Sierpinski triangle/Graphical: Difference between revisions

From Rosetta Code
Content added Content deleted
m (Typo)
m (→‎{{header|Sidef}}: code simplifications and performance improvements)
Line 1,436: Line 1,436:


=={{header|Sidef}}==
=={{header|Sidef}}==
[[File:Sierpinski_triangle_sidef.png|200px|thumb|right]]
Creates a PNG image.
<lang ruby>func sierpinski_triangle(n) -> Array {
<lang ruby>func sierpinski_triangle(n) -> Array {
var triangle = ['*'];
var triangle = ['*']
{ |i|
{ |i|
var sp = (' ' * Math.pow(2, i-1));
var sp = (' ' * Math.pow(2, i-1));
triangle = (triangle.map {|x| sp + x + sp} +
triangle = (triangle.map {|x| sp + x + sp} +
triangle.map {|x| x + ' ' + x});
triangle.map {|x| x + ' ' + x})
} * n;
} * n
triangle;
triangle
}
}


Line 1,452: Line 1,452:
var gd = (
var gd = (
try { require('GD::Simple') }
try { require('GD::Simple') }
catch { warn "GD::Simple is not installed!"; return };
catch { warn "GD::Simple is not installed!"; return }
);
);


var width = self.max_by{.len}.len;
var width = self.max_by{.len}.len
self.map!{|r| "%-#{width}s" % r};
self.map!{|r| "%-#{width}s" % r}


var img = gd.new(width * scale, self.len * scale);
var img = gd.new(width * scale, self.len * scale)


self.range.each { |i|
for i in ^self {
range(i * scale, i * scale + scale).each { |j|
for j in RangeNum(i*scale, i*scale + scale) {
var row = self[i];
var row = self[i]
img.moveTo(0, j);
img.moveTo(0, j)
loop {
var len = row.len
if ((var sp = row.count(/^\s+/)) > 0) {
while (len) {
row.substr!(sp);
row.gsub!(/^\s+/)
img.fgcolor(bgcolor);
var color = bgcolor
img.line(scale * sp);
if (len == row.len) {
}
row.gsub!(/^\S+/)
elsif ((var nsp = row.count(/^\S+/)) > 0) {
color = fgcolor
⚫
row.substr!(nsp);
⚫
img.fgcolor(fgcolor);
⚫
img.line(scale * nsp);
}
else {
⚫
break;
}
}
⚫
img.fgcolor(color)
⚫
var p = len-row.len
⚫
len = row.len
⚫
img.line(scale * p)
}
}
}
}
}
}
⚫
img.png

⚫
return img.png;
}
}
}
}


var triangle = sierpinski_triangle(8);
var triangle = sierpinski_triangle(8)
var raw_png = triangle.to_png(bgcolor:'black', fgcolor:'red');
var raw_png = triangle.to_png(bgcolor:'black', fgcolor:'red')


var file = %f'triangle.png';
var file = %f'triangle.png'
file.open('>:raw', \var fh, \var err)
var fh = file.open('>:raw')
⚫
fh.print(raw_png)
|| die "Can't write to file '#{file}': #{err}";
⚫
fh.close</lang>
⚫
fh.print(raw_png);
⚫
fh.close;</lang>


=={{header|Tcl}}==
=={{header|Tcl}}==

Revision as of 23:44, 7 April 2016

Task
Sierpinski triangle/Graphical
You are encouraged to solve this task according to the task description, using any language you may know.

Produce a graphical representation of a Sierpinski triangle of order N in any orientation.

An example of Sierpinski's triangle (order = 8) looks like this:

ActionScript

SierpinskiTriangle class: <lang ActionScript3> package { 

   import flash.display.GraphicsPathCommand;
   import flash.display.Sprite;
   
   /**
    * A Sierpinski triangle.
    */
   public class SierpinskiTriangle extends Sprite {
       
       /**
        * Creates a new SierpinskiTriangle object.
        * 
        * @param n The order of the Sierpinski triangle.
        * @param c1 The background colour.
        * @param c2 The foreground colour.
        * @param width The width of the triangle.
        * @param height The height of the triangle.
        */
       public function SierpinskiTriangle(n:uint, c1:uint, c2:uint, width:Number, height:Number):void {
           _init(n, c1, c2, width, height);
       }
       
       /**
        * Generates the triangle.
        * 
        * @param n The order of the Sierpinski triangle.
        * @param c1 The background colour.
        * @param c2 The foreground colour.
        * @param width The width of the triangle.
        * @param height The height of the triangle.
        * @private
        */
       private function _init(n:uint, c1:uint, c2:uint, width:Number, height:Number):void {
           
           if ( n <= 0 )
               return;
               
           // Draw the outer triangle.
           
           graphics.beginFill(c1);
           graphics.moveTo(width / 2, 0);
           graphics.lineTo(0, height);
           graphics.lineTo(width, height);
           graphics.lineTo(width / 2, 0);
           
           // Draw the inner triangle.
           
           graphics.beginFill(c2);
           graphics.moveTo(width / 4, height / 2);
           graphics.lineTo(width * 3 / 4, height / 2);
           graphics.lineTo(width / 2, height);
           graphics.lineTo(width / 4, height / 2);
           
           if ( n == 1 )
               return;
           
           // Recursively generate three Sierpinski triangles of half the size and order n - 1 and position them appropriately.    
           
           var sub1:SierpinskiTriangle = new SierpinskiTriangle(n - 1, c1, c2, width / 2, height / 2);
           var sub2:SierpinskiTriangle = new SierpinskiTriangle(n - 1, c1, c2, width / 2, height / 2);
           var sub3:SierpinskiTriangle = new SierpinskiTriangle(n - 1, c1, c2, width / 2, height / 2);
           
           sub1.x = width / 4;
           sub1.y = 0;
           sub2.x = 0;
           sub2.y = height / 2;
           sub3.x = width / 2;
           sub3.y = height / 2;
           
           addChild(sub1);
           addChild(sub2);
           addChild(sub3);
           
       }
       
   }

} </lang>

Document class: <lang ActionScript3> package { 

   import flash.display.Sprite;
   import flash.events.Event;
   
   public class Main extends Sprite {
       
       public function Main():void {
           if ( stage ) init();
           else addEventListener(Event.ADDED_TO_STAGE, init);
       }
       
       private function init(e:Event = null):void {
           var s:SierpinskiTriangle = new SierpinskiTriangle(5, 0x0000FF, 0xFFFF00, 300, 150 * Math.sqrt(3));
           // Equilateral triangle (blue and yellow)
           s.x = s.y = 20;
           addChild(s);
       }
       
   }

} </lang>

Asymptote

This simple-minded recursive apporach doesn't scale well to large orders, but neither would your PostScript viewer, so there's nothing to gain from a more efficient algorithm. Thus are the perils of vector graphics.

