Sunflower fractal

C

The colouring of the "fractal" is determined with every iteration to ensure that the resulting graphic looks similar to a real Sunflower, thus the parameter diskRatio determines the radius of the central disk as the maximum radius of the flower is known from the number of iterations. The scaling factor is currently hardcoded but can also be externalized. Requires the WinBGIm library.

<lang C> /*Abhishek Ghosh, 14th September 2018*/

include<graphics.h>
include<math.h>

define pi M_PI

void sunflower(int winWidth, int winHeight, double diskRatio, int iter){ double factor = .5 + sqrt(1.25),r,theta; double x = winWidth/2.0, y = winHeight/2.0; double maxRad = pow(iter,factor)/iter;

int i;

setbkcolor(LIGHTBLUE);

for(i=0;i<=iter;i++){ r = pow(i,factor)/iter;

r/maxRad < diskRatio?setcolor(BLACK):setcolor(YELLOW);

theta = 2*pi*factor*i; circle(x + r*sin(theta), y + r*cos(theta), 10 * i/(1.0*iter)); } }

int main() { initwindow(1000,1000,"Sunflower...");

sunflower(1000,1000,0.5,3000);

getch();

closegraph();

return 0; } </lang>

FreeBASIC

<lang freebasic> Const PI As Double = 4 * Atn(1) Const ancho = 400 Const alto = 400

Screenres ancho, alto, 8 Windowtitle" Pulsa una tecla para finalizar" Cls

Sub Sunflower(semillas As Integer)

   Dim As Double c = (Sqr(5)+1)/2
   
   For i As Integer = 0 To semillas
       Dim As Double r = (i^c) / semillas
       Dim As Double angulo = 2 * Pi * c * i
       Dim As Double x = r * Sin(angulo) + 200
       Dim As Double y = r * Cos(angulo) + 200
       
       Circle (x, y), i/semillas*10, i/semillas*10
   Next i

End Sub

Sunflower(2000) Bsave "sunflower_fractal.bmp",0 Sleep End </lang>

Go

Library: Go Graphics

Translation of: Ring

The image produced, when viewed with (for example) EOG, is similar to the Ring entry. <lang go>package main

import (

   "github.com/fogleman/gg"
   "math"

)

func main() {

   dc := gg.NewContext(400, 400)
   dc.SetRGB(1, 1, 1)
   dc.Clear()
   dc.SetRGB(0, 0, 1)
   c := (math.Sqrt(5) + 1) / 2
   numberOfSeeds := 3000
   for i := 0; i <= numberOfSeeds; i++ {
       fi := float64(i)
       fn := float64(numberOfSeeds)
       r := math.Pow(fi, c) / fn
       angle := 2 * math.Pi * c * fi
       x := r*math.Sin(angle) + 200
       y := r*math.Cos(angle) + 200
       fi /= fn / 5
       dc.DrawCircle(x, y, fi)
   }
   dc.SetLineWidth(1)
   dc.Stroke()
   dc.SavePNG("sunflower_fractal.png")

}</lang>

JavaScript

HTML to test

<!DOCTYPE html>
<html>
    <head>
        <meta charset="utf-8" />
        <meta http-equiv="X-UA-Compatible" content="IE=edge">
        <title>Vibrating rectangles</title>
        <meta name="viewport" content="width=device-width, initial-scale=1">
        <style>
            body{background-color:black;text-align:center;margin-top:150px}
        </style>
        <script src="sunflower.js"></script>
    </head>
    <body onload="start()">
        <div id='wnd'></div>
    </body>
</html>

<lang javascript> const SIZE = 400, HS = SIZE >> 1, WAIT = .005, SEEDS = 3000,

     TPI = Math.PI * 2, C = (Math.sqrt(10) + 1) / 2;

