Sunflower fractal: Difference between revisions
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→{{header|Fōrmulæ}}
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{{trans|Perl}}
<
phi = (1 + sqrt(5)) / 2
size = 600
Line 23:
r * cos(t) + size / 2, sqrt(i) / 13))
print(‘</svg>’)</
=={{header|Action!}}==
Calculations on a real Atari 8-bit computer take quite long time. It is recommended to use an emulator capable with increasing speed of Atari CPU.
{{libheader|Action! Tool Kit}}
{{libheader|Action! Real Math}}
<syntaxhighlight lang="action!">INCLUDE "H6:REALMATH.ACT"
INT ARRAY SinTab=[
0 4 9 13 18 22 27 31 36 40 44 49 53 58 62 66 71 75 79 83
88 92 96 100 104 108 112 116 120 124 128 132 136 139 143
147 150 154 158 161 165 168 171 175 178 181 184 187 190
193 196 199 202 204 207 210 212 215 217 219 222 224 226
228 230 232 234 236 237 239 241 242 243 245 246 247 248
249 250 251 252 253 254 254 255 255 255 256 256 256 256]
INT FUNC Sin(INT a)
WHILE a<0 DO a==+360 OD
WHILE a>360 DO a==-360 OD
IF a<=90 THEN
RETURN (SinTab(a))
ELSEIF a<=180 THEN
RETURN (SinTab(180-a))
ELSEIF a<=270 THEN
RETURN (-SinTab(a-180))
ELSE
RETURN (-SinTab(360-a))
FI
RETURN (0)
INT FUNC Cos(INT a)
RETURN (Sin(a-90))
PROC Circle(INT x0,y0,d)
BYTE MaxD=[13]
BYTE ARRAY Start=[0 1 2 4 6 9 12 16 20 25 30 36 42 49]
BYTE ARRAY MaxY=[0 0 1 1 2 2 3 3 4 4 5 5 6 6]
INT ARRAY CircleX=[
0 0 1 0 1 1 2 1 0 2 2 1 3 2 2 0 3 3 2 1
4 4 3 2 1 4 4 4 3 2 5 5 4 4 3 1 5 5 5 4 4 2
6 6 5 5 4 3 1 6 6 6 5 5 4 2]
INT i,ind,max
CARD x
BYTE dx,y
IF d>MAXD THEN d=MaxD FI
IF d<0 THEN d=0 FI
ind=Start(d)
max=MaxY(d)
FOR i=0 TO max
DO
dx=CircleX(ind)
y=y0-i
IF (y>=0) AND (y<=191) THEN
Plot(x0-dx,y) DrawTo(x0+dx,y)
FI
y=y0+i
IF (y>=0) AND (y<=191) THEN
Plot(x0-dx,y) DrawTo(x0+dx,y)
FI
ind==+1
OD
RETURN
PROC DrawFractal(CARD seeds INT x0,y0)
CARD i
REAL a,c,r,ir,tmp,tmp2,r256,rx,ry,rr,r360,c360,seeds2
INT ia,sc,x,y
IntToReal(256,r256)
ValR("1.618034",c) ;c=(sqrt(5)+1)/2
IntToReal(seeds/2,seeds2) ;seeds2=seeds/2
IntToReal(360,r360)
RealMult(r360,c,c360) ;c360=360*c
FOR i=0 TO seeds
DO
IntToReal(i,ir)
Power(ir,c,tmp)
RealDiv(tmp,seeds2,r) ;r=i^c/(seeds/2)
RealMult(c360,ir,a) ;a=360*c*i
WHILE RealGreaterOrEqual(a,r360)
DO
RealSub(a,r360,tmp)
RealAssign(tmp,a)
OD
ia=RealToInt(a)
sc=Sin(ia)
IntToRealForNeg(sc,tmp)
RealDiv(tmp,r256,tmp2)
RealMult(r,tmp2,rx)
x=Round(rx) ;x=r*sin(a)
sc=Cos(ia)
IntToRealForNeg(sc,tmp)
RealDiv(tmp,r256,tmp2)
RealMult(r,tmp2,ry)
y=Round(ry) ;y=r*cos(a)
Circle(x+x0,y+y0,10*i/seeds)
Poke(77,0) ;turn off the attract mode
OD
RETURN
PROC Main()
