# Sunflower fractal

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.

/*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;

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;
}

## 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

## Go

Library: Go Graphics
Translation of: Ring

The image produced, when viewed with (for example) EOG, is similar to the Ring entry.

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")
}

## JavaScript

HTML to test

<!DOCTYPE html>
<html>
<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>
<div id='wnd'></div>
</body>
</html>

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();
}

## Julia

Translation of: R

Run from REPL.

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()

## Microsoft Small Basic

Translation of: Ring
' 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
Output:

## Objeck

Translation of: C
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
}

## Perl

Translation of: Sidef
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";

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

use SVG;

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

constant= (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])] } ),
],
);

See: Phi packing (SVG image)

## 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()

## 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")
}

Output:

## Racket

Translation of: C
#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))

## Ring

# Project : Sunflower fractal

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() }

Output:

## Sidef

Translation of: Go
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")

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

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");
}();
Output:

Image at sunflower fractal