class Sunflower {

   constructor() {
       this.wait = WAIT;
       this.colorIndex = 0;
       this.dimension = 0;
       this.lastTime = 0;
       this.accumulator = 0;
       this.deltaTime = 1 / 60;
       this.colors = ["#ff0000", "#ff8000", "#ffff00", "#80ff00", "#00ff00", "#00ff80", 
                      "#00ffff", "#0080ff", "#0000ff", "#8000ff", "#ff00ff", "#ff0080"];
       this.canvas = document.createElement('canvas');
       this.canvas.width = SIZE;
       this.canvas.height = SIZE;
       const d = document.getElementById("wnd");
       d.appendChild(this.canvas);
       this.ctx = this.canvas.getContext('2d');
   }
   draw(clr, d) {
       let r = Math.pow(d, C) / SEEDS;
       let angle = TPI * C * d;
       let x = HS + r * Math.sin(angle), 
           y = HS + r * Math.cos(angle);
       this.ctx.strokeStyle = clr;
       this.ctx.beginPath();
       this.ctx.arc(x, y, d / (SEEDS / 50), 0, TPI);
       this.ctx.closePath();
       this.ctx.stroke();
   }
   update(dt) {
       if((this.wait -= dt) < 0) {
           this.draw(this.colors[this.colorIndex], this.dimension);
           this.wait = WAIT;
           if((this.dimension++) > 600) {
               this.dimension = 0;
               this.colorIndex = (this.colorIndex + 1) % this.colors.length;
           }
       }
   }
   start() {
       this.loop = (time) => {
           this.accumulator += (time - this.lastTime) / 1000;
           while(this.accumulator > this.deltaTime) {
               this.accumulator -= this.deltaTime;
               this.update(Math.min(this.deltaTime));
           }
           this.lastTime = time;
           requestAnimationFrame(this.loop);
       }
       this.loop(0);
   }

} function start() {

   const sunflower = new Sunflower();
   sunflower.start();

}

</lang>

Julia

Translation of: R

Run from REPL. <lang julia>using Makie

function sunflowerplot()

   len = 2000
   ϕ = 0.5 + sqrt(5) / 2
   r = LinRange(0.0, 100.0, len)
   θ = zeros(len)
   markersizes = zeros(Int, len)
   for i in 2:length(r)
       θ[i] = θ[i - 1] + 2π * ϕ
       markersizes[i] = div(i, 500) + 3
   end
   x = r .* cos.(θ)
   y = r .* sin.(θ)
   scene = Scene(backgroundcolor=:green)
   scatter!(scene, x, y, color=:gold, markersize=markersizes, strokewidth=1, fill=false, show_axis=false)

end

sunflowerplot() </lang>

Microsoft Small Basic

Translation of: Ring

<lang smallbasic>' Sunflower fractal - 24/07/2018

 GraphicsWindow.Width=410
 GraphicsWindow.Height=400
 c=(Math.SquareRoot(5)+1)/2
 numberofseeds=3000
 For i=0 To numberofseeds
   r=Math.Power(i,c)/numberofseeds
   angle=2*Math.Pi*c*i
   x=r*Math.Sin(angle)+200
   y=r*Math.Cos(angle)+200
   GraphicsWindow.DrawEllipse(x, y, i/numberofseeds*10, i/numberofseeds*10)
 EndFor </lang>

Output:

Sunflower fractal

Objeck

Translation of: C

<lang perl>use Game.SDL2; use Game.Framework;

class Test {

 @framework : GameFramework;
 @colors : Color[];
 
 function : Main(args : String[]) ~ Nil {
   Test->New()->Run();
 }
 
 New() {
   @framework := GameFramework->New(GameConsts->SCREEN_WIDTH, GameConsts->SCREEN_HEIGHT, "Test");
   @framework->SetClearColor(Color->New(0, 0, 0));
   @colors := Color->New[2];
   @colors[0] := Color->New(255,128,0); 
   @colors[1] := Color->New(255,255,25); 
 }
 
 method : Run() ~ Nil {
   if(@framework->IsOk()) {
     e := @framework->GetEvent();
     
     quit := false;
     while(<>quit) {
       # process input
       while(e->Poll() <> 0) {
         if(e->GetType() = EventType->SDL_QUIT) {
           quit := true;
         };
       };

       @framework->FrameStart();
       Render(525,525,0.50,3000);
       @framework->FrameEnd();
     };
   }
   else {
     "--- Error Initializing Environment ---"->ErrorLine();
     return;
   };

   leaving {
     @framework->Quit();
   };
 }

 method : Render(winWidth : Int, winHeight : Int, diskRatio : Float, iter : Int) ~ Nil {
   renderer := @framework->GetRenderer();

