Sierpinski pentagon: Difference between revisions
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{{
Produce a graphical or ASCII-art representation of a [[wp:N-flake#Pentaflake|Sierpinski pentagon]] (aka a Pentaflake) of order 5. Your code should also be able to correctly generate representations of lower orders: 1 to 4.
<br>
<br>
;See also
* [http://ecademy.agnesscott.edu/~lriddle/ifs/pentagon/pentagon.htm Sierpinski pentagon]
<br><br>
=={{header|Action!}}==
<syntaxhighlight lang="action!">PROC Main()
INT ARRAY xs=[249 200 96 80 175]
BYTE ARRAY ys=[82 176 159 55 7]
INT x,y
BYTE i,CH=$02FC,COLOR1=$02C5,COLOR2=$02C6
Graphics(8+16)
Color=1
COLOR1=$0C
COLOR2=$02
x=160+Rand(30)
y=96+Rand(30)
DO
i=Rand(5)
x=x+(xs(i)-x)*62/100
y=y+(ys(i)-y)*62/100
Plot(x,y)
UNTIL CH#$FF
OD
CH=$FF
RETURN</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Sierpinski_pentagon.png Screenshot from Atari 8-bit computer]
=={{header|AutoHotkey}}==
{{trans|Go}}
Requires [https://www.autohotkey.com/boards/viewtopic.php?t=6517 Gdip Library]
<syntaxhighlight lang="autohotkey">W := H := 640
hw := W / 2
margin := 20
radius := hw - 2 * margin
side := radius * Sin(PI := 3.141592653589793 / 5) * 2
order := 5
gdip1()
drawPentagon(hw, 3*margin, side, order, 1)
return
drawPentagon(x, y, side, depth, colorIndex){
global G, hwnd1, hdc, Width, Height
Red := "0xFFFF0000"
Green := "0xFF00FF00"
Blue := "0xFF0000FF"
Magenta := "0xFFFF00FF"
Cyan := "0xFF00FFFF"
Black := "0xFF000000"
Palette := [Red, Green, Blue, Magenta, Cyan]
PI := 3.141592653589793
Deg72 := 72 * PI/180
angle := 3 * Deg72
ScaleFactor := 1 / ( 2 + Cos(Deg72) * 2)
points .= x "," y
if (depth = 1) {
loop 5 {
prevx := x
prevy := y
x += Cos(angle) * side
y -= Sin(angle) * side
points .= "|" x "," y
pPen := Gdip_CreatePen(Black, 2)
Gdip_DrawLines(G, pPen, prevx "," prevy "|" x "," y)
angle += Deg72
}
pBrush := Gdip_BrushCreateSolid(Palette[colorIndex])
Gdip_FillPolygon(G, pBrush, Points)
UpdateLayeredWindow(hwnd1, hdc, 0, 0, Width, Height)
}
else{
side *= ScaleFactor
dist := side * (1 + (Cos(Deg72)*2))
loop 5{
x += Cos(angle) * dist
y -= Sin(angle) * dist
colorIndex := Mod(colorIndex+1, 5) + 1
drawPentagon(x, y, side, depth-1, colorIndex)
angle += Deg72
}
}
}
; ---------------------------------------------------------------
gdip1(){
global
If !pToken := Gdip_Startup(){
MsgBox, 48, gdiplus error!, Gdiplus failed to start. Please ensure you have gdiplus on your system
ExitApp
}
OnExit, Exit
Width := 640, Height := 640
Gui, 1: -Caption +E0x80000 +LastFound +OwnDialogs +Owner +AlwaysOnTop
Gui, 1: Show, NA
hwnd1 := WinExist()
hbm := CreateDIBSection(Width, Height)
hdc := CreateCompatibleDC()
obm := SelectObject(hdc, hbm)
G := Gdip_GraphicsFromHDC(hdc)
Gdip_SetSmoothingMode(G, 4)
blackCanvas := Gdip_BrushCreateSolid(0xFFFFFFFF)
Gdip_FillRectangle(G, blackCanvas, 0, 0, Width, Height)
UpdateLayeredWindow(hwnd1, hdc, 0, 0, Width, Height)
}
; ---------------------------------------------------------------
gdip2(){
global
Gdip_DeleteBrush(pBrush)
Gdip_DeletePen(pPen)
SelectObject(hdc, obm)
DeleteObject(hbm)
DeleteDC(hdc)
Gdip_DeleteGraphics(G)
}
; ---------------------------------------------------------------
Esc::
GuiEscape:
Exit:
gdip2()
Gdip_Shutdown(pToken)
ExitApp
Return</syntaxhighlight>
=={{header|C}}==
The Sierpinski fractals can be generated via the [http://mathworld.wolfram.com/ChaosGame.html Chaos Game]. This implementation thus generalizes the [[Chaos game]] C implementation on Rosettacode. As the number of sides increases, the number of iterations must increase dramatically for a well pronounced fractal ( 30000 for a pentagon). This is in keeping with the requirements that the implementation should work for polygons with sides 1 to 4 as well. Requires the [http://www.cs.colorado.edu/~main/bgi/cs1300/ WinBGIm] library.