BYTE CH=$02FC,COLOR1=$02C5,COLOR2=$02C6
Graphics(8+16)
Color=1
COLOR1=$12
COLOR2=$18
DrawFractal(1000,160,96)
DO UNTIL CH#$FF OD
CH=$FF
RETURN</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Sunflower_fractal.png Screenshot from Atari 8-bit computer]
=={{header|Applesoft BASIC}}==
<syntaxhighlight lang="gwbasic">HGR:A=PEEK(49234):C=(SQR(5)+1)/2:N=900:FORI=0TO1600:R=(I^C)/N:A=8*ATN(1)*C*I:X=R*SIN(A)+139:Y=R*COS(A)+96:F=7-4*((X-INT(X/2)*2)>=.75):X=(X>=0ANDX<280)*X:Y=(Y>=0ANDY<192)*Y:HCOLOR=F*(XANDY):HPLOTX,Y:NEXT</syntaxhighlight>
=={{header|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 [http://www.cs.colorado.edu/~main/bgi/cs1300/ WinBGIm] library.
<syntaxhighlight lang="c">
/*Abhishek Ghosh, 14th September 2018*/
Line 67 ⟶ 193:
return 0;
}
</syntaxhighlight>
=={{header|C++}}==
{{trans|Perl}}
<
#include <fstream>
#include <iostream>
Line 111 ⟶ 237:
}
return EXIT_SUCCESS;
}</
{{out}}
[[Media:Sunflower cpp.svg]]
=={{header|FreeBASIC}}==
<
Const PI As Double = 4 * Atn(1)
Const ancho = 400
Line 143 ⟶ 269:
Sleep
End
</syntaxhighlight>
=={{header|Fōrmulæ}}==
{{FormulaeEntry|page=https://formulae.org/?script=examples/Sunflower_model}}
'''Solution'''
The method consists in drawing points on a spriral, an archimedean spiral, where two contiguous points are separated (in angle) by the golden angle.
Because the points tend to agglomerate in the center, they are smaller there.
[[File:Fōrmulæ - Sunflower model 01.png]]
[[File:Fōrmulæ - Sunflower model 02.png]]
[[File:Fōrmulæ - Sunflower model 03.png]]
'''Improvement'''
Last result is not natural. Florets in a sunflower are all equal size.
H. Vogel proposed to use a Fermat spiral, in such a case, the florets are equally spaced, and we can use now circles with the same size:
[[File:Fōrmulæ - Sunflower model 04.png]]
[[File:Fōrmulæ - Sunflower model 05.png]]
[[File:Fōrmulæ - Sunflower model 06.png]]
=={{header|FutureBasic}}==
<syntaxhighlight lang="futurebasic">
window 1, @"Sunflower Fractal", ( 0, 0, 400, 400 )
WindowSetBackgroundColor( 1, fn ColorBlack )
void local fn SunflowerFractal
NSUinteger seeds = 4000
double c, i, angle, x, y, r
pen 2.0, fn ColorWithRGB( 0.997, 0.838, 0.038, 1.0 )
c = ( sqr(5) + 1 ) / 2
for i = 0 to seeds
r = (i ^ c) / seeds
angle = 2 * pi * c * i
x = r * sin(angle) + 200
y = r * cos(angle) + 200
oval ( x, y, i / seeds * 5, i / seeds * 5 )
next
end fn
fn SunflowerFractal
HandleEvents
</syntaxhighlight>
[[file:Sunflower_Fractal.png]]
=={{header|Go}}==
Line 150 ⟶ 331:
<br>
The image produced, when viewed with (for example) EOG, is similar to the Ring entry.
