitcnt(_clkfreq+cnt)
  ser.stop
Output:
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'+)%%%$$$$$#####"""""""""""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(+,)++&%$$$$$$######""""""
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*5:/+('&%%$$$$$$#######"""
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),:::::::,'&%%%%%$$$$########
!!!!!!!"""####################$$$$$$$$%%%&'())((())*,::::::/+))('&&&&)'%$$######
!!!!!!""###################$$$$$%%%%%%&&&'+.:::/::::::::::::::::/++:..93%%$#####
!!!!!"################$$$%%%%%%%%%%&&&&'),+2:::::::::::::::::::::::::1(&&%$$####
!!!!"##########$$$$$%%&(-(''''''''''''(*,5::::::::::::::::::::::::::::+)-&%$$###
!!!!####$$$$$$$$%%%%%&'(*-:1.+.:-4+))**:::::::::::::::::::::::::::::::4-(&%$$$##
!!!!#$$$$$$$$$%%%%%%'''++.6:::::::::8/0::::::::::::::::::::::::::::::::3(%%$$$$#
!!!#$$$$$$$%&&&&''()/-5.5::::::::::::::::::::::::::::::::::::::::::::::'&%%$$$$#
!!!(**+/+:523/80/46::::::::::::::::::::::::::::::::::::::::::::::::4+)'&&%%$$$$#
!!!#$$$$$$$%&&&&''().-2.:::::::::::::::::::::::::::::::::::::::::::::::'&%%$$$$#
!!!!#$$$$$$$$$%%%%%&'''/,.7::::::::::/0::::::::::::::::::::::::::::::::0'%%$$$$#
!!!!####$$$$$$$$%%%%%&'(*-:2.,/:-5+))**:::::::::::::::::::::::::::::::4+(&%$$$##
!!!!"##########$$$$$%%&(-(''''(''''''((*,4:::::::::::::::::::::::::::4+).&%$$###
!!!!!"################$$$%%%%%%%%%%&&&&'):,4:::::::::::::::::::::::::/('&%%$####
!!!!!!""##################$$$$$$%%%%%%&&&'*.:::0::::::::::::::::1,,://9)%%$#####
!!!!!!!"""####################$$$$$$$$%%%&(())((()**-::::::/+)))'&&&')'%$$######
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''(,:::::::+'&&%%%%%$$$########
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*7:0+('&%%%$$$$$#######"""
!!!!!!!!!!!"""""""######################$$$$$$$$$%%%&&(+-).*&%$$$$$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$%%'3(%%%$$$$$######""""""""""
!!!!!!!!!!!!!!!""""""""""""#####################################""""""""""""""""

SparForte

As a structured script.

#!/usr/local/bin/spar
pragma annotate( summary, "mandel" )
       @( description, "Create a color image of the Mandelbrot set" )
       @( author, "Ken O. Burtch" );
pragma license( unrestricted );

pragma restriction( no_external_commands );

procedure mandel is

  mandel_limit : constant long_float := 4.0;       -- reach this? it's the set
  max_iterations : constant integer := 128;        -- quit if looped this amt

  center_r : constant long_float := -0.75;         -- center of set (x=real)
  center_i : constant long_float := 0.0;           -- center of set (i=imag.)

  c_r : long_float;                                -- current point (x=real)
  c_i : long_float;                                -- current point (i=imag.)

  loop_count : integer;                            -- number of iterations

  z_r  : long_float;                               -- mandelbot set formula
  z_i  : long_float;                               -- variables
  z_r2 : long_float;
  z_i2 : long_float;

  c    : pen.canvas_id;                            -- bush drawing canvas
  plot : limited pen.rect;                         -- rectangle to draw with
  s    : string;

  bits : integer;                                  -- for determining color
  red  : pen.rgbcomponent;
  green: pen.rgbcomponent;
  blue : pen.rgbcomponent;
begin

  -- create the drawing canvas

  pen.new_window_canvas( 200, 200, 32, c );
  pen.set_title( c, "Mandelbrot" );

  -- loop for the size of the canvas (-50% to +50%)

  for i in -50..50 loop
      c_i := center_i - long_float(i)*0.025;
      pen.wait_to_reveal( c );
      for r in -50..50 loop
          c_r := center_r - long_float(r)*0.025;

      -- Evaluatuate how close point (c_z, c_i ) in complex number space
      -- is to the Mandelbrot set.  Return a number between 0 and
      -- max_iterations.  A value of max_iterations implies that the point
      -- is probably a member of the Mandelbrot set.

         z_r := c_r;
         z_i := c_i;
         loop_count := 1;
         loop
            z_i2 := z_i*z_i;
            z_r2 := z_r*z_r;
            z_i := 2.0 * z_r * z_i + c_i;
            z_r := z_r2 - z_i2 + c_r;
            loop_count := @+1;
            exit when not ( (z_r2 + z_i2 < mandel_limit) and (loop_count /= max_iterations) );
         end loop;

         -- pick a color based on loop_count (mandelbrot set is black)

         if loop_count = max_iterations then
            red := 0.0;
            green := 0.0;
            blue := 0.0;
         else
            bits := (loop_count and 3 );
            red := 100.0-pen.rgbcomponent((100*bits/3));
            bits := (loop_count / 3 ) and 3;
            green := 100.0-pen.rgbcomponent((100*bits/3));
            bits := (loop_count / 27 ) and 2;
            blue := 100.0-pen.rgbcomponent((100*bits)/2);
         end if;
         pen.set_pen_ink( c, red, green, blue );

         -- Draw the point, reversing the X axis

         pen.set_rect( plot, 100-(r+50),i+50, 100-(r+49), i+51 );
         pen.paint_rect( c, plot );
      end loop;
      pen.reveal( c );
  end loop;

  ? "Press return";
  s := get_line;

end mandel;

SPL

w,h = #.scrsize()
sfx = -2.5; sfy = -2*h/w; fs = 4/w
#.aaoff()
> y, 1...h
  > x, 1...w
    fx = sfx + x*fs; fy = sfy + y*fs
    #.drawpoint(x,y,color(fx,fy):3)
  <
<
color(x,y)=
  zr = x; zi = y; n = 0; maxn = 150
  > zr*zr+zi*zi<4 & n<maxn
    zrn = zr*zr-zi*zi+x; zin = 2*zr*zi+y
    zr = zrn; zi = zin; n += 1
  <
  ? n=maxn, <= 0,0,0
  <= #.hsv2rgb(n/maxn*360,1,1):3
.


Swift

Using the Swift Numerics package, as well as the C library Quick 'N Dirty BMP imported in Swift.

import Foundation
import Numerics
import QDBMP

public typealias Color = (red: UInt8, green: UInt8, blue: UInt8)

public class BitmapDrawer {
  public let imageHeight: Int
  public let imageWidth: Int

  var grid: [[Color?]]

  private let bmp: OpaquePointer

  public init(height: Int, width: Int) {
    self.imageHeight = height
    self.imageWidth = width
    self.grid = [[Color?]](repeating: [Color?](repeating: nil, count: height), count: width)
    self.bmp = BMP_Create(UInt(width), UInt(height), 24)

    checkError()
  }

  deinit {
    BMP_Free(bmp)
  }

  private func checkError() {
    let err = BMP_GetError()

    guard err == BMP_STATUS(0) else {
      fatalError("\(err)")
    }
  }

  public func save(to path: String = "~/Desktop/out.bmp") {
    for x in 0..<imageWidth {
      for y in 0..<imageHeight {
        guard let color = grid[x][y] else { continue }

        BMP_SetPixelRGB(bmp, UInt(x), UInt(y), color.red, color.green, color.blue)
        checkError()
      }
    }

    (path as NSString).expandingTildeInPath.withCString {s in
      BMP_WriteFile(bmp, s)
    }
  }

  public func setPixel(x: Int, y: Int, to color: Color?) {
    grid[x][y] = color
  }
}

let imageSize = 10_000
let canvas = BitmapDrawer(height: imageSize, width: imageSize)
let maxIterations = 256
let cxMin = -2.0
let cxMax = 1.0
let cyMin = -1.5
let cyMax = 1.5
let scaleX = (cxMax - cxMin) / Double(imageSize)
let scaleY = (cyMax - cyMin) / Double(imageSize)

for x in 0..<imageSize {
  for y in 0..<imageSize {
    let cx = cxMin + Double(x) * scaleX
    let cy = cyMin + Double(y) * scaleY

    let c = Complex(cx, cy)
    var z = Complex(0.0, 0.0)
    var i = 0

    for t in 0..<maxIterations {
      if z.magnitude > 2 {
        break
      }

      z = z * z + c
      i = t
    }

    canvas.setPixel(x: x, y: y, to: Color(red: UInt8(i), green: UInt8(i), blue: UInt8(i)))
  }
}

canvas.save()