<syntaxhighlight lang="c">
#include<graphics.h>
#include<stdlib.h>
#include<stdio.h>
#include<math.h>
#include<time.h>
#define pi M_PI
int main(){
time_t t;
double side, **vertices,seedX,seedY,windowSide = 500,sumX=0,sumY=0;
int i,iter,choice,numSides;
printf("Enter number of sides : ");
scanf("%d",&numSides);
printf("Enter polygon side length : ");
scanf("%lf",&side);
printf("Enter number of iterations : ");
scanf("%d",&iter);
initwindow(windowSide,windowSide,"Polygon Chaos");
vertices = (double**)malloc(numSides*sizeof(double*));
for(i=0;i<numSides;i++){
vertices[i] = (double*)malloc(2 * sizeof(double));
vertices[i][0] = windowSide/2 + side*cos(i*2*pi/numSides);
vertices[i][1] = windowSide/2 + side*sin(i*2*pi/numSides);
sumX+= vertices[i][0];
sumY+= vertices[i][1];
putpixel(vertices[i][0],vertices[i][1],15);
}
srand((unsigned)time(&t));
seedX = sumX/numSides;
seedY = sumY/numSides;
putpixel(seedX,seedY,15);
for(i=0;i<iter;i++){
choice = rand()%numSides;
seedX = (seedX + (numSides-2)*vertices[choice][0])/(numSides-1);
seedY = (seedY + (numSides-2)*vertices[choice][1])/(numSides-1);
putpixel(seedX,seedY,15);
}
free(vertices);
getch();
closegraph();
return 0;
}
</syntaxhighlight>
=={{header|C++}}==
{{trans|D}}
<syntaxhighlight lang="cpp">#include <iomanip>
#include <iostream>
#define _USE_MATH_DEFINES
#include <math.h>
constexpr double degrees(double deg) {
const double tau = 2.0 * M_PI;
return deg * tau / 360.0;
}
const double part_ratio = 2.0 * cos(degrees(72));
const double side_ratio = 1.0 / (part_ratio + 2.0);
/// Define a position
struct Point {
double x, y;
friend std::ostream& operator<<(std::ostream& os, const Point& p);
};
std::ostream& operator<<(std::ostream& os, const Point& p) {
auto f(std::cout.flags());
os << std::setprecision(3) << std::fixed << p.x << ',' << p.y << ' ';
std::cout.flags(f);
return os;
}
/// Mock turtle implementation sufficiant to handle "drawing" the pentagons
struct Turtle {
private:
Point pos;
double theta;
bool tracing;
public:
Turtle() : theta(0.0), tracing(false) {
pos.x = 0.0;
pos.y = 0.0;
}
Turtle(double x, double y) : theta(0.0), tracing(false) {
pos.x = x;
pos.y = y;
}
Point position() {
return pos;
}
void position(const Point& p) {
pos = p;
}
double heading() {
return theta;
}
void heading(double angle) {
theta = angle;
}
/// Move the turtle through space
void forward(double dist) {
auto dx = dist * cos(theta);
auto dy = dist * sin(theta);
pos.x += dx;
pos.y += dy;
if (tracing) {
std::cout << pos;
}
}
/// Turn the turtle
void right(double angle) {
theta -= angle;
}
/// Start/Stop exporting the points of the polygon
void begin_fill() {
if (!tracing) {
std::cout << "<polygon points=\"";
tracing = true;
}
}
void end_fill() {
if (tracing) {
std::cout << "\"/>\n";
tracing = false;
}
}
};
/// Use the provided turtle to draw a pentagon of the specified size
void pentagon(Turtle& turtle, double size) {
turtle.right(degrees(36));
turtle.begin_fill();
for (size_t i = 0; i < 5; i++) {
turtle.forward(size);
turtle.right(degrees(72));
}
turtle.end_fill();
}
/// Draw a sierpinski pentagon of the desired order
void sierpinski(int order, Turtle& turtle, double size) {
turtle.heading(0.0);
auto new_size = size * side_ratio;
if (order-- > 1) {
// create four more turtles
for (size_t j = 0; j < 4; j++) {
