Sunflower fractal
You are encouraged to solve this task according to the task description, using any language you may know.
Draw a 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>
Go
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>
Microsoft Small Basic
<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:
Objeck
<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
<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
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:
Ring
<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:
Sidef
<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
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