Tcl

Library: Tk

This code makes extensive use of Tk's built-in photo image system, which provides a 32-bit RGBA plotting surface that can be then quickly drawn in any number of places in the application. It uses a computational color scheme that was easy to code...

package require Tk

proc mandelIters {cx cy} {
    set x [set y 0.0]
    for {set count 0} {hypot($x,$y) < 2 && $count < 255} {incr count} {
        set x1 [expr {$x*$x - $y*$y + $cx}]
        set y1 [expr {2*$x*$y + $cy}]
        set x $x1; set y $y1
    }
    return $count
}
proc mandelColor {iter} {
    set r [expr {16*($iter % 15)}]
    set g [expr {32*($iter % 7)}]
    set b [expr {8*($iter % 31)}]
    format "#%02x%02x%02x" $r $g $b
}
image create photo mandel -width 300 -height 300
# Build picture in strips, updating as we go so we have "progress" monitoring
# Also set the cursor to tell the user to wait while we work.
pack [label .mandel -image mandel -cursor watch]
update
for {set x 0} {$x < 300} {incr x} {
    for {set y 0} {$y < 300} {incr y} {
        set i [mandelIters [expr {($x-220)/100.}] [expr {($y-150)/90.}]]
        mandel put [mandelColor $i] -to $x $y
    }
    update
}
.mandel configure -cursor {}

Plain TeX

Library: pst-fractal

The pst-fractal package includes a Mandelbrot set drawn by emitting PostScript code (using PSTricks), so the actual work done in the printer or PostScript interpreter.

\input pst-fractal
\psfractal[type=Mandel,xWidth=14cm,yWidth=12cm,maxIter=30,dIter=20] (-2.5,-1.5)(1,1.5)
\end

The coordinates are a rectangle in the complex plane to draw, scaled up to xWidth,yWidth.

More iterations with maxIter is higher resolution but slower.

dIter is a scale factor for the colours.

LaTeX

The pstricks-examples package which is samples from the PSTricks book includes similar for LaTeX (25-02-6.ltx and 33-02-6.ltx).

Library: PGF

The PGF shadings library includes a Mandelbrot set.

In PGF 3.0 the calculations are done in PostScript code emitted, so the output size is small but it only does 10 iterations so is very low resolution.

\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{shadings}
\begin{document}
\begin{tikzpicture}
    \shade[shading=Mandelbrot set] (0,0) rectangle (4,4);
\end{tikzpicture}
\end{document}

LuaTeX

Library: LuaTeX

LuaLaTeX plus pgfplots code can be found at http://texwelt.de/wissen/fragen/3960/fraktale-mit-pgfplots.

The calculations are done by inline Lua code and the resulting bitmap shown with a PGF plot.

TI-83 BASIC

Based on the BASIC Version. Due to the TI-83's lack of power, it takes around 2 hours to complete at 16 iterations.

PROGRAM:MANDELBR
:Input "ITER. ",D
:For(A,Xmin,Xmax,ΔX)
:For(B,Ymin,Ymax,ΔY)
:0→X
:0→Y
:0→I
:D→M
:While X^2+Y^2≤4 and I<M
:X^2-Y^2+A→R
:2XY+B→Y
:R→X
:I+1→I
:End
:If I≠M
:Then
:I→C
:Else
:0→C
:End
:If C<1
:Pt-On(A,B)
:End
:End
:End

Transact-SQL‎

This is a Transact-SQL version of SQL Server to generate Mandelbrot set. Export the final result to a .ppm file to view the image. More details are available here.

-- Mandelbrot Set
-- SQL Server 2017 and above
SET NOCOUNT ON
GO

-- Plot area 800 X 800
DECLARE @width INT = 800
DECLARE @height INT = 800

DECLARE @r_min DECIMAL (10, 8) = -2.5;
DECLARE @r_max DECIMAL (10, 8) = 1.5;
DECLARE @r_step DECIMAL (10, 8) = 0.005;
DECLARE @i_min DECIMAL (10, 8) = -2;
DECLARE @i_max DECIMAL (10, 8) = 2;
DECLARE @i_step DECIMAL (10, 8) = 0.005;

DECLARE @iter INT = 255; -- Iteration

DROP TABLE IF EXISTS dbo.Numbers
DROP TABLE IF EXISTS dbo.mandelbrot_set;

CREATE TABLE dbo.Numbers (n INT);

-- Generate a number table of 1000 rows
;WITH N1(n) AS
(
    SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL 
    SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL 
    SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1
), -- 10
N2(n) AS (SELECT 1 FROM N1 CROSS JOIN N1 AS b), -- 10*10
N3(n) AS (SELECT 1 FROM N1 CROSS JOIN N2) -- 10*100
INSERT INTO dbo.Numbers (n)
SELECT n = ROW_NUMBER() OVER (ORDER BY n) 
FROM N3 ORDER BY n;
/*
-- If the version is SQL Server 2022 and above
INSERT INTO dbo.Numbers (n)
SELECT value FROM GENERATE_SERIES(0, 1000);
*/


CREATE TABLE dbo.mandelbrot_set
(
	a INT,
	b INT,
	c_re DECIMAL (10, 8),
	c_im DECIMAL (10, 8),
	z_re DECIMAL (10, 8) DEFAULT 0,
	z_im DECIMAL (10, 8) DEFAULT 0,
	znew_re DECIMAL (10, 8) DEFAULT 0,
	znew_im DECIMAL (10, 8) DEFAULT 0,
	steps INT DEFAULT 0,
	active BIT DEFAULT 1,
)

-- Store all the c_re, c_im corresponding to each point in the plot area
-- Generate 640,000 rows (800 X 800)
INSERT INTO dbo.mandelbrot_set (a, b, c_re, c_im, steps)
SELECT   a.n as a, b.n as b
		,(@r_min + (a.n * @r_step)) AS c_re
		,(@i_min + (b.n * @i_step)) AS c_im
		,@iter AS steps 
FROM
		(
		SELECT n - 1 as n FROM dbo.Numbers WHERE n <= @width
		) as a
CROSS JOIN
		(
		SELECT n - 1 as n FROM dbo.Numbers WHERE n <= @height
		) as b;

-- Iteration
WHILE (@iter > 1)
	BEGIN

		UPDATE dbo.mandelbrot_set
		SET
			znew_re = POWER(z_re,2)-POWER(z_im,2)+c_re,
			znew_im = 2*z_re*z_im+c_im,
			steps = steps-1
		WHERE active=1;

		UPDATE dbo.mandelbrot_set 
		SET
			z_re=znew_re,
			z_im=znew_im,
			active= CASE
						WHEN POWER(znew_re,2)+POWER(znew_im,2)>4 THEN 0
						ELSE 1
					END
		WHERE active=1;

		SET @iter = @iter - 1;
	END

-- Generating PPM File
-- Save the below query results to a file with extension .ppm
-- NOTE : All the unwanted info like 'rows affected', 'completed time' etc. needs to be 
-- removed from the file. Most of the image editing softwares and online viewers can display the .ppm file
SELECT 'P3' UNION ALL
SELECT CAST(@width AS VARCHAR(5)) + ' ' + CAST(@height AS VARCHAR(5)) UNION ALL
SELECT '255' UNION ALL
SELECT 
	STRING_AGG(CAST(CASE WHEN active = 1 THEN 0 ELSE 55 + steps % 200 END AS VARCHAR(10)) + ' ' -- R
	+ CAST(CASE WHEN active = 1 THEN 0 ELSE 55+POWER(steps,3) %  200 END AS VARCHAR(10)) + ' '  -- G
	+ CAST(CASE WHEN active = 1 THEN 0 ELSE 55+ POWER(steps,2) % 200 END AS VARCHAR(10))		-- B
	, ' ') WITHIN GROUP (ORDER BY c_re, c_im)
FROM dbo.mandelbrot_set 
GROUP BY c_re, c_im;

OUTPUT

TXR

Translation of: Scheme

Creates same mandelbrot.pgm file.

