Sunflower fractal
Draw a Sunflower fractal
You are encouraged to solve this task according to the task description, using any language you may know.
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>
C++
<lang cpp>#include <cmath>
- include <fstream>
- include <iostream>
bool sunflower(const char* filename) {
std::ofstream out(filename);
if (!out)
return false;
constexpr int size = 600; constexpr int seeds = 5 * size; constexpr double pi = 3.14159265359; constexpr double phi = 1.61803398875; out << "<svg xmlns='http://www.w3.org/2000/svg\' width='" << size; out << "' height='" << size << "' style='stroke:gold'>\n"; out << "<rect width='100%' height='100%' fill='black'/>\n"; out << std::setprecision(2) << std::fixed; for (int i = 1; i <= seeds; ++i) { double r = 2 * std::pow(i, phi)/seeds; double theta = 2 * pi * phi * i; double x = r * std::sin(theta) + size/2; double y = r * std::cos(theta) + size/2; double radius = std::sqrt(i)/13; out << "<circle cx='" << x << "' cy='" << y << "' r='" << radius << "'/>\n"; } out << "</svg>\n"; return true;
}
int main(int argc, char *argv[]) {
if (argc != 2) {
std::cerr << "usage: " << argv[0] << " filename\n";
return EXIT_FAILURE;
}
if (!sunflower(argv[1])) {
std::cerr << "image generation failed\n";
return EXIT_FAILURE;
}
return EXIT_SUCCESS;
}</lang>
- Output:
See: sunflower.svg (offsite SVG image)
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
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>Sunflower</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
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>
Liberty BASIC
<lang lb> nomainwin UpperLeftX=1:UpperLeftY=1 WindowWidth=800:WindowHeight=600 open "Sunflower Fractal" for graphics_nf_nsb as #1
- 1 "trapclose [q];down;fill darkred;flush;size 3"
c=1.618033988749895 seeds=8000 rd=gn=bl=int(rnd(1)*255)
for i=0 to seeds
rd=rd+5:if rd>254 then rd=1
gn=gn+3:if gn>254 then gn=1
bl=bl+1:if bl>254 then bl=1
#1 "color ";rd;" ";gn;" ";bl
#1 "backcolor ";rd;" ";gn;" ";bl
r=(i^c)/seeds
angle=2*3.14159*c*i
x=r*sin(angle)+400
y=r*cos(angle)+280
#1 "place ";x;" ";y
#1 "circlefilled ";i/seeds*5
scan
next i
wait
[q]
close #1 end
</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)
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
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")
IupCloseOnEscape(dlg)
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>
Python
<lang python> from turtle import * from math import *
- Based on C implementation
iter = 3000 diskRatio = .5
factor = .5 + sqrt(1.25)
screen = getscreen()
(winWidth, winHeight) = screen.screensize()
- x = winWidth/2.0
- y = winHeight/2.0
x = 0.0 y = 0.0
maxRad = pow(iter,factor)/iter;
bgcolor("light blue")
hideturtle()
tracer(0, 0)
for i in range(iter+1):
r = pow(i,factor)/iter;
if r/maxRad < diskRatio:
pencolor("black")
else:
pencolor("yellow")
theta = 2*pi*factor*i;
up()
setposition(x + r*sin(theta), y + r*cos(theta))
down()
circle(10.0 * i/(1.0*iter))
update()
done() </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:
Racket
<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>
Raku
(formerly 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)
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
Wren
<lang ecmascript>import "graphics" for Canvas, Color import "dome" for Window
class Game {
static init() {
Window.title = "Sunflower fractal"
var width = 400
var height = 400
Window.resize(width, height)
Canvas.resize(width, height)
Canvas.cls(Color.black)
var col = Color.green
var seeds = 3000
sunflower(seeds, col)
}
static update() {}
static draw(alpha) {}
static sunflower(seeds, col) {
var c = (5.sqrt + 1) / 2
for (i in 0..seeds) {
var r = i.pow(c) / seeds
var angle = 2 * Num.pi * c * i
var x = r*angle.sin + 200
var y = r*angle.cos + 200
Canvas.circle(x, y, i/seeds*5, col)
}
}
}</lang>
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