turtle.right(degrees(36));
double small = size * side_ratio / part_ratio;
auto distList = { small, size, size, small };
auto dist = *(distList.begin() + j);
Turtle spawn{ turtle.position().x, turtle.position().y };
spawn.heading(turtle.heading());
spawn.forward(dist);
// recurse for each spawned turtle
sierpinski(order, spawn, new_size);
}
// recurse for the original turtle
sierpinski(order, turtle, new_size);
} else {
// The bottom has been reached for this turtle
pentagon(turtle, size);
}
if (order > 0) {
std::cout << '\n';
}
}
/// Run the generation of a P(5) sierpinksi pentagon
int main() {
const int order = 5;
double size = 500;
Turtle turtle{ size / 2.0, size };
std::cout << "<?xml version=\"1.0\" standalone=\"no\"?>\n";
std::cout << "<!DOCTYPE svg PUBLIC \" -//W3C//DTD SVG 1.1//EN\"\n";
std::cout << " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n";
std::cout << "<svg height=\"" << size << "\" width=\"" << size << "\" style=\"fill:blue\" transform=\"translate(" << size / 2 << ", " << size / 2 << ") rotate(-36)\"\n";
std::cout << " version=\"1.1\" xmlns=\"http://www.w3.org/2000/svg\">\n";
size *= part_ratio;
sierpinski(order, turtle, size);
std::cout << "</svg>";
}</syntaxhighlight>
=={{header|D}}==
{{trans|Raku}}
{{trans|Python}}
This solution combines the turtle graphics concept used in Python, with the SVG output format of the Raku solution.
This runs very quickly compared to the Python version.
<syntaxhighlight lang="d">import std.math;
import std.stdio;
/// Convert degrees into radians, as that is the accepted unit for sin/cos etc...
real degrees(real deg) {
immutable tau = 2.0 * PI;
return deg * tau / 360.0;
}
immutable part_ratio = 2.0 * cos(72.degrees);
immutable side_ratio = 1.0 / (part_ratio + 2.0);
/// Use the provided turtle to draw a pentagon of the specified size
void pentagon(Turtle turtle, real size) {
turtle.right(36.degrees);
turtle.begin_fill();
foreach(i; 0..5) {
turtle.forward(size);
turtle.right(72.degrees);
}
turtle.end_fill();
}
/// Draw a sierpinski pentagon of the desired order
void sierpinski(int order, Turtle turtle, real size) {
turtle.setheading(0.0);
auto new_size = size * side_ratio;
if (order-- > 1) {
// create four more turtles
foreach(j; 0..4) {
turtle.right(36.degrees);
real small = size * side_ratio / part_ratio;
auto dist = [small, size, size, small][j];
auto spawn = new Turtle();
spawn.setposition(turtle.position);
spawn.setheading(turtle.heading);
spawn.forward(dist);
// recurse for each spawned turtle
sierpinski(order, spawn, new_size);
}
// recurse for the original turtle
sierpinski(order, turtle, new_size);
} else {
// The bottom has been reached for this turtle
pentagon(turtle, size);
}
}
/// Run the generation of a P(5) sierpinksi pentagon
void main() {
int order = 5;
real size = 500;
auto turtle = new Turtle(size/2, size);
// Write the header to an SVG file for the image
writeln(`<?xml version="1.0" standalone="no"?>`);
writeln(`<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"`);
writeln(` "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">`);
writefln(`<svg height="%s" width="%s" style="fill:blue" transform="translate(%s,%s) rotate(-36)"`, size, size, size/2, size/2);
writeln(` version="1.1" xmlns="http://www.w3.org/2000/svg">`);