(defvar x-centre -0.5)
(defvar y-centre 0.0)
(defvar width 4.0)
(defvar i-max 800)
(defvar j-max 600)
(defvar n 100)
(defvar r-max 2.0)
(defvar file "mandelbrot.pgm")
(defvar colour-max 255)
(defvar pixel-size (/ width i-max))
(defvar x-offset (- x-centre (* 0.5 pixel-size (+ i-max 1))))
(defvar y-offset (+ y-centre (* 0.5 pixel-size (+ j-max 1))))

;; with-output-to-file macro
(defmacro with-output-to-file (name . body)
  ^(let ((*stdout* (open-file ,name "w")))
     (unwind-protect (progn ,*body) (close-stream *stdout*))))

;; complex number library
(defmacro cplx (x y) ^(cons ,x ,y))
(defmacro re (c) ^(car ,c))
(defmacro im (c) ^(cdr ,c))

(defsymacro c0 '(0 . 0))

(macro-time 
  (defun with-cplx-expand (specs body)
    (tree-case specs
       (((re im expr) . rest) 
        ^(tree-bind (,re . ,im) ,expr ,(with-cplx-expand rest body)))
       (() (tree-case body
             ((a b . rest) ^(progn ,a ,b ,*rest))
             ((a) a)
             (x (error "with-cplx: invalid body ~s" body))))
       (x (error "with-cplx: bad args ~s" x)))))

(defmacro with-cplx (specs . body)
  (with-cplx-expand specs body))

(defun c+ (x y)
  (with-cplx ((a b x) (c d y))
    (cplx (+ a c) (+ b d))))

(defun c* (x y)
  (with-cplx ((a b x) (c d y))
    (cplx (- (* a c) (* b d)) (+ (* b c) (* a d)))))

(defun modulus (z)
  (with-cplx ((a b z))
    (sqrt (+ (* a a) (* b b)))))

;; Mandelbrot routines
(defun inside-p (z0 : (z c0) (n n))
  (and (< (modulus z) r-max)
       (or (zerop n)
           (inside-p z0 (c+ (c* z z) z0) (- n 1)))))

(defmacro int-bool (b)
  ^(if ,b colour-max 0))

(defun pixel (i j)
  (int-bool
    (inside-p
      (cplx (+ x-offset (* pixel-size i))
            (- y-offset (* pixel-size j))))))

;; Mandelbrot loop and output
(defun plot ()
  (with-output-to-file file
    (format t "P2\n~s\n~s\n~s\n" i-max j-max colour-max)
    (each ((j (range 1 j-max)))
      (each ((i (range 1 i-max)))
        (format *stdout* "~s " (pixel i j)))
      (put-line "" *stdout*))))

(plot)

uBasic/4tH

uBasic does not support floating point calculations, so fixed point arithmetic is used, with Value 10000 representing 1.0. The Mandelbrot image is drawn using ASCII characters 1-9 to show number of iterations. Iteration count 10 or more is represented with '@'. To compensate the aspect ratio of the font, step sizes in x and y directions are different.

A =-21000                              ' Left Edge = -2.1
B = 15000                              ' Right Edge = 1.5
C = 15000                              ' Top Edge = 1.5
D =-15000                              ' Bottom Edge = -1.5
E = 200                                ' Max Iteration Depth
F = 350                                ' X Step Size
G = 750                                ' Y Step Size

For L = C To D Step -G                 ' Y0
    For K = A To B-1 Step F            ' X0
        V = 0                          ' Y
        U = 0                          ' X
        I = 32                         ' Char To Be Displayed
        For O = 0 To E-1               ' Iteration
            X = (U/10 * U) / 1000      ' X*X
            Y = (V/10 * V) / 1000      ' Y*Y
            If (X + Y > 40000)
                I = 48 + O             ' Print Digit 0...9
                If (O > 9)             ' If Iteration Count > 9,
                    I = 64             '  Print '@'
                Endif
                Break
            Endif
            Z = X - Y + K              ' Temp = X*X - Y*Y + X0
            V = (U/10 * V) / 500 + L   ' Y = 2*X*Y + Y0
            U = Z                      ' X = Temp
        Next
        Gosub I                        '  Ins_char(I)
    Next
    Print
Next

End
                                       ' Translate number to ASCII
32 Print " "; : Return
48 Print "0"; : Return
49 Print "1"; : Return
50 Print "2"; : Return
51 Print "3"; : Return
52 Print "4"; : Return
53 Print "5"; : Return
54 Print "6"; : Return
55 Print "7"; : Return
56 Print "8"; : Return
57 Print "9"; : Return
64 Print "@"; : Return

Output:

1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333322222222222222222222222222222222222222
1111111111111222222222233333333333333333333333344444457655544443333332222222222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
11111111111222222333333333333333333333334444444445555678@@@@7654444443333332222222222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98655544444433333332222222222222222222222222
1111111122222333333333333333333333344444444445556668@@@   @@@@76555544444333333322222222222222222222222
1111111122233333333333333333333344444444445566667778@@      @987666555544433333333222222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@    @@@@@@87777@95443333333322222222222222222222
1111112233333333333333333334444455555556678@@  @@                @@@@@@@8544333333333222222222222222222
1111122333333333333333334445555555555666789@@@                        @86554433333333322222222222222222
1111123333333333333444466666555556666778@@@@                         @@87655443333333332222222222222222
111123333333344444455568@887789@8777788@@@                            @@@@65443333333332222222222222222
1111333344444444455556679@@@@@@@@@@@99@@@                              @@765444333333333222222222222222
1111334444444455555567789@@         @@@@                                @855444333333333222222222222222
11114444444455555668@99@@@            @                                @@655444433333333322222222222222
11134555556666677789@@@ @                                             @86655444433333333322222222222222
111                                                                 @@876555444433333333322222222222222
11134555556666677789@@@ @                                             @86655444433333333322222222222222
11114444444455555668@99@@@            @                                @@655444433333333322222222222222
1111334444444455555567789@@         @@@@                                @855444333333333222222222222222
1111333344444444455556679@@@@@@@@@@@99@@@                              @@765444333333333222222222222222
111123333333344444455568@887789@8777788@@@                            @@@@65443333333332222222222222222
1111123333333333333444466666555556666778@@@@                         @@87655443333333332222222222222222
1111122333333333333333334445555555555666789@@@                        @86554433333333322222222222222222
1111112233333333333333333334444455555556678@@  @@                @@@@@@@8544333333333222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@    @@@@@@87777@95443333333322222222222222222222
1111111122233333333333333333333344444444445566667778@@      @987666555544433333333222222222222222222222
1111111122222333333333333333333333344444444445556668@@@   @@@@76555544444333333322222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98655544444433333332222222222222222222222222
11111111111222222333333333333333333333334444444445555678@@@@7654444443333332222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
1111111111111222222222233333333333333333333333344444457655544443333332222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333322222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111

0 OK, 0:1726    

UNIX Shell

Works with: Bourne Again SHell version 4
function mandelbrot() {
  local -ir maxiter=100
  local -i i j {x,y}m{in,ax} d{x,y}
  local -ra C=( {0..9} )
  local -i lC=${#C[*]}
  local -i columns=${COLUMNS:-72} lines=${LINES:-24}

  ((
    xmin=-21*4096/10,
    xmax=  7*4096/10,
    
    ymin=-12*4096/10,
    ymax= 12*4096/10,

    dx=(xmax-xmin)/columns,
    dy=(ymax-ymin)/lines
  ))

  for ((cy=ymax, i=0; i<lines; cy-=dy, i++))
  do for ((cx=xmin, j=0; j<columns; cx+=dx, j++))
    do (( x=0, y=0, x2=0, y2=0 ))
      for (( iter=0; iter<maxiter && x2+y2<=16384; iter++ ))
      do
        ((
          y=((x*y)>>11)+cy,
          x=x2-y2+cx,
          x2=(x*x)>>12,
          y2=(y*y)>>12
        ))
      done
      ((c=iter%lC))
      echo -n "${C[c]}"
    done
    echo
  done
}
Output:
1111111111111222222222222333333333333333333333333333333333222222222222222
1111111111112222222233333333333333333333344444456015554444333332222222222
1111111111222222333333333333333333333444444445556704912544444433333222222
1111111112222333333333333333333333444444444555678970508655544444333333222
1111111222233333333333333333333444444444556667807000002076555544443333333
1111112223333333333333333333444444455577898889016000003099766662644333333
1111122333333333333333334444455555566793000800000000000000931045875443333
1111123333333333333344455555555566668014000000000000000000000009865544333
1111233333333344445568277777777777880600000000000000000000000009099544433
1111333344444445555678041513450199023000000000000000000000000000807544433
1112344444445555556771179000000000410000000000000000000000000000036544443
1114444444566667782404400000000000000000000000000000000000000000775544443
1119912160975272040000000000000000000000000000000000000000000219765544443
1114444444566667792405800000000000000000000000000000000000000000075544443
1113344444445555556773270000000000500000000000000000000000000000676544443
1111333344444445555678045623255199020000000000000000000000000000707544433
1111233333333444445568177777877777881500000000000000000000000009190544433
1111123333333333333344455555555566668126000000000000000000000009865544333
1111122333333333333333334444455555566793000100000000000000941355975443333
1111112223333333333333333334444444455588908889016000003099876670654433333
1111111222233333333333333333334444444445556667800000002976555554443333333
1111111112222333333333333333333333444444444555679060608655544444333333222
1111111111222222333333333333333333333444444445556702049544444433333222222
1111111111112222222233333333333333333333344444456205554444333333222222222
1111111111111222222222222333333333333333333333333333333333222222222222222