<lang asymptote>path subtriangle(path p, real node) { 

   return
       point(p, node) --
       point(p, node + 1/2) --
       point(p, node - 1/2) --
       cycle;

}

void sierpinski(path p, int order) { 

   if (order == 0)
       fill(p);
   else {
       sierpinski(subtriangle(p, 0), order - 1);
       sierpinski(subtriangle(p, 1), order - 1);
       sierpinski(subtriangle(p, 2), order - 1);
   }

}

sierpinski((0, 0) -- (5 inch, 1 inch) -- (2 inch, 6 inch) -- cycle, 10);</lang>

AutoHotkey

Library: GDIP

<lang AutoHotkey>#NoEnv

  1. SingleInstance, Force

SetBatchLines, -1

Parameters

Width := 512, Height := Width/2*3**0.5, n := 8 ; iterations = 8

Uncomment if Gdip.ahk is not in your standard library
  1. Include ..\lib\Gdip.ahkl

If !pToken := Gdip_Startup() ; Start gdi+ { MsgBox, 48, gdiplus error!, Gdiplus failed to start. Please ensure you have gdiplus on your system ExitApp }

I've added a simple new function here, just to ensure if anyone is having any problems then to make sure they are using the correct library version

if (Gdip_LibraryVersion() < 1.30) { MsgBox, 48, Version error!, Please download the latest version of the gdi+ library ExitApp } OnExit, Exit

Create a layered window (+E0x80000
must be used for UpdateLayeredWindow to work!) that is always on top (+AlwaysOnTop), has no taskbar entry or caption

Gui, -Caption +E0x80000 +LastFound +OwnDialogs +Owner +AlwaysOnTop Gui, Show hwnd1 := WinExist() OnMessage(0x201, "WM_LBUTTONDOWN")

, hbm := CreateDIBSection(Width, Height) , hdc := CreateCompatibleDC() , obm := SelectObject(hdc, hbm) , G := Gdip_GraphicsFromHDC(hdc) , Gdip_SetSmoothingMode(G, 4)

Sierpinski triangle by subtracting triangles

, pBrushBlack := Gdip_BrushCreateSolid(0xff000000) , rectangle := 0 "," 0 "|" 0 "," Height "|" Width "," Height "|" Width "," 0 , Gdip_FillPolygon(G, pBrushBlack, rectangle, FillMode=0)

, pBrushBlue := Gdip_BrushCreateSolid(0xff0000ff) , triangle := Width/2 "," 0 "|" 0 "," Height "|" Width "," Height , Gdip_FillPolygon(G, pBrushBlue, triangle, FillMode=0) , Gdip_DeleteBrush(pBrushBlue)

, UpdateLayeredWindow(hwnd1, hdc, (A_ScreenWidth-Width)/2, (A_ScreenHeight-Height)/2, Width, Height)

, k:=2, x:=0, y:=0, i:=1 Loop, % n { Sleep 0.5*1000 While x*y<Width*Height { triangle := x "," y "|" x+Width/2/k "," y+Height/k "|" x+Width/k "," y , Gdip_FillPolygon(G, pBrushBlack, triangle, FillMode=0) , x += Width/k , (x >= Width) ? (x := i*Width/2/k, y += Height/k, i:=!i) : "" } UpdateLayeredWindow(hwnd1, hdc, (A_ScreenWidth-Width)/2, (A_ScreenHeight-Height)/2, Width, Height) , k*=2, x:=0, y:=0, i:=1 }

Gdip_DeleteBrush(pBrushBlack)

, UpdateLayeredWindow(hwnd1, hdc, (A_ScreenWidth-Width)/2, (A_ScreenHeight-Height)/2, Width, Height) Sleep, 1*1000

Bonus
Sierpinski triangle by random dots

Gdip_GraphicsClear(G, 0xff000000) , pBrushBlue := Gdip_BrushCreateSolid(0xff0000ff) , x1:=Width/2, y1:=0, x2:=0, y2:=Height, x3:=Width, y3:=Height , x:= Width/2, y:=Height/2 ; I'm to lazy to pick a random point. Loop, % n { Loop, % 10*10**(A_Index/2) { Random, rand, 1, 3 x := abs(x+x%rand%)/2 , y := abs(y+y%rand%)/2 , Gdip_FillEllipse(G, pBrushBlue, x, y, 1, 1) } UpdateLayeredWindow(hwnd1, hdc, (A_ScreenWidth-Width)/2, (A_ScreenHeight-Height)/2, Width, Height) Sleep, 0.5*1000 } SelectObject(hdc, obm) , DeleteObject(hbm) , DeleteDC(hdc) , Gdip_DeleteGraphics(G) Return

Exit: Gdip_Shutdown(pToken) ExitApp

WM_LBUTTONDOWN() { If (A_Gui = 1) PostMessage, 0xA1, 2 }</lang>

BBC BASIC

Works with: BBC BASIC for Windows

<lang bbcbasic> order% = 8 

     size% = 2^order%
     VDU 23,22,size%;size%;8,8,16,128
     FOR Y% = 0 TO size%-1
       FOR X% = 0 TO size%-1
         IF (X% AND Y%)=0 PLOT X%*2,Y%*2
       NEXT
     NEXT Y%

</lang>

C

Code lifted from Dragon curve. Given a depth n, draws a triangle of size 2^n in a PNM file to the standard output. Usage: gcc -lm stuff.c -o sierp; ./sierp 9 > triangle.pnm. Sample image generated with depth 9. Generated image's size depends on the depth: it plots dots, but does not draw lines, so a large size with low depth is not possible.

<lang C>#include <stdio.h>

  1. include <stdlib.h>
  2. include <string.h>
  3. include <math.h>

long long x, y, dx, dy, scale, clen, cscale; typedef struct { double r, g, b; } rgb; rgb ** pix;

void sc_up() { scale *= 2; x *= 2; y *= 2; cscale *= 3; }

void h_rgb(long long x, long long y) { rgb *p = &pix[y][x];

  1. define SAT 1

double h = 6.0 * clen / cscale; double VAL = 1; double c = SAT * VAL; double X = c * (1 - fabs(fmod(h, 2) - 1));

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 iter_string(const char * str, int d) { long long len; while (*str != '\0') { switch(*(str++)) { case 'X': if (d) iter_string("XHXVX", d - 1); else{ clen ++; h_rgb(x/scale, y/scale); x += dx; y -= dy; } continue; case 'V': len = 1LLU << d; while (len--) { clen ++; h_rgb(x/scale, y/scale); y += dy; } continue; case 'H': len = 1LLU << d; while(len --) { clen ++; h_rgb(x/scale, y/scale); x -= dx; } continue; } } }

void sierp(long leng, int depth) { long i; long h = leng + 20, w = leng + 20;