<
import (
Line 177 ⟶ 358:
dc.Stroke()
dc.SavePNG("sunflower_fractal.png")
}</
=={{header|javascript}}==
Line 199 ⟶ 380:
</html>
</pre>
<
TPI = Math.PI * 2, C = (Math.sqrt(10) + 1) / 2;
class Sunflower {
Line 255 ⟶ 436:
const sunflower = new Sunflower();
sunflower.start();
}</
=={{header|J}}==
This (currently draft) task really needs an adequate description. Still, it's straightforward to derive code from another implementation on this page.
This implementation assumes a recent J implementation (for example, J903):
<syntaxhighlight lang="j">require'format/printf'
sunfract=: {{ NB. y: number of "sunflower seeds"
phi=. 0.5*1+%:5
XY=. (y%10)+(2*(I^phi)%y) * +.^j.2*1p1*phi*I=.1+i.y
XY,.(%:I)%13
}}
sunfractsvg=: {{
fract=. sunfract x
C=.,'\n<circle cx="%.2f" cy="%.2f" r="%.1f" />' sprintf fract
({{)n
<svg xmlns="http://www.w3.org/2000/svg" width="%d" height="%d" style="stroke:gold">
<rect width="100%%" height="100%%" fill="black" />
%s
</svg>
}} sprintf (;/<.20+}:>./fract),<C) fwrite y}}
</syntaxhighlight>
Example use:
<syntaxhighlight lang="j">
3000 sunfractsvg '~/sunfract.html'
129147
</syntaxhighlight>
(The number displayed is the size of the generated file.)
=={{header|jq}}==
'''Adapted from [[#Perl|Perl]]'''
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
<syntaxhighlight lang="jq"># SVG headers
def svg(size):
"<svg xmlns='http://www.w3.org/2000/svg' width='\(size)'",
"height='\(size)' style='stroke:gold'>",
"<rect width='100%' height='100%' fill='black'/>";
# emit the "<circle />" elements
def sunflower(size):
def rnd: 100*.|round/100;
(5 * size) as $seeds
| ((1|atan) * 4) as $pi
| ((1 + (5|sqrt)) / 2) as $phi
| range(1; 1 + $seeds) as $i
| {}
| .r = 2 * pow($i; $phi)/$seeds
| .theta = 2 * $pi * $phi * $i
| .x = .r * (.theta|sin) + size/2
| .y = .r * (.theta|cos) + size/2
| .radius = ($i|sqrt)/13
| "<circle cx='\(.x|rnd)' cy='\(.y|rnd)' r='\(.radius|rnd)' />" ;
def end_svg:
"</svg>";
svg(600),
sunflower(600),
end_svg</syntaxhighlight>
=={{header|Julia}}==
{{trans|R}}
Run from REPL.