Vala

public class Example: Gtk.Application {
  private Gtk.ApplicationWindow window;
  private Gtk.DrawingArea drawing_area;
  public Example() {
    Object(application_id: "my.application", flags: ApplicationFlags.FLAGS_NONE);
    this.activate.connect(() => {
      window = new Gtk.ApplicationWindow(this);
      drawing_area = new Gtk.DrawingArea();
      drawing_area.set_draw_func(draw_mandelbrot);
      window.set_child(drawing_area);
      window.present();
    });
  }

  private void draw_mandelbrot(Gtk.DrawingArea area, Cairo.Context cr, int width, int height) {
    cr.set_source_rgb(0, 0, 0);
    cr.paint();
    int x0 = -1;
    double x_increment = 2.47 / (float) width;
    double y_increment = 2.24 / (float) height;
    for (double x = -2.0; x < 0.47; x += x_increment, x0++) {
      int y0 = -1;
      for (double y = -1.12; y < 1.12; y += y_increment, y0++) {
        double c_re = x;
        double c_im = y;
        double x_ = 0,
        y_ = 0;
        int iterations = 0;
        int max_iterations = 50;
        while (iterations < max_iterations && x_ * x_ + y_ * y_ <= 4.0) {
          double x_new = x_ * x_ - y_ * y_ + c_re;
          y_ = 2.0 * x_ * y_ + c_im;
          x_ = x_new;
          iterations++;
        }
        if (iterations < max_iterations) {
          cr.set_source_rgb((float) iterations / (float) max_iterations, 0, 0);
          cr.rectangle(x0, y0, 1, 1);
          cr.fill();
        }
      }
    }
  }

  public static int main(string[] argv) {
    var app = new Example();
    return app.run(argv);
  }
}

VBScript

option explicit

' Raster graphics class in VBSCRIPT by Antoni Gual
'--------------------------------------------
' An array keeps the image allowing to set pixels, draw lines and boxes in it. 
' at class destroy a bmp file is saved to disk and the default viewer is called
' The class can work with 8 and 24 bit bmp. With 8 bit uses a built-in palette or can import a custom one


'Declaration : 
' Set MyObj = (New ImgClass)(name,width,height, orient,bits_per_pixel,palette_array)
' name:path and name of the file created
' width, height of the canvas
' orient is the way the coord increases, 1 to 4 think of the 4 cuadrants of the caterian plane
'    1 X:l>r Y:b>t   2 X:r>l Y:b>t  3 X:r>l Y:t>b   4 X:l>r  Y:t>b 
' bits_per_pixel can bs only 8 and 24
' palette array only to substitute the default palette for 8 bits, else put a 0
' it sets the origin at the corner of the image (bottom left if orient=1) 

Class ImgClass
  Private ImgL,ImgH,ImgDepth,bkclr,loc,tt
  private xmini,xmaxi,ymini,ymaxi,dirx,diry
  public ImgArray()  'rgb in 24 bit mode, indexes to palette in 8 bits
  private filename   
  private Palette,szpal 
  
  Public Property Let depth (x) 
  if depth=8 or depth =24 then 
    Imgdepth=depth
  else 
    Imgdepth=8
  end if
  bytepix=imgdepth/8
  end property        
  
  Public Property Let Pixel (x,y,color)
  If (x>=ImgL) or x<0 then exit property
  if y>=ImgH or y<0 then exit property
  ImgArray(x,y)=Color   
  End Property
  
  Public Property Get Pixel (x,y)
  If (x<ImgL) And (x>=0) And (y<ImgH) And (y>=0) Then
    Pixel=ImgArray(x,y)
  End If
  End Property
  
  Public Property Get ImgWidth ()
  ImgWidth=ImgL-1
  End Property
  
  Public Property Get ImgHeight ()
  ImgHeight=ImgH-1
  End Property     
  
  'constructor (fn,w*2,h*2,32,0,0)
  Public Default Function Init(name,w,h,orient,dep,bkg,mipal)
  'offx, offy posicion de 0,0. si ofx+ , x se incrementa de izq a der, si offy+ y se incrementa de abajo arriba
  dim i,j
  ImgL=w
  ImgH=h
  tt=timer
  set0 0,0   'origin blc positive up and right
  redim imgArray(ImgL-1,ImgH-1)
  bkclr=bkg
  if bkg<>0 then 
    for i=0 to ImgL-1 
      for j=0 to ImgH-1 
        imgarray(i,j)=bkg
      next
    next  
  end if 
  Select Case orient
    Case 1: dirx=1 : diry=1   
    Case 2: dirx=-1 : diry=1
    Case 3: dirx=-1 : diry=-1
    Case 4: dirx=1 : diry=-1
  End select    
  filename=name
  ImgDepth =dep
  'load user palette if provided  
  if imgdepth=8 then  
    loadpal(mipal)
  end if       
  set init=me
  end function

  private sub loadpal(mipale)
    if isarray(mipale) Then
      palette=mipale
      szpal=UBound(mipale)+1
    Else
      szpal=256  
    'Default palette recycled from ATARI
  
   End if  
  End Sub
  public sub set0 (x0,y0) 'origin can be changed during drawing
    if x0<0 or x0>=imgl or y0<0 or y0>imgh then err.raise 9 
    xmini=-x0
    ymini=-y0
    xmaxi=xmini+imgl-1
    ymaxi=ymini+imgh-1 
    
  end sub

    
  Private Sub Class_Terminate
  if err <>0 then wscript.echo "Error " & err.number
  wscript.echo "writing bmp to file"
    savebmp
    wscript.echo "opening " & filename
    CreateObject("Shell.Application").ShellExecute filename
  wscript.echo timer-tt & " seconds"
  End Sub


 'writes a 32bit integr value as binary to an utf16 string
 function long2wstr( x)  'falta muy poco!!!
      dim k1,k2,x1
      k1=  (x and &hffff&)' or (&H8000& And ((X And &h8000&)<>0)))
      k2=((X And &h7fffffff&) \ &h10000&) Or (&H8000& And (x<0))
      long2wstr=chrw(k1) & chrw(k2)
    end function 
    
    function int2wstr(x)
        int2wstr=ChrW((x and &h7fff) or (&H8000 And (X<0)))
    End Function


  Public Sub SaveBMP
    'Save the picture to a bmp file
    Dim s,ostream, x,y,loc
   
    const hdrs=54 '14+40 
    dim bms:bms=ImgH* 4*(((ImgL*imgdepth\8)+3)\4)  'bitmap size including padding
    dim palsize:if (imgdepth=8) then palsize=szpal*4 else palsize=0

    with  CreateObject("ADODB.Stream") 'auxiliary ostream, it creates an UNICODE with bom stream in memory
      .Charset = "UTF-16LE"    'o "UTF16-BE" 
      .Type =  2' adTypeText  
      .open 
      
      'build a header
      'bmp header: VBSCript does'nt have records nor writes binary values to files, so we use strings of unicode chars!! 
      'BMP header  
      .writetext ChrW(&h4d42)                           ' 0 "BM" 4d42 
      .writetext long2wstr(hdrs+palsize+bms)            ' 2 fiesize  
      .writetext long2wstr(0)                           ' 6  reserved 
      .writetext long2wstr (hdrs+palsize)               '10 image offset 
       'InfoHeader 
      .writetext long2wstr(40)                          '14 infoheader size
      .writetext long2wstr(Imgl)                        '18 image length  
      .writetext long2wstr(imgh)                        '22 image width
      .writetext int2wstr(1)                            '26 planes
      .writetext int2wstr(imgdepth)                     '28 clr depth (bpp)
      .writetext long2wstr(&H0)                         '30 compression used 0= NOCOMPR
       