/* allocate pixel buffer */ rgb *buf = malloc(sizeof(rgb) * w * h); pix = malloc(sizeof(rgb *) * h); for (i = 0; i < h; i++) pix[i] = buf + w * i; memset(buf, 0, sizeof(rgb) * w * h); 

       /* init coords; scale up to desired; exec string */

x = y = 10; dx = leng; dy = leng; scale = 1; clen = 0; cscale = 3; for (i = 0; i < depth; i++) sc_up(); iter_string("VXH", depth);

/* write color PNM file */ unsigned char *fpix = malloc(w * h * 3); double maxv = 0, *dbuf = (double*)buf;

for (i = 3 * w * h - 1; i >= 0; i--) if (dbuf[i] > maxv) maxv = dbuf[i]; for (i = 3 * h * w - 1; i >= 0; i--) fpix[i] = 255 * dbuf[i] / maxv;

printf("P6\n%ld %ld\n255\n", w, h); fflush(stdout); /* printf and fwrite may treat buffer differently */ fwrite(fpix, h * w * 3, 1, stdout); }

int main(int c, char ** v) { int size, depth;

depth = (c > 1) ? atoi(v[1]) : 10; size = 1 << depth;

fprintf(stderr, "size: %d depth: %d\n", size, depth); sierp(size, depth + 2);

return 0; }</lang>

C++

<lang cpp>

  1. include <windows.h>
  2. include <string>
  3. include <iostream>

const int BMP_SIZE = 612;

class myBitmap { public: 

   myBitmap() : pen( NULL ), brush( NULL ), clr( 0 ), wid( 1 ) {}
   ~myBitmap() {
       DeleteObject( pen ); DeleteObject( brush );
       DeleteDC( hdc ); DeleteObject( bmp );
   }
   bool create( int w, int h ) {
       BITMAPINFO bi;
       ZeroMemory( &bi, sizeof( bi ) );
       bi.bmiHeader.biSize        = sizeof( bi.bmiHeader );
       bi.bmiHeader.biBitCount    = sizeof( DWORD ) * 8;
       bi.bmiHeader.biCompression = BI_RGB;
       bi.bmiHeader.biPlanes      = 1;
       bi.bmiHeader.biWidth       =  w;
       bi.bmiHeader.biHeight      = -h;
       HDC dc = GetDC( GetConsoleWindow() );
       bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 );
       if( !bmp ) return false;
       hdc = CreateCompatibleDC( dc );
       SelectObject( hdc, bmp );
       ReleaseDC( GetConsoleWindow(), dc );
       width = w; height = h;
       return true;
   }
   void clear( BYTE clr = 0 ) {
       memset( pBits, clr, width * height * sizeof( DWORD ) );
   }
   void setBrushColor( DWORD bClr ) {
       if( brush ) DeleteObject( brush );
       brush = CreateSolidBrush( bClr );
       SelectObject( hdc, brush );
   }
   void setPenColor( DWORD c ) {
       clr = c; createPen();
   }
   void setPenWidth( int w ) {
       wid = w; createPen();
   }
   void saveBitmap( std::string path ) {
       BITMAPFILEHEADER fileheader;
       BITMAPINFO       infoheader;
       BITMAP           bitmap;
       DWORD            wb;
       GetObject( bmp, sizeof( bitmap ), &bitmap );
       DWORD* dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight];
       ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) );
       ZeroMemory( &infoheader, sizeof( BITMAPINFO ) );
       ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );
       infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
       infoheader.bmiHeader.biCompression = BI_RGB;
       infoheader.bmiHeader.biPlanes = 1;
       infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader );
       infoheader.bmiHeader.biHeight = bitmap.bmHeight;
       infoheader.bmiHeader.biWidth = bitmap.bmWidth;
       infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );
       fileheader.bfType    = 0x4D42;
       fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER );
       fileheader.bfSize    = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;
       GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );
       HANDLE file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS, 
                                 FILE_ATTRIBUTE_NORMAL, NULL );
       WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL );
       WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL );
       WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL );
       CloseHandle( file );
       delete [] dwpBits;
   }
   HDC getDC() const     { return hdc; }
   int getWidth() const  { return width; }
   int getHeight() const { return height; }

private: 

   void createPen() {
       if( pen ) DeleteObject( pen );
       pen = CreatePen( PS_SOLID, wid, clr );
       SelectObject( hdc, pen );
   }
   HBITMAP bmp; HDC    hdc;
   HPEN    pen; HBRUSH brush;
   void    *pBits; int    width, height, wid;
   DWORD    clr;

}; class sierpinski { public: 

   void draw( int o ) {
       colors[0] = 0xff0000; colors[1] = 0x00ff33; colors[2] = 0x0033ff;
       colors[3] = 0xffff00; colors[4] = 0x00ffff; colors[5] = 0xffffff;
       bmp.create( BMP_SIZE, BMP_SIZE ); HDC dc = bmp.getDC(); 
       drawTri( dc, 0, 0, ( float )BMP_SIZE, ( float )BMP_SIZE, o / 2 );
       bmp.setPenColor( colors[0] ); MoveToEx( dc, BMP_SIZE >> 1, 0, NULL ); 
       LineTo( dc, 0, BMP_SIZE - 1 ); LineTo( dc, BMP_SIZE - 1, BMP_SIZE - 1 );
       LineTo( dc, BMP_SIZE >> 1, 0 ); bmp.saveBitmap( "./st.bmp" );
   }

private: 

   void drawTri( HDC dc, float l, float t, float r, float b, int i ) {
       float w = r - l, h = b - t, hh = h / 2.f, ww = w / 4.f; 
       if( i ) {
           drawTri( dc, l + ww, t, l + ww * 3.f, t + hh, i - 1 );
           drawTri( dc, l, t + hh, l + w / 2.f, t + h, i - 1 );
           drawTri( dc, l + w / 2.f, t + hh, l + w, t + h, i - 1 );
       }
       bmp.setPenColor( colors[i % 6] );
       MoveToEx( dc, ( int )( l + ww ),          ( int )( t + hh ), NULL );
       LineTo  ( dc, ( int )( l + ww * 3.f ),    ( int )( t + hh ) );
       LineTo  ( dc, ( int )( l + ( w / 2.f ) ), ( int )( t + h ) );
       LineTo  ( dc, ( int )( l + ww ),          ( int )( t + hh ) );
   }
   myBitmap bmp;
   DWORD colors[6];

}; int main(int argc, char* argv[]) { 

   sierpinski s; s.draw( 12 );
   return 0;

} </lang>

D

The output image is the same as the Go version. This requires the module from the Grayscale image Task.