   @framework->Clear();

   factor := 0.5 + 1.25->SquareRoot();
   x := winWidth / 2.0;
   y := winHeight / 2.0;
   maxRad := Float->Power(iter, factor) / iter;

   for(i:=0;i<=iter;i+=1;) {
     r := Float->Power(i,factor)/iter;
     color := r/maxRad < diskRatio ? @colors[0] : @colors[1];
     theta := 2*Float->Pi()*factor*i;
     renderer->CircleColor(x + r*theta->Sin(), y + r*theta->Cos(), 10 * i/(1.0*iter), color);
   };
       
   @framework->Show();
 }

}

consts GameConsts {

 SCREEN_WIDTH := 640,
 SCREEN_HEIGHT := 480

} </lang>

Perl

Translation of: Sidef

<lang perl>use utf8; use constant π => 3.14159265; use constant φ => (1 + sqrt(5)) / 2;

my $scale = 600; my $seeds = 5*$scale;

print qq{<svg xmlns="http://www.w3.org/2000/svg" width="$scale" height="$scale" style="stroke:gold">

          <rect width="100%" height="100%" fill="black" />\n};

for $i (1..$seeds) {

   $r = 2 * ($i**φ) / $seeds;
   $t = 2 * π * φ * $i;
   $x = $r * sin($t) + $scale/2;
   $y = $r * cos($t) + $scale/2;
   printf qq{<circle cx="%.2f" cy="%.2f" r="%.1f" />\n}, $x, $y, sqrt($i)/13;

}

print "</svg>\n";</lang> See Phi-packing image (SVG image)

Perl 6

Works with: Rakudo version 2018.06

This is not really a fractal. It is more accurately an example of a Fibonacci spiral or Phi-packing.

Or, to be completely accurate: It is a variation of a generative Fermat's spiral using the Vogel model to implement phi-packing. See: https://thatsmaths.com/2014/06/05/sunflowers-and-fibonacci-models-of-efficiency

<lang perl6>use SVG;

my $seeds = 3000; my @center = 300, 300; my $scale = 5;

constant \φ = (3 - 5.sqrt) / 2;

my @c = map {

   my ($x, $y) = ($scale * .sqrt) «*« |cis($_ * φ * τ).reals »+« @center;
   [ $x.round(.01), $y.round(.01), (.sqrt * $scale / 100).round(.1) ]

}, 1 .. $seeds;

say SVG.serialize(

   svg => [
       :600width, :600height, :style<stroke:yellow>,
       :rect[:width<100%>, :height<100%>, :fill<black>],
       |@c.map( { :circle[:cx(.[0]), :cy(.[1]), :r(.[2])] } ),
   ],

);</lang> See: Phi packing (SVG image)

Phix

<lang Phix>constant numberofseeds = 3000

include pGUI.e

Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas

procedure cdCanvasCircle(cdCanvas cddbuffer, atom x, y, r)

   cdCanvasArc(cddbuffer,x,y,r,r,0,360)

end procedure

function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)

   integer {hw, hh} = sq_floor_div(IupGetIntInt(canvas, "DRAWSIZE"),2)
   atom s = min(hw,hh)/150,
        f = min(hw,hh)*8/125
   cdCanvasActivate(cddbuffer)
   cdCanvasClear(cddbuffer)
   atom c = (sqrt(5)+1)/2
   for i=0 to numberofseeds do
       atom r = power(i,c)/numberofseeds,
            angle = 2*PI*c*i,
            x = s*r*sin(angle)+hw,
            y = s*r*cos(angle)+hh
       cdCanvasCircle(cddbuffer,x,y,i/numberofseeds*f)
   end for 
   cdCanvasFlush(cddbuffer)
   return IUP_DEFAULT

end function

function map_cb(Ihandle ih)

   cdcanvas = cdCreateCanvas(CD_IUP, ih)
   cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
   cdCanvasSetBackground(cddbuffer, CD_WHITE)
   cdCanvasSetForeground(cddbuffer, CD_BLACK)
   return IUP_DEFAULT

end function

function esc_close(Ihandle /*ih*/, atom c)

   if c=K_ESC then return IUP_CLOSE end if
   return IUP_CONTINUE

end function

procedure main()