      .writetext long2wstr(bms)                         '34 imgsize
      .writetext long2wstr(&Hc4e)                       '38 bpp hor
      .writetext long2wstr(&hc43)                       '42 bpp vert
      .writetext long2wstr(szpal)                       '46  colors in palette
      .writetext long2wstr(&H0)                         '50 important clrs 0=all
     
      'write bitmap
      'precalc data for orientation
       Dim x1,x2,y1,y2
       If dirx=-1 Then x1=ImgL-1 :x2=0 Else x1=0:x2=ImgL-1
       If diry=-1 Then y1=ImgH-1 :y2=0 Else y1=0:y2=ImgH-1 
       
      Select Case imgdepth
      
      Case 32
        For y=y1 To y2  step diry   
          For x=x1 To x2 Step dirx
           'writelong fic, Pixel(x,y) 
           .writetext long2wstr(Imgarray(x,y))
          Next
        Next
        
      Case 8
        'palette
        For x=0 to szpal-1
          .writetext long2wstr(palette(x))  '52
        Next
        'image
        dim pad:pad=ImgL mod 4
        For y=y1 to y2 step diry
          For x=x1 To x2 step dirx*2
             .writetext chrw((ImgArray(x,y) and 255)+ &h100& *(ImgArray(x+dirx,y) and 255))
          Next
          'line padding
          if pad and 1 then .writetext  chrw(ImgArray(x2,y))
          if pad >1 then .writetext  chrw(0)
         Next
         
      Case Else
        WScript.Echo "ColorDepth not supported : " & ImgDepth & " bits"
      End Select

      'use a second stream to save to file starting past the BOM  the first ADODB.Stream has added
      Dim outf:Set outf= CreateObject("ADODB.Stream") 
      outf.Type    = 1 ' adTypeBinary  
      outf.Open
      .position=2              'remove bom (1 wchar) 
      .CopyTo outf
      .close
      outf.savetofile filename,2   'adSaveCreateOverWrite
      outf.close
    end with
  End Sub
End Class

function mandelpx(x0,y0,maxit)
   dim x,y,xt,i,x2,y2
   i=0:x2=0:y2=0
   Do While i< maxit
     i=i+1
     xt=x2-y2+x0
     y=2*x*y+y0
     x=xt 
     x2=x*x:y2=y*y 
     If (x2+y2)>=4 Then Exit do
   loop 
   if i=maxit then
      mandelpx=0
   else   
     mandelpx = i
   end if  
end function   

Sub domandel(x1,x2,y1,y2) 
 Dim i,ii,j,jj,pix,xi,yi,ym
 ym=X.ImgHeight\2
 'get increments in the mandel plane
 xi=Abs((x1-x2)/X.ImgWidth)
 yi=Abs((y2-0)/(X.ImgHeight\2))
 j=0
 For jj=0.  To y2 Step yi
   i=0
   For ii=x1 To x2 Step xi
      pix=mandelpx(ii,jj,256)
      'use simmetry
      X.imgarray(i,ym-j)=pix
      X.imgarray(i,ym+j)=pix
      i=i+1   
   Next
   j=j+1   
 next
End Sub

'main------------------------------------
Dim i,x
'custom palette
dim pp(255)
for i=1 to 255
   pp(i)=rgb(0,0,255*(i/255)^.25)  'VBS' RGB function is for the web, it's bgr for Windows BMP !!
next  
 
dim fn:fn=CreateObject("Scripting.FileSystemObject").GetSpecialFolder(2)& "\mandel.bmp"
Set X = (New ImgClass)(fn,580,480,1,8,0,pp)
domandel -2.,1.,-1.2,1.2
Set X = Nothing
Output:

Vedit macro language

Vedit macro language does not support floating point calculations, so fixed point arithmetic is used, with Value 10000 representing 1.0. The Mandelbrot image is drawn using ASCII characters 1-9 to show number of iterations. Iteration count 10 or more is represented with '@'. To compensate the aspect ratio of the font, step sizes in x and y directions are different.

#1 =-21000              // left edge = -2.1
#2 = 15000              // right edge = 1.5
#3 = 15000              // top edge = 1.5
#4 =-15000              // bottom edge = -1.5
#5 = 200                // max iteration depth
#6 = 350                // x step size
#7 = 750                // y step size

Buf_Switch(Buf_Free)
for (#12 = #3; #12 > #4; #12 -= #7) {                   // y0
    for (#11 = #1; #11 < #2; #11 += #6) {               // x0
        #22 = 0                                         // y
        #21 = 0                                         // x
        #9 = ' '                                        // char to be displayed
        for (#15 = 0; #15 < #5; #15++) {                // iteration
            #31 = (#21/10 * #21) / 1000                 // x*x
            #32 = (#22/10 * #22) / 1000                 // y*y
            if (#31 + #32 > 40000) {
                #9 = '0' + #15                          // print digit 0...9
                if (#15 > 9) {                          // if iteration count > 9,
                    #9 = '@'                            //  print '@'
                }
                break
            }
            #33 = #31 - #32 + #11                       // temp = x*x - y*y + x0
            #22 = (#21/10 * #22) / 500 + #12            // y = 2*x*y + y0
            #21 = #33                                   // x = temp
        }
        Ins_Char(#9)
    }
    Ins_Newline
}
BOF
Output:

1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333322222222222222222222222222222222222222
1111111111111222222222233333333333333333333333344444457655544443333332222222222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
11111111111222222333333333333333333333334444444445555678@@@@7654444443333332222222222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98655544444433333332222222222222222222222222
1111111122222333333333333333333333344444444445556668@@@   @@@@76555544444333333322222222222222222222222
1111111122233333333333333333333344444444445566667778@@      @987666555544433333333222222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@    @@@@@@87777@95443333333322222222222222222222
1111112233333333333333333334444455555556678@@  @@                @@@@@@@8544333333333222222222222222222
1111122333333333333333334445555555555666789@@@                        @86554433333333322222222222222222
1111123333333333333444466666555556666778@@@@                         @@87655443333333332222222222222222
111123333333344444455568@887789@8777788@@@                            @@@@65443333333332222222222222222
1111333344444444455556679@@@@@@@@@@@99@@@                              @@765444333333333222222222222222
1111334444444455555567789@@         @@@@                                @855444333333333222222222222222
11114444444455555668@99@@@            @                                @@655444433333333322222222222222
11134555556666677789@@@ @                                             @86655444433333333322222222222222
111                                                                 @@876555444433333333322222222222222
11134555556666677789@@@ @                                             @86655444433333333322222222222222
11114444444455555668@99@@@            @                                @@655444433333333322222222222222
1111334444444455555567789@@         @@@@                                @855444333333333222222222222222
1111333344444444455556679@@@@@@@@@@@99@@@                              @@765444333333333222222222222222
111123333333344444455568@887789@8777788@@@                            @@@@65443333333332222222222222222
1111123333333333333444466666555556666778@@@@                         @@87655443333333332222222222222222
1111122333333333333333334445555555555666789@@@                        @86554433333333322222222222222222
1111112233333333333333333334444455555556678@@  @@                @@@@@@@8544333333333222222222222222222
111111122333333333333333333333444444455556@@@@@99@@@@@@    @@@@@@87777@95443333333322222222222222222222
1111111122233333333333333333333344444444445566667778@@      @987666555544433333333222222222222222222222
1111111122222333333333333333333333344444444445556668@@@   @@@@76555544444333333322222222222222222222222
1111111112222223333333333333333333333444444444455556789@@@@98655544444433333332222222222222222222222222
11111111111222222333333333333333333333334444444445555678@@@@7654444443333332222222222222222222222222222
1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222
1111111111111222222222233333333333333333333333344444457655544443333332222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333322222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211

V (Vlang)