Translation of: Go

<lang d>void main() { 

   import grayscale_image;

   enum order = 8,
        margin = 10,
        width = 2 ^^ order;

   auto im = new Image!Gray(width + 2 * margin, width + 2 * margin);
   im.clear(Gray.white);

   foreach (immutable y; 0 .. width)
       foreach (immutable x; 0 .. width)
           if ((x & y) == 0)
               im[x + margin, y + margin] = Gray.black;
   im.savePGM("sierpinski.pgm");

}</lang>

ERRE

<lang ERRE> PROGRAM SIERPINSKY

!$INCLUDE="PC.LIB"

BEGIN 

  ORDER%=8
  SIZE%=2^ORDER%
  SCREEN(9)
  GR_WINDOW(0,0,520,520)
  FOR Y%=0 TO SIZE%-1 DO
    FOR X%=0 TO SIZE%-1 DO
       IF (X% AND Y%)=0 THEN PSET(X%*2,Y%*2,2) END IF
    END FOR
  END FOR
  GET(K$)

END PROGRAM </lang>

FreeBASIC

<lang FreeBASIC>' version 06-07-2015 ' compile with: fbc -s console or with: fbc -s gui

  1. Define black 0
  2. Define white RGB(255,255,255)

Dim As Integer x, y Dim As Integer order = 9 Dim As Integer size = 2 ^ order

ScreenRes size, size, 32 Line (0,0) - (size -1, size -1), black, bf

For y = 0 To size -1 

   For x = 0 To size -1
       If (x And y) = 0 Then PSet(x, y)    ' ,white
   Next

Next

' empty keyboard buffer While Inkey <> "" : Var _key_ = Inkey : Wend WindowTitle "Hit any key to end program" Sleep End</lang>

gnuplot

Generating X,Y coordinates by the ternary digits of parameter t.

<lang gnuplot># triangle_x(n) and triangle_y(n) return X,Y coordinates for the

  1. Sierpinski triangle point number n, for integer n.

triangle_x(n) = (n > 0 ? 2*triangle_x(int(n/3)) + digit_to_x(int(n)%3) : 0) triangle_y(n) = (n > 0 ? 2*triangle_y(int(n/3)) + digit_to_y(int(n)%3) : 0) digit_to_x(d) = (d==0 ? 0 : d==1 ? -1 : 1) digit_to_y(d) = (d==0 ? 0 : 1)

  1. Plot the Sierpinski triangle to "level" many replications.
  2. "trange" and "samples" are chosen so the parameter t runs through
  3. integers t=0 to 3**level-1, inclusive.

level=6 set trange [0:3**level-1] set samples 3**level set parametric set key off plot triangle_x(t), triangle_y(t) with points</lang>

Go

Output png
Translation of: Icon and Unicon

<lang go>package main

import ( 

   "fmt"
   "image"
   "image/color"
   "image/draw"
   "image/png"
   "os"

)

func main() { 

   const order = 8
   const width = 1 << order
   const margin = 10
   bounds := image.Rect(-margin, -margin, width+2*margin, width+2*margin)
   im := image.NewGray(bounds)
   gBlack := color.Gray{0}
   gWhite := color.Gray{255}
   draw.Draw(im, bounds, image.NewUniform(gWhite), image.ZP, draw.Src)

   for y := 0; y < width; y++ {
       for x := 0; x < width; x++ {
           if x&y == 0 {
               im.SetGray(x, y, gBlack)
           }
       }
   }
   f, err := os.Create("sierpinski.png")
   if err != nil {
       fmt.Println(err)
       return
   }
   if err = png.Encode(f, im); err != nil {
       fmt.Println(err)
   }
   if err = f.Close(); err != nil {
       fmt.Println(err)
   }

}</lang>

Haskell

This program uses the diagrams package to produce the Sierpinski triangle. The package implements an embedded DSL for producing vector graphics. Depending on the command-line arguments, the program can generate SVG, PNG, PDF or PostScript output.

For fun, we take advantage of Haskell's layout rules, and the operators provided by the diagrams package, to give the reduce function the shape of a triangle. It could also be written as reduce t = t === (t ||| t).

The command to produce the SVG output is sierpinski -o Sierpinski-Haskell.svg.

Sierpinski Triangle

<lang haskell>import Diagrams.Prelude import Diagrams.Backend.Cairo.CmdLine

triangle = eqTriangle # fc black # lw 0

reduce t = t 

             ===
          (t ||| t)

sierpinski = iterate reduce triangle

main = defaultMain $ sierpinski !! 7 </lang>

Icon and Unicon

The following code is adapted from a program by Ralph Griswold that demonstrates an interesting way to draw the Sierpinski Triangle. Given an argument of the order it will calculate the canvas size needed with margin. It will not stop you from asking for a triangle larger than you display. For an explanation, see "Chaos and Fractals", Heinz-Otto Peitgen, Harmut Jurgens, and Dietmar Saupe, Springer-Verlag, 1992, pp. 132-134.

Sample Output for order=8

<lang Icon>link wopen

procedure main(A) 

  local width, margin, x, y
  
  width := 2 ^ (order := (0 < integer(\A[1])) | 8)
  wsize := width + 2 * (margin := 30 )
  WOpen("label=Sierpinski", "size="||wsize||","||wsize) | 
     stop("*** cannot open window")

  every y := 0 to width - 1 do
     every x := 0 to width - 1 do
        if iand(x, y) = 0 then DrawPoint(x + margin, y + margin)

 Event()

end</lang>

Library: Icon Programming Library

Original source IPL Graphics/sier1.

J

Solution: <lang j> load 'viewmat' 

  'rgb'viewmat--. |. (~:_1&|.)^:(<@#) (2^8){.1

</lang>

or

<lang j> load'viewmat' viewmat(,~,.~)^:8,1 </lang>

Java

Solution: <lang java>import javax.swing.*; import java.awt.*;

/**

  • SierpinskyTriangle.java
  • Draws a SierpinskyTriangle in a JFrame
  • The order of complexity is given from command line, but
  • defaults to 3
  • @author Istarnion
  • /

class SierpinskyTriangle {

public static void main(String[] args) { int i = 3; // Default to 3 if(args.length >= 1) { try { i = Integer.parseInt(args[0]); } catch(NumberFormatException e) { System.out.println("Usage: 'java SierpinskyTriangle [level]'\nNow setting level to "+i); } } final int level = i;

JFrame frame = new JFrame("Sierpinsky Triangle - Java"); frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