   IupOpen()
   
   canvas = IupCanvas(NULL)
   IupSetAttribute(canvas, "RASTERSIZE", "602x502") -- initial size
   IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))

   dlg = IupDialog(canvas)
   IupSetAttribute(dlg, "TITLE", "Sunflower")
   IupSetCallback(dlg, "K_ANY",     Icallback("esc_close"))
   IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))

   IupMap(dlg)
   IupSetAttribute(canvas, "RASTERSIZE", NULL) -- release the minimum limitation
   IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
   IupMainLoop()
   IupClose()

end procedure main()</lang>

R

<lang R> phi=1/2+sqrt(5)/2 r=seq(0,1,length.out=2000) theta=numeric(length(r)) theta[1]=0 for(i in 2:length(r)){

 theta[i]=theta[i-1]+phi*2*pi

} x=r*cos(theta) y=r*sin(theta) par(bg="black") plot(x,y) size=seq(.5,2,length.out = length(x)) thick=seq(.1,2,length.out = length(x)) for(i in 1:length(x)){

 points(x[i],y[i],cex=size[i],lwd=thick[i],col="goldenrod1")

} </lang>

Output:

Sunflower

Racket

Translation of: C

<lang racket>#lang racket

(require 2htdp/image)

(define N 3000) (define DISK-RATIO 0.5) (define factor (+ 0.5 (sqrt 1.25))) (define WIDTH 500) (define HEIGHT 500) (define max-rad (/ (expt N factor) N))

(for/fold ([image (empty-scene WIDTH HEIGHT)]) ([i (in-range N)])

 (define r (/ (expt i factor) N))
 (define color (if (< (/ r max-rad) DISK-RATIO) 'brown 'darkyellow))
 (define theta (* 2 pi factor i))
 (place-image (circle (* 10 i (/ 1 N)) 'outline color)
              (+ (/ WIDTH 2) (* r (sin theta)))
              (+ (/ HEIGHT 2) (* r (cos theta)))
              image))</lang>

Ring

Project : Sunflower fractal

load "guilib.ring"

paint = null

new qapp

       {
       win1 = new qwidget() {
                 setwindowtitle("Sunflower fractal")
                 setgeometry(100,100,320,500)
                 label1 = new qlabel(win1) {
                             setgeometry(10,10,400,400)
                             settext("")
                 }
                 new qpushbutton(win1) {
                         setgeometry(100,400,100,30)
                         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)
       }
       paint = new qpainter() {
                 begin(p1)
                 setpen(pen)

       c = (sqrt(5) + 1) / 2
       numberofseeds = 3000
       for i = 0 to numberofseeds
             r = pow(i, c ) / (numberofseeds)
             angle = 2 * 3.14 * c * i
             x = r * sin(angle) + 100
             y = r * cos(angle) + 100
            drawellipse(x, y, i / (numberofseeds / 10), i / (numberofseeds / 10))
       next

       endpaint()
       }
       label1 { setpicture(p1) show() }

</lang> Output:

Sunflower fractal

Sidef

Translation of: Go

<lang ruby>require('Imager')

func draw_sunflower(seeds=3000) {

   var img = %O<Imager>.new(
       xsize => 400,
       ysize => 400,
   )

   var c = (sqrt(1.25) + 0.5)
   { |i|
       var r = (i**c / seeds)
       var θ = (2 * Num.pi * c * i)
       var x = (r * sin(θ) + 200)
       var y = (r * cos(θ) + 200)
       img.circle(x => x, y => y, r => i/(5*seeds))
   } * seeds

   return img

}

var img = draw_sunflower() img.write(file => "sunflower.png")</lang> Output image: Sunflower fractal

zkl

Translation of: Go

Uses Image Magick and the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl <lang zkl>fcn sunflower(seeds=3000){

  img,color := PPM(400,400), 0x00ff00;		// green
  c:=((5.0).sqrt() + 1)/2;
  foreach n in ([0.0 .. seeds]){  // floats
     r:=n.pow(c)/seeds;
     x,y := r.toRectangular(r.pi*c*n*2);
     r=(n/seeds*5).toInt();
     img.circle(200 + x, 200 + y, r,color);
  }
  img.writeJPGFile("sunflower.zkl.jpg");

}();</lang>

Output:

Image at sunflower fractal