Graphical

// updates and contributors at: github.com/vlang/v/blob/master/examples/gg/mandelbrot.v
// graphics are moveable by keyboard or mouse and resizable with window
import gg
import gx
import runtime
import time

const (
	pwidth = 800
	pheight = 600
	chunk_height = 2 // image recalculated in chunks, each chunk processed in separate thread
	zoom_factor = 1.1
	max_iterations = 255
)

struct ViewRect {
	mut:
	x_min f64
	x_max f64
	y_min f64
	y_max f64
}

fn (v &ViewRect) width() f64 {
	return v.x_max - v.x_min
}

fn (v &ViewRect) height() f64 {
	return v.y_max - v.y_min
}

struct AppState {
	mut:
	gg      &gg.Context = unsafe { nil }
	iidx    int
	pixels  &u32     = unsafe { vcalloc(pwidth * pheight * sizeof(u32)) }
	npixels &u32     = unsafe { vcalloc(pwidth * pheight * sizeof(u32)) } // drawings here, results swapped at the end
	view    ViewRect = ViewRect{-3.0773593290970673, 1.4952456603855397, -2.019938598189011, 2.3106642054225945}
	scale   int      = 1
	ntasks  int      = runtime.nr_jobs()
}

const colors = [gx.black, gx.blue, gx.red, gx.green, gx.yellow, gx.orange, gx.purple, gx.white,
	gx.indigo, gx.violet, gx.black, gx.blue, gx.orange, gx.yellow, gx.green].map(u32(it.abgr8()))

struct MandelChunk {
	cview ViewRect
	ymin  f64
	ymax  f64
}

fn (mut state AppState) update() {
	mut chunk_channel := chan MandelChunk{cap: state.ntasks}
	mut chunk_ready_channel := chan bool{cap: 1000}
	mut threads := []thread{cap: state.ntasks}
	defer {
		chunk_channel.close()
		threads.wait()
	}
	for t in 0 .. state.ntasks {
		threads << spawn state.worker(t, chunk_channel, chunk_ready_channel)
	}
	//
	mut oview := ViewRect{}
	mut sw := time.new_stopwatch()
	for {
		sw.restart()
		cview := state.view
		if oview == cview {
			time.sleep(5 * time.millisecond)
			continue
		}
		// schedule chunks, describing the work:
		mut nchunks := 0
		for start := 0; start < pheight; start += chunk_height {
			chunk_channel <- MandelChunk{
				cview: cview
				ymin: start
				ymax: start + chunk_height
			}
			nchunks++
		}
		// wait for all chunks to be processed:
		for _ in 0 .. nchunks {
			_ := <-chunk_ready_channel
		}
		// everything is done, swap the buffer pointers
		state.pixels, state.npixels = state.npixels, state.pixels
		println('${state.ntasks:2} threads; ${sw.elapsed().milliseconds():3} ms / frame; scale: ${state.scale:4}')
		oview = cview
	}
}

[direct_array_access]
fn (mut state AppState) worker(id int, input chan MandelChunk, ready chan bool) {
	for {
		chunk := <-input or { break }
		yscale := chunk.cview.height() / pheight
		xscale := chunk.cview.width() / pwidth
		mut x, mut y, mut iter := 0.0, 0.0, 0
		mut y0 := chunk.ymin * yscale + chunk.cview.y_min
		mut x0 := chunk.cview.x_min
		for y_pixel := chunk.ymin; y_pixel < chunk.ymax && y_pixel < pheight; y_pixel++ {
			yrow := unsafe { &state.npixels[int(y_pixel * pwidth)] }
			y0 += yscale
			x0 = chunk.cview.x_min
			for x_pixel := 0; x_pixel < pwidth; x_pixel++ {
				x0 += xscale
				x, y = x0, y0
				for iter = 0; iter < max_iterations; iter++ {
					x, y = x * x - y * y + x0, 2 * x * y + y0
					if x * x + y * y > 4 {
						break
					}
				}
				unsafe {
					yrow[x_pixel] = colors[iter & 15]
				}
			}
		}
		ready <- true
	}
}

fn (mut state AppState) draw() {
	mut istream_image := state.gg.get_cached_image_by_idx(state.iidx)
	istream_image.update_pixel_data(unsafe { &u8(state.pixels) })
	size := gg.window_size()
	state.gg.draw_image(0, 0, size.width, size.height, istream_image)
}

fn (mut state AppState) zoom(zoom_factor f64) {
	c_x, c_y := (state.view.x_max + state.view.x_min) / 2, (state.view.y_max + state.view.y_min) / 2
	d_x, d_y := c_x - state.view.x_min, c_y - state.view.y_min
	state.view.x_min = c_x - zoom_factor * d_x
	state.view.x_max = c_x + zoom_factor * d_x
	state.view.y_min = c_y - zoom_factor * d_y
	state.view.y_max = c_y + zoom_factor * d_y
	state.scale += if zoom_factor < 1 { 1 } else { -1 }
}

fn (mut state AppState) center(s_x f64, s_y f64) {
	c_x, c_y := (state.view.x_max + state.view.x_min) / 2, (state.view.y_max + state.view.y_min) / 2
	d_x, d_y := c_x - state.view.x_min, c_y - state.view.y_min
	state.view.x_min = s_x - d_x
	state.view.x_max = s_x + d_x
	state.view.y_min = s_y - d_y
	state.view.y_max = s_y + d_y
}

// gg callbacks:

fn graphics_init(mut state AppState) {
	state.iidx = state.gg.new_streaming_image(pwidth, pheight, 4, pixel_format: .rgba8)
}

fn graphics_frame(mut state AppState) {
	state.gg.begin()
	state.draw()
	state.gg.end()
}

fn graphics_click(x f32, y f32, btn gg.MouseButton, mut state AppState) {
	if btn == .right {
		size := gg.window_size()
		m_x := (x / size.width) * state.view.width() + state.view.x_min
		m_y := (y / size.height) * state.view.height() + state.view.y_min
		state.center(m_x, m_y)
	}
}

fn graphics_move(x f32, y f32, mut state AppState) {
	if state.gg.mouse_buttons.has(.left) {
		size := gg.window_size()
		d_x := (f64(state.gg.mouse_dx) / size.width) * state.view.width()
		d_y := (f64(state.gg.mouse_dy) / size.height) * state.view.height()
		state.view.x_min -= d_x
		state.view.x_max -= d_x
		state.view.y_min -= d_y
		state.view.y_max -= d_y
	}
}

fn graphics_scroll(e &gg.Event, mut state AppState) {
	state.zoom(if e.scroll_y < 0 { zoom_factor } else { 1 / zoom_factor })
}

fn graphics_keydown(code gg.KeyCode, mod gg.Modifier, mut state AppState) {
	s_x := state.view.width() / 5
	s_y := state.view.height() / 5
	// movement
	mut d_x, mut d_y := 0.0, 0.0
	if code == .enter {
		println('> ViewRect{${state.view.x_min}, ${state.view.x_max}, ${state.view.y_min}, ${state.view.y_max}}')
	}
	if state.gg.pressed_keys[int(gg.KeyCode.left)] {
		d_x -= s_x
	}
	if state.gg.pressed_keys[int(gg.KeyCode.right)] {
		d_x += s_x
	}
	if state.gg.pressed_keys[int(gg.KeyCode.up)] {
		d_y -= s_y
	}
	if state.gg.pressed_keys[int(gg.KeyCode.down)] {
		d_y += s_y
	}
	state.view.x_min += d_x
	state.view.x_max += d_x
	state.view.y_min += d_y
	state.view.y_max += d_y
	// zoom in/out
	if state.gg.pressed_keys[int(gg.KeyCode.left_bracket)]
		|| state.gg.pressed_keys[int(gg.KeyCode.z)] {
		state.zoom(1 / zoom_factor)
		return
	}
	if state.gg.pressed_keys[int(gg.KeyCode.right_bracket)]
		|| state.gg.pressed_keys[int(gg.KeyCode.x)] {
		state.zoom(zoom_factor)
		return
	}
}

fn main() {
	mut state := &AppState{}
	state.gg = gg.new_context(
		width: 800
		height: 600
		create_window: true
		window_title: 'The Mandelbrot Set'
		init_fn: graphics_init
		frame_fn: graphics_frame
		click_fn: graphics_click
		move_fn: graphics_move
		keydown_fn: graphics_keydown
		scroll_fn: graphics_scroll
		user_data: state
	)
	spawn state.update()
	state.gg.run()
}