JPanel panel = new JPanel() { @Override public void paintComponent(Graphics g) { g.setColor(Color.BLACK); drawSierpinskyTriangle(level, 20, 20, 360, (Graphics2D)g); } };

panel.setPreferredSize(new Dimension(400, 400));

frame.add(panel); frame.pack(); frame.setResizable(false); frame.setLocationRelativeTo(null); frame.setVisible(true); }

private static void drawSierpinskyTriangle(int level, int x, int y, int size, Graphics2D g) { if(level <= 0) return;

g.drawLine(x, y, x+size, y); g.drawLine(x, y, x, y+size); g.drawLine(x+size, y, x, y+size);

drawSierpinskyTriangle(level-1, x, y, size/2, g); drawSierpinskyTriangle(level-1, x+size/2, y, size/2, g); drawSierpinskyTriangle(level-1, x, y+size/2, size/2, g); } }</lang> Animated version

Works with: Java version 8

<lang java>import java.awt.*; import java.awt.event.ActionEvent; import java.awt.geom.Path2D; import javax.swing.*;

public class SierpinskiTriangle extends JPanel { 

   private final int dim = 512;
   private final int margin = 20;

   private int limit = dim;

   public SierpinskiTriangle() {
       setPreferredSize(new Dimension(dim + 2 * margin, dim + 2 * margin));
       setBackground(Color.white);
       setForeground(Color.green.darker());

       new Timer(2000, (ActionEvent e) -> {
           limit /= 2;
           if (limit <= 2)
               limit = dim;
           repaint();
       }).start();
   }

   void drawTriangle(Graphics2D g, int x, int y, int size) {
       if (size <= limit) {
           Path2D p = new Path2D.Float();
           p.moveTo(x, y);
           p.lineTo(x + size / 2, y + size);
           p.lineTo(x - size / 2, y + size);
           g.fill(p);
       } else {
           size /= 2;
           drawTriangle(g, x, y, size);
           drawTriangle(g, x + size / 2, y + size, size);
           drawTriangle(g, x - size / 2, y + size, size);
       }
   }

   @Override
   public void paintComponent(Graphics gg) {
       super.paintComponent(gg);
       Graphics2D g = (Graphics2D) gg;
       g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
               RenderingHints.VALUE_ANTIALIAS_ON);
       g.translate(margin, margin);
       drawTriangle(g, dim / 2, 0, dim);
   }

   public static void main(String[] args) {
       SwingUtilities.invokeLater(() -> {
           JFrame f = new JFrame();
           f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
           f.setTitle("Sierpinski Triangle");
           f.setResizable(false);
           f.add(new SierpinskiTriangle(), BorderLayout.CENTER);
           f.pack();
           f.setLocationRelativeTo(null);
           f.setVisible(true);
       });
   }

}</lang>

Kotlin

From Java code: <lang kotlin>import javax.swing.* import java.awt.*

fun main(args: Array<String>) { 

   var i = 8     // Default
   if (args.any())
       try {
           i = args.first().toInt()
       } catch (e: NumberFormatException) {
           i = 8
           println("Usage: 'java SierpinskyTriangle [level]'\nNow setting level to $i")
       }

   object : JFrame("Sierpinsky Triangle - Kotlin") {
       val panel = object : JPanel() {
           val size = 800

           init {
               preferredSize = Dimension(size, size)
           }

           public override fun paintComponent(g: Graphics) {
               g.color = Color.BLACK
               if (g is Graphics2D)
                   g.drawSierpinskyTriangle(i, 20, 20, size - 40)
           }
       }

       init {
           defaultCloseOperation = JFrame.EXIT_ON_CLOSE
           add(panel)
           pack()
           isResizable = false
           setLocationRelativeTo(null)
           isVisible = true
       }
   }

}

internal fun Graphics2D.drawSierpinskyTriangle(level: Int, x: Int, y: Int, size: Int) { 

   if (level > 0) {
       drawLine(x, y, x + size, y)
       drawLine(x, y, x, y + size)
       drawLine(x + size, y, x, y + size)

       drawSierpinskyTriangle(level - 1, x, y, size / 2)
       drawSierpinskyTriangle(level - 1, x + size / 2, y, size / 2)
       drawSierpinskyTriangle(level - 1, x, y + size / 2, size / 2)
   }

}</lang>

Liberty BASIC

The ability of LB to handle very large integers makes the Pascal triangle method very attractive. If you alter the rem'd line you can ask it to print the last, central term... <lang lb> nomainwin

open "test" for graphics_nsb_fs as #gr

  1. gr "trapclose quit"
  2. gr "down; home"
  3. gr "posxy cx cy"

order =10

w =cx *2: h =cy *2

dim a( h, h) 'line, col

  1. gr "trapclose quit"
  2. gr "down; home"

a( 1, 1) =1

for i = 2 to 2^order -1 

   scan
   a( i, 1) =1
   a( i, i) =1
   for j = 2 to i -1
       'a(i,j)=a(i-1,j-1)+a(i-1,j)         'LB is quite capable for crunching BIG numbers
       a( i, j) =(a( i -1, j -1) +a( i -1, j)) mod 2  'but for this task, last bit is enough (and it much faster)
   next
   for j = 1 to i
       if a( i, j) mod 2 then #gr "set "; cx +j -i /2; " "; i
   next

next

  1. gr "flush"

wait

sub quit handle$ 

   close #handle$
   end

end sub </lang> Up to order 10 displays on a 1080 vertical pixel screen.


This will draw a graphical Sierpinski gasket using turtle graphics. <lang logo>to sierpinski :n :length 

 if :n = 0 [stop]
 repeat 3 [sierpinski :n-1 :length/2  fd :length rt 120]

end seth 30 sierpinski 5 200</lang>

Lua

Library: LÖVE

<lang Lua>-- The argument 'tri' is a list of co-ords: {x1, y1, x2, y2, x3, y3} function sierpinski (tri, order) 

   local new, p, t = {}
   if order > 0 then
       for i = 1, #tri do
           p = i + 2
           if p > #tri then p = p - #tri end
           new[i] = (tri[i] + tri[p]) / 2
       end
       sierpinski({tri[1],tri[2],new[1],new[2],new[5],new[6]}, order-1)
       sierpinski({new[1],new[2],tri[3],tri[4],new[3],new[4]}, order-1)
       sierpinski({new[5],new[6],new[3],new[4],tri[5],tri[6]}, order-1)
   else
       love.graphics.polygon("fill", tri)
   end

end

-- Callback function used to draw on the screen every frame function love.draw () 

   sierpinski({400, 100, 700, 500, 100, 500}, 7)

end</lang>

Mathematica

<lang Mathematica>Sierpinski[n_] :=Nest[Flatten[Table[{{ 

      #i, 1, (#i, 1 + #i, 2)/2, (#i, 1 + #i, 3)/
       2}, {(#i, 1 + #i, 2)/2, #[[i, 
       2]], (#i, 2 + #i, 3)/2}, {(#i, 1 + #i, 3)/
       2, (#i, 2 + #i, 3)/2, #i, 3}}, {i, Length[#]}], 
   1] &, {{{0, 0}, {1/2, 1}, {1, 0}}}, n]