<
function sunflowerplot()
Line 270 ⟶ 519:
for i in 2:length(r)
θ[i] = θ[i - 1] + 2π * ϕ
markersizes[i] = div(i, 500) +
end
x = r .* cos.(θ)
y = r .* sin.(θ)
ax = Axis(f[1, 1], backgroundcolor = :green)
scatter!(ax, x, y, color = :gold, markersize = markersizes, strokewidth = 1)
hidespines!(ax)
hidedecorations!(ax)
return f
end
sunflowerplot()
</syntaxhighlight>
{{output}}
[[File:Sunflower-julia.png|center|thumb]]
=={{header|Liberty BASIC}}==
<syntaxhighlight lang="lb">
nomainwin
UpperLeftX=1:UpperLeftY=1
Line 312 ⟶ 570:
close #1
end
</syntaxhighlight>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<
pts = Table[
i = N[ni];
Line 324 ⟶ 582:
{ni, numseeds}
];
Graphics[pts]</
=={{header|Microsoft Small Basic}}==
{{trans|Ring}}
<
GraphicsWindow.Width=410
GraphicsWindow.Height=400
Line 339 ⟶ 597:
y=r*Math.Cos(angle)+200
GraphicsWindow.DrawEllipse(x, y, i/numberofseeds*10, i/numberofseeds*10)
EndFor </
{{out}}
[https://1drv.ms/u/s!AoFH_AlpH9oZgf5kvtRou1Wuc5lSCg Sunflower fractal]
Line 346 ⟶ 604:
{{trans|Go}}
{{libheader|imageman}}
<
import imageman
Line 369 ⟶ 627:
image.drawCircle(x, y, toInt(8 * fi / Fn), Foreground)
image.savePNG("sunflower.png", compression = 9)</
=={{header|Objeck}}==
{{trans|C}}
<
use Game.Framework;
Line 445 ⟶ 703:
SCREEN_HEIGHT := 480
}
</syntaxhighlight>
=={{header|Perl}}==
{{trans|Sidef}}
<
use constant π => 3.14159265;
use constant φ => (1 + sqrt(5)) / 2;
Line 467 ⟶ 725:
}
print "</svg>\n";</
See [https://github.com/SqrtNegInf/Rosettacode-Perl5-Smoke/blob/master/ref/sunflower.svg Phi-packing image] (SVG image)
Line 474 ⟶ 732:
{{libheader|Phix/online}}
You can run this online [http://phix.x10.mx/p2js/SunflowerFractal.htm here].
<!--<
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">numberofseeds</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">3000</span>
Line 529 ⟶ 787:
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</
=={{header|Processing}}==
{{trans|C}}
<syntaxhighlight lang="java">
//Abhishek Ghosh, 26th June 2022
size(1000,1000);
surface.setTitle("Sunflower...");
int iter = 3000;
float factor = .5 + sqrt(1.25),r,theta,diskRatio=0.5;
float x = width/2.0, y = height/2.0;
double maxRad = pow(iter,factor)/iter;
int i;
background(#add8e6); //Lightblue background
for(i=0;i<=iter;i++){
r = pow(i,factor)/iter;
if(r/maxRad < diskRatio){
stroke(#000000); // Black central disk
}
else
stroke(#ffff00); // Yellow Petals
theta = 2*PI*factor*i;
ellipse(x + r*sin(theta), y + r*cos(theta), 10 * i/(1.0*iter),10 * i/(1.0*iter));
}
</syntaxhighlight>
=={{header|Python}}==
<
from turtle import *
from math import *
Line 583 ⟶ 871:
done()
</syntaxhighlight>
=={{header|R}}==
<syntaxhighlight lang="r">
phi=1/2+sqrt(5)/2
r=seq(0,1,length.out=2000)
Line 603 ⟶ 891:
points(x[i],y[i],cex=size[i],lwd=thick[i],col="goldenrod1")
}
</syntaxhighlight>
{{Out}}
[https://raw.githubusercontent.com/schwartstack/sunflower/master/sunflower2.png Sunflower]
Line 611 ⟶ 899:
{{trans|C}}
<
(require 2htdp/image)
Line 629 ⟶ 917:
(+ (/ WIDTH 2) (* r (sin theta)))
(+ (/ HEIGHT 2) (* r (cos theta)))
image))</
=={{header|Raku}}==
Line 638 ⟶ 926:
Or, to be completely accurate: It is a variation of a generative [[wp:Fermat's_spiral|Fermat's spiral]] using the Vogel model to implement phi-packing. See: [https://thatsmaths.com/2014/06/05/sunflowers-and-fibonacci-models-of-efficiency/ https://thatsmaths.com/2014/06/05/sunflowers-and-fibonacci-models-of-efficiency]
<syntaxhighlight lang="raku"
my $seeds = 3000;
Line 657 ⟶ 945:
|@c.map( { :circle[:cx(.[0]), :cy(.[1]), :r(.[2])] } ),
],
);</
See: [https://github.com/thundergnat/rc/blob/master/img/phi-packing-perl6.svg Phi packing] (SVG image)
=={{header|Ring}}==
<
# Project : Sunflower fractal
Line 713 ⟶ 1,001:
}
label1 { setpicture(p1) show() }
</syntaxhighlight>
Output:
Line 720 ⟶ 1,008:
=={{header|Sidef}}==
{{trans|Go}}
<
func draw_sunflower(seeds=3000) {
Line 741 ⟶ 1,029:
var img = draw_sunflower()
img.write(file => "sunflower.png")</
Output image: [https://github.com/trizen/rc/blob/master/img/sunflower-sidef.png Sunflower fractal]
=={{header|V (Vlang)}}==
<syntaxhighlight lang="v (vlang)">import gg
import gx
import math
fn main() {
mut context := gg.new_context(
bg_color: gx.rgb(255, 255, 255)
width: 400
height: 400
frame_fn: frame
)
context.run()
}
fn frame(mut ctx gg.Context) {
ctx.begin()
c := (math.sqrt(5) + 1) / 2
num_of_seeds := 3000
for i := 0; i <= num_of_seeds; i++ {
mut fi := f64(i)
n := f64(num_of_seeds)
r := math.pow(fi, c) / n
angle := 2 * math.pi * c * fi
x := r*math.sin(angle) + 200
y := r*math.cos(angle) + 200
fi /= n / 5
ctx.draw_circle_filled(f32(x), f32(y), f32(fi), gx.black)
}
ctx.end()
}</syntaxhighlight>
=={{header|Wren}}==
{{trans|Go}}
{{libheader|DOME}}
<
import "dome" for Window
Line 777 ⟶ 1,097:
}
}
}</
=={{header|XPL0}}==
[[File:SunflowerXPL0.gif|200px|thumb|right]]
<syntaxhighlight lang "XPL0">
proc DrawCircle(X0, Y0, R, Color);
int X0, Y0, R, Color;
int X, Y, R2;
[R2:= R*R;
for Y:= -R to +R do
for X:= -R to +R do
if X*X + Y*Y <= R2 then
Point(X+X0, Y+Y0, Color);
];
def Seeds = 3000, Color = $0E; \yellow
def ScrW = 800, ScrH = 600;
def Phi = (sqrt(5.)+1.) / 2.; \golden ratio (1.618...)
def Pi = 3.14159265358979323846;
real R, Angle, X, Y;
int I;
[SetVid($103);
for I:= 0 to Seeds-1 do
[R:= Pow(float(I), Phi) / float(Seeds/2);
Angle:= 2. * Pi * Phi * float(I);
X:= R*Sin(Angle);
Y:= R*Cos(Angle);
DrawCircle(ScrW/2+fix(X), ScrH/2-fix(Y), I*7/Seeds, Color);
];
]</syntaxhighlight>
=={{header|Yabasic}}==
{{trans|Wren}}
<syntaxhighlight lang="yabasic">// Rosetta Code problem: http://rosettacode.org/wiki/Sunflower_fractal
// Adapted from Wren to Yabasic by Galileo, 01/2022
width = 400
height = 400
open window width, height
backcolor 0,0,0
clear window
color 0,255,0
seeds = 3000
c = (sqrt(5) + 1) / 2
for i = 0 to seeds
r = (i ** c) / seeds
angle = 2 * pi * c * i
x = r * sin(angle) + 200
y = r * cos(angle) + 200
circle x, y, i / seeds * 5
next</syntaxhighlight>
=={{header|zkl}}==
Line 783 ⟶ 1,157:
Uses Image Magick and
the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl
<
img,color := PPM(400,400), 0x00ff00; // green
c:=((5.0).sqrt() + 1)/2;
Line 793 ⟶ 1,167:
}
img.writeJPGFile("sunflower.zkl.jpg");
}();</
{{out}}
Image at [http://www.zenkinetic.com/Images/RosettaCode/sunflower.zkl.jpg sunflower fractal]
| |||