Wren

Translation of: Kotlin
Library: DOME
import "graphics" for Canvas, Color
import "dome" for Window

var MaxIters = 570
var Zoom = 150

class MandelbrotSet {
    construct new(width, height) {
        Window.title = "Mandelbrot Set"
        Window.resize(width, height)
        Canvas.resize(width, height)
        _w = width
        _h = height
    }

    init() {
        createMandelbrot()
    }

    createMandelbrot() {
        for (x in 0..._w) {
            for (y in 0..._h) {
                var zx = 0
                var zy = 0
                var cX = (x - 400) / Zoom
                var cY = (y - 300) / Zoom
                var i = MaxIters
                while (zx * zx + zy * zy < 4 && i > 0) {
                    var tmp = zx * zx - zy * zy + cX
                    zy = 2 * zx * zy + cY
                    zx = tmp
                    i = i - 1
                }
                var r = i * 255 / MaxIters
                Canvas.pset(x, y, Color.rgb(r, r, r))
            }
        }
    }

    update() {}

    draw(alpha) {}
}

var Game = MandelbrotSet.new(800, 600)
Output:

File:Wren-Mandelbrot set.png

XPL0

include c:\cxpl\codes;          \intrinsic 'code' declarations
int     X, Y,                   \screen coordinates of current point
        Cnt;                    \iteration counter
real    Cx, Cy,                 \coordinates scaled to +/-2 range
        Zx, Zy,                 \complex accumulator
        Temp;                   \temporary scratch
[SetVid($112);                                  \set 640x480x24 graphics mode
for Y:= 0 to 480-1 do                           \for all points on the screen...
    for X:= 0 to 640-1 do
        [Cx:= (float(X)/640.0 - 0.5) * 4.0;     \range: -2.0 to +2.0
         Cy:= (float(Y-240)/240.0) * 1.5;       \range: -1.5 to +1.5
         Cnt:= 0;  Zx:= 0.0;  Zy:= 0.0;         \initialize
         loop   [if Zx*Zx + Zy*Zy > 2.0 then    \Z heads toward infinity
                    [Point(X, Y, Cnt<<21+Cnt<<10+Cnt<<3); \set color of pixel to
                    quit;                       \ rate it approached infinity
                    ];                          \move on to next point
                Temp:= Zx*Zy;
                Zx:= Zx*Zx - Zy*Zy + Cx;        \calculate next iteration of Z
                Zy:= 2.0*Temp + Cy;
                Cnt:= Cnt+1;                    \count number of iterations
                if Cnt >= 1000 then quit;       \assume point is in Mandelbrot
                ];                              \ set and leave it colored black
        ];
X:= ChIn(1);                                    \wait for keystroke
SetVid($03);                                    \restore normal text display
]
Output:

XSLT

The fact that you can create an image of the Mandelbrot Set with XSLT is sometimes under-appreciated. However, it has been discussed extensively on the internet so is best reproduced here, and the code can be executed directly in your browser at that site.

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">

<!-- XSLT Mandelbrot - written by Joel Yliluoma 2007, http://iki.fi/bisqwit/ -->

<xsl:output method="html" indent="no"
  doctype-public="-//W3C//DTD HTML 4.01//EN"
  doctype-system="http://www.w3.org/TR/REC-html40/strict.dtd"
 />

<xsl:template match="/fractal">
 <html>
  <head>
   <title>XSLT fractal</title>
   <style type="text/css">
body { color:#55F; background:#000 }
pre { font-family:monospace; font-size:7px }
pre span { background:<xsl:value-of select="background" /> }
   </style>
  </head>
  <body>
   <div style="position:absolute;top:20px;left:20em">
    Copyright © 1992,2007 Joel Yliluoma
    (<a href="http://iki.fi/bisqwit/">http://iki.fi/bisqwit/</a>)
   </div>
   <h1 style="margin:0px">XSLT fractal</h1>
   <pre><xsl:call-template name="bisqwit-mandelbrot" /></pre>
  </body>
 </html>
</xsl:template>

<xsl:template name="bisqwit-mandelbrot"
  ><xsl:call-template name="bisqwit-mandelbrot-line">
   <xsl:with-param name="y" select="y/min"/>
  </xsl:call-template
></xsl:template>

<xsl:template name="bisqwit-mandelbrot-line"
 ><xsl:param name="y"
 /><xsl:call-template name="bisqwit-mandelbrot-column">
  <xsl:with-param name="x" select="x/min"/>
  <xsl:with-param name="y" select="$y"/>
 </xsl:call-template
 ><xsl:if test="$y < y/max"
  ><br
  /><xsl:call-template name="bisqwit-mandelbrot-line">
   <xsl:with-param name="y" select="$y + y/step"/>
  </xsl:call-template
 ></xsl:if
></xsl:template>

<xsl:template name="bisqwit-mandelbrot-column"
 ><xsl:param name="x"
 /><xsl:param name="y"
 /><xsl:call-template name="bisqwit-mandelbrot-slot">
  <xsl:with-param name="x" select="$x" />
  <xsl:with-param name="y" select="$y" />
  <xsl:with-param name="zr" select="$x" />
  <xsl:with-param name="zi" select="$y" />
 </xsl:call-template
 ><xsl:if test="$x < x/max"
  ><xsl:call-template name="bisqwit-mandelbrot-column">
   <xsl:with-param name="x" select="$x + x/step"/>
   <xsl:with-param name="y" select="$y" />
  </xsl:call-template
 ></xsl:if
></xsl:template>

<xsl:template name="bisqwit-mandelbrot-slot"
><xsl:param name="x"
 /><xsl:param name="y"
 /><xsl:param name="zr"
 /><xsl:param name="zi"
 /><xsl:param name="iter" select="0"
 /><xsl:variable name="zrsqr" select="($zr * $zr)"
 /><xsl:variable name="zisqr" select="($zi * $zi)"
 /><xsl:choose>
  <xsl:when test="(4*scale*scale >= $zrsqr + $zisqr) and (maxiter > $iter+1)"
   ><xsl:call-template name="bisqwit-mandelbrot-slot">
    <xsl:with-param name="x" select="$x" />
    <xsl:with-param name="y" select="$y" />
    <xsl:with-param name="zi" select="(2 * $zr * $zi) div scale + $y" />
    <xsl:with-param name="zr" select="($zrsqr - $zisqr) div scale + $x" />
    <xsl:with-param name="iter" select="$iter + 1" />
   </xsl:call-template
  ></xsl:when>
  <xsl:otherwise
   ><xsl:variable name="magnitude" select="magnitude[@value=$iter]"
    /><span style="color:{$magnitude/color}"
   ><xsl:value-of select="$magnitude/symbol"
  /></span></xsl:otherwise>
 </xsl:choose
></xsl:template>
 
</xsl:stylesheet>

Z80 Assembly

;
;  Compute a Mandelbrot set on a simple Z80 computer.
;
; Porting this program to another Z80 platform should be easy and straight-
; forward: The only dependencies on my homebrew machine are the system-calls 
; used to print strings and characters. These calls are performed by loading
; IX with the number of the system-call and performing an RST 08. To port this
; program to another operating system just replace these system-calls with 
; the appropriate versions. Only three system-calls are used in the following:
; _crlf: Prints a CR/LF, _puts: Prints a 0-terminated string (the adress of 
; which is expected in HL), and _putc: Print a single character which is 
; expected in A. RST 0 give control back to the monitor.
;
#include        "mondef.asm"

                org     ram_start

scale           equ     256                     ; Do NOT change this - the 
                                                ; arithmetic routines rely on
                                                ; this scaling factor! :-)
divergent       equ     scale * 4

                ld      hl, welcome             ; Print a welcome message
                ld      ix, _puts
                rst     08

; for (y = <initial_value> ; y <= y_end; y += y_step)
; {
outer_loop      ld      hl, (y_end)             ; Is y <= y_end?
                ld      de, (y)
                and     a                       ; Clear carry
                sbc     hl, de                  ; Perform the comparison
                jp      m, mandel_end           ; End of outer loop reached

;    for (x = x_start; x <= x_end; x += x_step)
;    {
                ld      hl, (x_start)           ; x = x_start
                ld      (x), hl
inner_loop      ld      hl, (x_end)             ; Is x <= x_end?
                ld      de, (x)
                and     a
                sbc     hl, de
                jp      m, inner_loop_end       ; End of inner loop reached

;      z_0 = z_1 = 0;
                ld      hl, 0
                ld      (z_0), hl
                ld      (z_1), hl