Show[Graphics[{Opacity[1], Black, Map[Polygon, Sierpinski[8], 1]}, AspectRatio -> 1]]</lang>

<lang Mathematica>sierpinski[v_, 0] := Polygon@v; sierpinski[v_, n_] := sierpinski[#, n - 1] & /@ (Mean /@ # & /@ v~Tuples~2~Partition~3); Graphics@sierpinski[N@{{0, 0}, {1, 0}, {.5, .8}}, 3]</lang>

<lang Mathematica>sierpinski = Map[Mean, Partition[Tuples[#, 2], 3], {2}] &; p = Nest[Join @@ sierpinski /@ # &, {{{0, 0}, {1, 0}, {.5, .8}}}, 3]; Graphics[Polygon@p]</lang>

OCaml

<lang ocaml>open Graphics

let round v = 

 int_of_float (floor (v +. 0.5))

let middle (x1, y1) (x2, y2) = 

 ((x1 +. x2) /. 2.0,
  (y1 +. y2) /. 2.0)

let draw_line (x1, y1) (x2, y2) = 

 moveto (round x1) (round y1);
 lineto (round x2) (round y2);

let draw_triangle (p1, p2, p3) = 

 draw_line p1 p2;
 draw_line p2 p3;
 draw_line p3 p1;

let () = 

 open_graph "";
 let width = float (size_x ()) in
 let height = float (size_y ()) in
 let pad = 20.0 in
 let initial_triangle =
   ( (pad, pad),
     (width -. pad, pad),
     (width /. 2.0, height -. pad) )
 in
 let rec loop step tris =
   if step <= 0 then tris else
     loop (pred step) (
       List.fold_left (fun acc (p1, p2, p3) ->
         let m1 = middle p1 p2
         and m2 = middle p2 p3
         and m3 = middle p3 p1 in
         let tri1 = (p1, m1, m3)
         and tri2 = (p2, m2, m1)
         and tri3 = (p3, m3, m2) in
         tri1 :: tri2 :: tri3 :: acc
       ) [] tris
     )
 in
 let res = loop 6 [ initial_triangle ] in
 List.iter draw_triangle res;
 ignore (read_key ())</lang>

run with: 

ocaml graphics.cma sierpinski.ml

Perl

Writes out an EPS given an arbitrary triangle. The perl code only calculates the bounding box, while real work is done in postscript. <lang Perl>use List::Util qw'min max sum';

sub write_eps { my @x = @_[0, 2, 4]; my @y = @_[1, 3, 5]; my $sx = sum(@x) / 3; my $sy = sum(@y) / 3; @x = map { $_ - $sx } @x; @y = map { $_ - $sy } @y;

print <<"HEAD"; %!PS-Adobe-3.0 %%BoundingBox: @{[min(@x) - 10]} @{[min(@y) - 10]} @{[max(@x) + 10]} @{[max(@y) + 10]} /v1 { $x[0] $y[0] } def /v2 { $x[1] $y[1] } def /v3 { $x[2] $y[2] } def /t { translate } def /r { .5 .5 scale 2 copy t 2 index sierp pop neg exch neg exch t 2 2 scale } def

/sierp { dup 1 sub dup 0 ne { v1 r v2 r v3 r } { v1 moveto v2 lineto v3 lineto} ifelse pop } def

9 sierp fill pop showpage %%EOF HEAD }

write_eps 0, 0, 300, 215, -25, 200;</lang>

Perl 6

This is a recursive solution. It is not really practical for more than 8 levels of recursion, but anything more than 7 is barely visible anyway. <lang perl6>my $side = 512; my $height = get_height($side); my $levels = 8;

sub get_height ($side) { $side * 3.sqrt / 2 }

sub triangle ( $x1, $y1, $x2, $y2, $x3, $y3, $fill?, $animate? ) { 

   print "<polygon points=\"$x1,$y1 $x2,$y2 $x3,$y3\"";
   if $fill { print " style=\"fill: $fill; stroke-width: 0;\"" };
   if $animate 
   {
       say ">\n  <animate attributeType=\"CSS\" attributeName=\"opacity\"\n  values=\"1;0;1\""
         ~ " keyTimes=\"0;.5;1\" dur=\"20s\" repeatCount=\"indefinite\" />\n</polygon>"
   }
   else
   {        
      say ' />';
   }

}

sub fractal ( $x1, $y1, $x2, $y2, $x3, $y3, $r is copy ) { 

    triangle( $x1, $y1, $x2, $y2, $x3, $y3 );
    return unless --$r;
    my $side = abs($x3 - $x2) / 2;
    my $height = get_height($side);
    fractal( $x1, $y1-$height*2, $x1-$side/2, $y1-3*$height, $x1+$side/2, $y1-3*$height, $r);
    fractal( $x2, $y1, $x2-$side/2, $y1-$height, $x2+$side/2, $y1-$height, $r);
    fractal( $x3, $y1, $x3-$side/2, $y1-$height, $x3+$side/2, $y1-$height, $r);

}

say '<?xml version="1.0" standalone="no"?> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"> <svg width="100%" height="100%" version="1.1" xmlns="http://www.w3.org/2000/svg"> <defs> 

 <radialGradient id="basegradient" cx="50%" cy="65%" r="50%" fx="50%" fy="65%">
   <stop offset="10%" stop-color="#ff0" />
   <stop offset="60%" stop-color="#f00" />
   <stop offset="99%" stop-color="#00f" />
 </radialGradient>

</defs>';

triangle( $side/2, 0, 0, $height, $side, $height, 'url(#basegradient)' ); triangle( $side/2, 0, 0, $height, $side, $height, '#000', 'animate' ); say '<g style="fill: #fff; stroke-width: 0;">'; fractal( $side/2, $height, $side*3/4, $height/2, $side/4, $height/2, $levels ); say '</g></svg>';</lang>

PicoLisp

Slight modification of the text version, requires ImageMagick's display: <lang PicoLisp>(de sierpinski (N) 

  (let (D '("1")  S "0")
     (do N
        (setq
           D (conc
              (mapcar '((X) (pack S X S)) D)
              (mapcar '((X) (pack X "0" X)) D) )
           S (pack S S) ) )
     D ) )

(out '(display -) 

  (let Img (sierpinski 7)
     (prinl "P1")
     (prinl (length (car Img)) " " (length Img))
     (mapc prinl Img) ) )

</lang>

PostScript

<lang PostScript>%!PS

/sierp { % level ax ay bx by cx cy 

   6 cpy triangle
   sierpr

} bind def

/sierpr { 

   12 cpy
   10 -4 2 {
       5 1 roll exch 4 -1 roll
       add 0.5 mul 3 1 roll
       add 0.5 mul 3 -1 roll
       2 roll
   } for       % l a b c bc ac ab
   13 -1 roll dup 0 gt {
       1 sub
       dup 4 cpy 18 -2 roll sierpr
       dup 7 index 7 index 2 cpy 16 -2 roll sierpr
       9 3 roll 1 index 1 index 2 cpy 13 4 roll sierpr
   } { 13 -6 roll 7 { pop } repeat } ifelse
   triangle

} bind def

/cpy { { 5 index } repeat } bind def

/triangle { 

   newpath moveto lineto lineto closepath stroke

} bind def

6 50 100 550 100 300 533 sierp showpage</lang>

Prolog

Works with SWI-Prolog and XPCE.

Recursive version

Works up to sierpinski(13). <lang Prolog>sierpinski(N) :- sformat(A, 'Sierpinski order ~w', [N]), new(D, picture(A)), draw_Sierpinski(D, N, point(350,50), 600), send(D, size, size(690,690)), send(D, open).

draw_Sierpinski(Window, 1, point(X, Y), Len) :- X1 is X - round(Len/2), X2 is X + round(Len/2), Y1 is Y + Len * sqrt(3) / 2, send(Window, display, new(Pa, path)), 

       (

send(Pa, append, point(X, Y)), send(Pa, append, point(X1, Y1)), send(Pa, append, point(X2, Y1)), send(Pa, closed, @on), send(Pa, fill_pattern, colour(@default, 0, 0, 0)) ).


draw_Sierpinski(Window, N, point(X, Y), Len) :- Len1 is round(Len/2), X1 is X - round(Len/4), X2 is X + round(Len/4), Y1 is Y + Len * sqrt(3) / 4, N1 is N - 1, draw_Sierpinski(Window, N1, point(X, Y), Len1), draw_Sierpinski(Window, N1, point(X1, Y1), Len1), draw_Sierpinski(Window, N1, point(X2, Y1), Len1).</lang>

Iterative version

<lang Prolog>:- dynamic top/1.

sierpinski_iterate(N) :- retractall(top(_)), sformat(A, 'Sierpinski order ~w', [N]), new(D, picture(A)), draw_Sierpinski_iterate(D, N, point(550, 50)), send(D, open).

draw_Sierpinski_iterate(Window, N, point(X,Y)) :- assert(top([point(X,Y)])), NbTours is 2 ** (N - 1), % Size is given here to preserve the "small" triangles when N is big Len is 10, forall(between(1, NbTours, _I), ( retract(top(Lst)), assert(top([])), forall(member(P, Lst), draw_Sierpinski(Window, P, Len)))).

draw_Sierpinski(Window, point(X, Y), Len) :- X1 is X - round(Len/2), X2 is X + round(Len/2), Y1 is Y + round(Len * sqrt(3) / 2), send(Window, display, new(Pa, path)), 

       (

send(Pa, append, point(X, Y)), send(Pa, append, point(X1, Y1)), send(Pa, append, point(X2, Y1)), send(Pa, closed, @on), send(Pa, fill_pattern, colour(@default, 0, 0, 0)) ), retract(top(Lst)), ( member(point(X1, Y1), Lst) -> select(point(X1,Y1), Lst, Lst1) ; Lst1 = [point(X1, Y1)|Lst]),

( member(point(X2, Y1), Lst1) -> select(point(X2,Y1), Lst1, Lst2) ; Lst2 = [point(X2, Y1)|Lst1]),

assert(top(Lst2)).</lang>

Python

Library: Numpy
Library: Turtle

<lang python>#!/usr/bin/env python

  2. import necessary modules
  3. ------------------------

from numpy import * import turtle

  2. Functions defining the drawing actions
  3. (used by the function DrawSierpinskiTriangle).
  4. ----------------------------------------------

def Left(turn, point, fwd, angle, turt): turt.left(angle) return [turn, point, fwd, angle, turt] def Right(turn, point, fwd, angle, turt): turt.right(angle) return [turn, point, fwd, angle, turt] def Forward(turn, point, fwd, angle, turt): turt.forward(fwd) return [turn, point, fwd, angle, turt] </lang> <lang python>##########################################################################################

  1. The drawing function
  2. --------------------
  4. level level of Sierpinski triangle (minimum value = 1)
  5. ss screensize (Draws on a screen of size ss x ss. Default value = 400.)
  6. -----------------------------------------------------------------------------------------

def DrawSierpinskiTriangle(level, ss=400): # typical values turn = 0 # initial turn (0 to start horizontally) angle=60.0 # in degrees

# Initialize the turtle turtle.hideturtle() turtle.screensize(ss,ss) turtle.penup() turtle.degrees()

# The starting point on the canvas fwd0 = float(ss) point=array([-fwd0/2.0, -fwd0/2.0])

# Setting up the Lindenmayer system # Assuming that the triangle will be drawn in the following way: # 1.) Start at a point # 2.) Draw a straight line - the horizontal line (H) # 3.) Bend twice by 60 degrees to the left (--) # 4.) Draw a straight line - the slanted line (X) # 5.) Bend twice by 60 degrees to the left (--) # 6.) Draw a straight line - another slanted line (X) # This produces the triangle in the first level. (so the axiom to begin with is H--X--X) # 7.) For the next level replace each horizontal line using # X->XX # H -> H--X++H++X--H # The lengths will be halved.


decode = {'-':Left, '+':Right, 'X':Forward, 'H':Forward} axiom = 'H--X--X'

# Start the drawing turtle.goto(point[0], point[1]) turtle.pendown() turtle.hideturtle() turt=turtle.getpen() startposition=turt.clone()

# Get the triangle in the Lindenmayer system fwd = fwd0/(2.0**level) path = axiom for i in range(0,level): path=path.replace('X','XX') path=path.replace('H','H--X++H++X--H')

# Draw it. for i in path: [turn, point, fwd, angle, turt]=decode[i](turn, point, fwd, angle, turt)

DrawSierpinskiTriangle(5) </lang>

Racket

<lang Racket>

  1. lang racket

(require 2htdp/image) (define (sierpinski n) 

 (if (zero? n)
   (triangle 2 'solid 'red)
   (let ([t (sierpinski (- n 1))])
     (freeze (above t (beside t t))))))

</lang> Test: <lang racket>

the following will show the graphics if run in DrRacket

(sierpinski 8)

or use this to dump the image into a file, shown on the right

(require file/convertible) (display-to-file (convert (sierpinski 8) 'png-bytes) "sierpinski.png") </lang>