;      for (iteration = iteration_max; iteration; iteration--)
;      {
                ld      a, (iteration_max)
                ld      b, a
iteration_loop  push    bc                      ; iteration -> stack
;        z2 = (z_0 * z_0 - z_1 * z_1) / SCALE;
                ld      de, (z_1)               ; Compute DE HL = z_1 * z_1
                ld      bc, de
                call    mul_16
                ld      (z_0_square_low), hl    ; z_0 ** 2 is needed later again
                ld      (z_0_square_high), de

                ld      de, (z_0)               ; Compute DE HL = z_0 * z_0
                ld      bc, de
                call    mul_16
                ld      (z_1_square_low), hl    ; z_1 ** 2 will be also needed
                ld      (z_1_square_high), de

                and     a                       ; Compute subtraction
                ld      bc, (z_0_square_low)
                sbc     hl, bc
                ld      (scratch_0), hl         ; Save lower 16 bit of result
                ld      hl, de
                ld      bc, (z_0_square_high)
                sbc     hl, bc
                ld      bc, (scratch_0)         ; HL BC = z_0 ** 2 - z_1 ** 2

                ld      c, b                    ; Divide by scale = 256
                ld      b, l                    ; Discard the rest
                push    bc                      ; We need BC later

;        z3 = 2 * z0 * z1 / SCALE;
                ld      hl, (z_0)               ; Compute DE HL = 2 * z_0 * z_1
                add     hl, hl
                ld      de, hl
                ld      bc, (z_1)
                call    mul_16

                ld      b, e                    ; Divide by scale (= 256)
                ld      c, h                    ; BC contains now z_3

;        z1 = z3 + y;
                ld      hl, (y)
                add     hl, bc
                ld      (z_1), hl

;        z_0 = z_2 + x;
                pop     bc                      ; Here BC is needed again :-)
                ld      hl, (x)
                add     hl, bc
                ld      (z_0), hl

;        if (z0 * z0 / SCALE + z1 * z1 / SCALE > 4 * SCALE)
                ld      hl, (z_0_square_low)    ; Use the squares computed
                ld      de, (z_1_square_low)    ; above
                add     hl, de
                ld      bc, hl                  ; BC contains lower word of sum

                ld      hl, (z_0_square_high)
                ld      de, (z_1_square_high)
                adc     hl, de

                ld      h, l                    ; HL now contains (z_0 ** 2 + 
                ld      l, b                    ; z_1 ** 2) / scale

                ld      bc, divergent
                and     a
                sbc     hl, bc

;          break;
                jp      c, iteration_dec        ; No break
                pop     bc                      ; Get latest iteration counter
                jr      iteration_end           ; Exit loop

;        iteration++;
iteration_dec   pop     bc                      ; Get iteration counter
                djnz    iteration_loop          ; We might fall through!
;      }
iteration_end
;      printf("%c", display[iteration % 7]);
                ld      a, b
                and     $7                      ; lower three bits only (c = 0)
                sbc     hl, hl
                ld      l, a
                ld      de, display             ; Get start of character array
                add     hl, de                  ; address and load the 
                ld      a, (hl)                 ; character to be printed
                ld      ix, _putc               ; Print the character
                rst     08

                ld      de, (x_step)            ; x += x_step
                ld      hl, (x)
                add     hl, de
                ld      (x), hl

                jp      inner_loop
;    }
;    printf("\n");
inner_loop_end  ld      ix, _crlf               ; Print a CR/LF pair
                rst     08

                ld      de, (y_step)            ; y += y_step
                ld      hl, (y)
                add     hl, de
                ld      (y), hl                 ; Store new y-value

                jp      outer_loop
; }

mandel_end      ld      hl, finished            ; Print finished-message
                ld      ix, _puts
                rst     08

                rst     0                       ; Return to the monitor

welcome         defb    "Generating a Mandelbrot set"
                defb    cr, lf, eos
finished        defb    "Computation finished.", cr, lf, eos

iteration_max   defb    10                      ; How many iterations
x               defw    0                       ; x-coordinate
x_start         defw    -2 * scale              ; Minimum x-coordinate
x_end           defw    5 *  scale / 10         ; Maximum x-coordinate
x_step          defw    4  * scale / 100        ; x-coordinate step-width
y               defw    -1 * scale              ; Minimum y-coordinate
y_end           defw    1  * scale              ; Maximum y-coordinate
y_step          defw    1  * scale / 10         ; y-coordinate step-width
z_0             defw    0
z_1             defw    0
scratch_0       defw    0
z_0_square_high defw    0
z_0_square_low  defw    0
z_1_square_high defw    0
z_1_square_low  defw    0
display         defb    " .-+*=#@"              ; 8 characters for the display

;
;   Compute DEHL = BC * DE (signed): This routine is not too clever but it 
; works. It is based on a standard 16-by-16 multiplication routine for unsigned
; integers. At the beginning the sign of the result is determined based on the
; signs of the operands which are negated if necessary. Then the unsigned
; multiplication takes place, followed by negating the result if necessary.
;
mul_16          xor     a                       ; Clear carry and A (-> +)
                bit     7, b                    ; Is BC negative?
                jr      z, bc_positive          ; No
                sub     c                       ; A is still zero, complement
                ld      c, a
                ld      a, 0
                sbc     a, b
                ld      b, a
                scf                             ; Set carry (-> -)
bc_positive     bit     7, D                    ; Is DE negative?
                jr      z, de_positive          ; No
                push    af                      ; Remember carry for later!
                xor     a
                sub     e
                ld      e, a
                ld      a, 0
                sbc     a, d
                ld      d, a
                pop     af                      ; Restore carry for complement
                ccf                             ; Complement Carry (-> +/-?)
de_positive     push    af                      ; Remember state of carry
                and     a                       ; Start multiplication
                sbc     hl, hl
                ld      a, 16                   ; 16 rounds
mul_16_loop     add     hl, hl
                rl      e
                rl      d
                jr      nc, mul_16_exit
                add     hl, bc
                jr      nc, mul_16_exit
                inc     de
mul_16_exit     dec     a
                jr      nz, mul_16_loop
                pop     af                      ; Restore carry from beginning
                ret     nc                      ; No sign inversion necessary
                xor     a                       ; Complement DE HL
                sub     l
                ld      l, a
                ld      a, 0
                sbc     a, h
                ld      h, a
                ld      a, 0
                sbc     a, e
                ld      e, a
                ld      a, 0
                sbc     a, d
                ld      d, a
                ret
Output:
Generating a Mandelbrot set
.......       @@@@@@@@@@@@@@@@@@@@########===*+  .  *######@@@@@ 
......     @@@@@@@@@@@@@@@@@@@@#########====+-.    -*===#####@@@@
.....   @@@@@@@@@@@@@@@@@@@@#########===**+-         +*====####@@
....  @@@@@@@@@@@@@@@@@@@########==*+-.-+-..         .-+****+*##@
...  @@@@@@@@@@@@@@@@@#####=====**+-                          -=#
.. @@@@@@@@@@@@@@@###=========***+-                          -*==
..@@@@@@@@@@####==- +*******++++-                             -+=
. @@@@#######===**-          ...                               -*
.@@#######======++-                                            +=
.#######=****+-                                               +*=
.=**++ .-....                                               .+*==
.#=====****+++.                                              -*==
.@#######=====*---                                            .*=
.@@@########====*++.                                           +=
. @@@@@@@######==*+ .-++- --++--.                               =
.. @@@@@@@@@@@@@##==*=======****+                            -+*=
... @@@@@@@@@@@@@@@@####=======***+-                          +==
...  @@@@@@@@@@@@@@@@@@@######====*-    .               --+-  *##
....   @@@@@@@@@@@@@@@@@@@@########==****++-        .-+**====###@
.....    @@@@@@@@@@@@@@@@@@@@##########===*+         *===#####@@@
.......     @@@@@@@@@@@@@@@@@@@@@########===*+-.  .+*=######@@@@@
Computation finished.

zkl

Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl

Translation of: XPL0
fcn mandelbrot{  // lord this is slooooow
   bitmap:=PPM(640,480);
   foreach y,x in ([0..479],[0..639]){
      cx:=(x.toFloat()/640 - 0.5)*4.0;     //range: -2.0 to +2.0
      cy:=((y-240).toFloat()/240.0)*1.5;   //range: -1.5 to +1.5
      cnt:=0; zx:=0.0; zy:=0.0;
      do(1000){
      	 if(zx*zx + zy*zy > 2.0){	//z heads toward infinity
	    //set color of pixel to rate it approaches infinity
	    bitmap[x,y]=cnt.shiftLeft(21) + cnt.shiftLeft(10) + cnt*8;
	    break;
	 }
	 temp:=zx*zy;
	 zx=zx*zx - zy*zy + cx;		//calculate next iteration of z
	 zy=2.0*temp + cy;
	 cnt+=1;
      }
   }
   bitmap.write(File("foo.ppm","wb"));
}();