Ruby

Library: Shoes

<lang ruby>Shoes.app(:height=>540,:width=>540, :title=>"Sierpinski Triangle") do 

 def triangle(slot, tri, color)
   x, y, len = tri
   slot.append do
     fill color
     shape do
       move_to(x,y)
       dx = len * Math::cos(Math::PI/3)
       dy = len * Math::sin(Math::PI/3)
       line_to(x-dx, y+dy)
       line_to(x+dx, y+dy)
       line_to(x,y)
     end
   end
 end
 @s = stack(:width => 520, :height => 520) {}
 @s.move(10,10)

 length = 512
 @triangles = length/2,0,length
 triangle(@s, @triangles[0], rgb(0,0,0))

 @n = 1
 animate(1) do
   if @n <= 7
     @triangles = @triangles.inject([]) do |sum, (x, y, len)|
       dx = len/2 * Math::cos(Math::PI/3)
       dy = len/2 * Math::sin(Math::PI/3)
       triangle(@s, [x, y+2*dy, -len/2], rgb(255,255,255))
       sum += [[x, y, len/2], [x-dx, y+dy, len/2], [x+dx, y+dy, len/2]]
     end
   end
   @n += 1
 end

 keypress do |key|
   case key
   when :control_q, "\x11" then exit
   end
 end

end</lang>

Run BASIC

<lang runbasic>graphic #g, 300,300 order = 8 width = 100 w = width * 11 dim canvas(w,w) canvas(1,1) = 1

for x = 2 to 2^order -1 

   canvas(x,1) = 1
   canvas(x,x) = 1
   for y = 2 to x -1
       canvas( x, y) = (canvas(x -1,y -1) + canvas(x -1, y)) mod 2
       if canvas(x,y) mod 2 then #g "set "; width + (order*3) + y - x / 2;" "; x
   next y

next x render #g

  1. g "flush"

wait</lang>

Seed7

<lang seed7>$ include "seed7_05.s7i"; 

 include "draw.s7i";
 include "keybd.s7i";

const proc: main is func 

 local
   const integer: order is 8;
   const integer: width is 1 << order;
   const integer: margin is 10;
   var integer: x is 0;
   var integer: y is 0;
 begin
   screen(width + 2 * margin, width + 2 * margin);
   clear(curr_win, white);
   KEYBOARD := GRAPH_KEYBOARD;
   for y range 0 to pred(width) do
     for x range 0 to pred(width) do
       if bitset conv x & bitset conv y = bitset.value then
         point(margin + x, margin + y, black);
       end if;
     end for;
   end for;
   ignore(getc(KEYBOARD));
 end func;</lang>

Original source: [1]

Sidef

<lang ruby>func sierpinski_triangle(n) -> Array { 

 var triangle = ['*']
 { |i|
   var sp = (' ' * Math.pow(2, i-1));
   triangle = (triangle.map {|x| sp + x + sp} +
               triangle.map {|x| x + ' ' + x})
 } * n
 triangle

}

class Array { 

 method to_png(scale=1, bgcolor='white', fgcolor='black') {

   var gd = (
     try   { require('GD::Simple') }
     catch { warn "GD::Simple is not installed!"; return }
   );

   var width = self.max_by{.len}.len
   self.map!{|r| "%-#{width}s" % r}

   var img = gd.new(width * scale, self.len * scale)

   for i in ^self {
     for j in RangeNum(i*scale, i*scale + scale) {
       var row = self[i]
       img.moveTo(0, j)
       var len = row.len
       while (len) {
         row.gsub!(/^\s+/)
         var color = bgcolor
         if (len == row.len) {
           row.gsub!(/^\S+/)
           color = fgcolor
         }
         img.fgcolor(color)
         var p = len-row.len
         len = row.len
         img.line(scale * p)
       }
     }
   }
   img.png
 }

}

var triangle = sierpinski_triangle(8) var raw_png = triangle.to_png(bgcolor:'black', fgcolor:'red')

var file = %f'triangle.png' var fh = file.open('>:raw') fh.print(raw_png) fh.close</lang>

Tcl

This code maintains a queue of triangles to cut out; though a stack works just as well, the observed progress is more visually pleasing when a queue is used.

Library: Tk

<lang tcl>package require Tcl 8.5 package require Tk

proc mean args {expr {[::tcl::mathop::+ {*}$args] / [llength $args]}} proc sierpinski {canv coords order} { 

   $canv create poly $coords -fill black -outline {}
   set queue [list [list {*}$coords $order]]
   while {[llength $queue]} {

lassign [lindex $queue 0] x1 y1 x2 y2 x3 y3 order set queue [lrange $queue 1 end] if {[incr order -1] < 0} continue set x12 [mean $x1 $x2]; set y12 [mean $y1 $y2] set x23 [mean $x2 $x3]; set y23 [mean $y2 $y3] set x31 [mean $x3 $x1]; set y31 [mean $y3 $y1] $canv create poly $x12 $y12 $x23 $y23 $x31 $y31 -fill white -outline {} update idletasks; # So we can see progress lappend queue [list $x1 $y1 $x12 $y12 $x31 $y31 $order] \ [list $x12 $y12 $x2 $y2 $x23 $y23 $order] \ [list $x31 $y31 $x23 $y23 $x3 $y3 $order] 

   }

}

pack [canvas .c -width 400 -height 400 -background white] update; # So we can see progress sierpinski .c {200 10 390 390 10 390} 7</lang>

TI-83 BASIC

<lang ti83b>:1→X:1→Y

Zdecimal
Horizontal 3.1
Vertical -4.5
While 1
X+1→X
DS<(Y,1
While 0
X→Y
1→X
End
If pxl-Test(Y-1,X) xor (pxl-Test(Y,X-1
PxlOn(Y,X
End</lang>

This could be made faster, but I just wanted to use the DS<( command

XPL0

<lang XPL0>include c:\cxpl\codes; \intrinsic 'code' declarations def Order=7, Size=1<<Order; int X, Y; [SetVid($13); \set 320x200 graphics video mode for Y:= 0 to Size-1 do 

   for X:= 0 to Size-1 do
       if (X&Y)=0 then Point(X, Y, 4\red\);

X:= ChIn(1); \wait for keystroke SetVid(3); \restore normal text display ]</lang>

zkl

Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl

Translation of: XPL0

<lang zkl>const Order=8, Size=(1).shiftLeft(Order); img:=PPM(300,300); foreach y,x in (Size,Size){ if(x.bitAnd(y)==0) img[x,y]=0xff0000 } img.write(File("sierpinskiTriangle.ppm","wb"));</lang>

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