// Write the close tag when the interior points have been written
scope(success) writeln("</svg>");
// Scale the initial turtle so that it stays in the inner pentagon
size *= part_ratio;
// Begin rendering
sierpinski(order, turtle, size);
}
/// Define a position
struct Point {
real x;
real y;
/// When a point is written, do it in the form "x,y " to three decimal places
void toString(scope void delegate(const(char)[]) sink) const {
import std.format;
formattedWrite(sink, "%0.3f", x);
sink(",");
formattedWrite(sink, "%0.3f", y);
sink(" ");
}
}
/// Mock turtle implementation sufficiant to handle "drawing" the pentagons
class Turtle {
/////////////////////////////////
private:
Point pos;
real theta;
bool tracing;
/////////////////////////////////
public:
this() {
// empty
}
this(real x, real y) {
pos.x = x;
pos.y = y;
}
// Get/Set the turtle position
Point position() {
return pos;
}
void setposition(Point pos) {
this.pos = pos;
}
// Get/Set the turtle's heading
real heading() {
return theta;
}
void setheading(real angle) {
theta = angle;
}
// Move the turtle through space
void forward(real dist) {
// Calculate both components at once for the specified angle
auto delta = dist * expi(theta);
pos.x += delta.re;
pos.y += delta.im;
if (tracing) {
write(pos);
}
}
// Turn the turle
void right(real angle) {
theta = theta - angle;
}
// Start/Stop exporting the points of the polygon
void begin_fill() {
write(`<polygon points="`);
tracing = true;
}
void end_fill() {
writeln(`"/>`);
tracing = false;
}
}</syntaxhighlight>
=={{header|EasyLang}}==
{{Trans|Processing}}
[https://easylang.dev/show/#cod=pZHNrsIgEIX3PMVJ3GgbsSVpdNOHacroJemFBog/by+DqHXh3Vx2w/mYc2ZwXpNHj06sIMaJBi8mY+lidPxBI5UI4zBRAlrssFaoMbqAvUIFteE3s3cjZrJxODmLK24IRhM0zamBhBQAzLHUPRqu0/l1Z2K6lEfnMdhTdmoQIs3sER3U4VCQdK6o++z/QKts9ZZvLAdjv8g818IyJ6MpPIkcu0oNeOByp02I6B9SXYjFAv4Xnpv/Ef5T/rbhLdrlPFJI8UJVh7ZD18DlT2b0Dg== Run it]
<syntaxhighlight lang="easylang">
order = 5
#
clear
linewidth 0.2
scale = 1 / (2 + cos 72 * 2)
#
proc pentagon x y side depth . .
if depth = 0
move x y
for angle = 0 step 72 to 288
x += cos angle * side
y += sin angle * side
line x y
.
else
side *= scale
dist = side + side * cos 72 * 2
for angle = 0 step 72 to 288
x += cos angle * dist
y += sin angle * dist
pentagon x y side depth - 1
.
.
.
pentagon 25 15 50 order - 1
</syntaxhighlight>
=={{header|FreeBASIC}}==
{{trans|XPL0}}
<syntaxhighlight lang="vb">#define pi 4 * Atn(1)
#define yellow Rgb(255,255,0)
Dim As Byte orden = 5 'can also set this to 1, 2, 3, or 4
Dim Shared As Single deg72
deg72 = 72 * pi / 180 '72 degrees in radians
Dim As Integer HW = 640/2
Dim As Byte tam = 20
Dim As Integer radio = HW - 2*tam
Dim Shared As Single ScaleFactor
Sub DrawPentagon(posX As Integer, posY As Integer, largo As Single, fondo As Byte)
Dim As Byte i
Dim As Single angulo = 3 * deg72, dist
If fondo = 0 Then
Pset (posX, posY)
For i = 0 To 4
posX += Fix(largo * Cos(angulo))
posY -= Fix(largo * Sin(angulo))
Line - (posX, posY), yellow
angulo += Deg72
Next
Else
largo *= ScaleFactor
dist = largo * (1 + Cos(Deg72) * 2)
For i = 0 To 4
posX += Fix(dist * Cos(angulo))
posY -= Fix(dist * Sin(angulo))
DrawPentagon(posX, posY, largo, fondo-1)
angulo += deg72
Next
End If
End Sub
Screenres 640, 640, 32
ScaleFactor = 1 / (2 + Cos(Deg72) * 2)
Dim As Single largo
largo = radio * Sin(Pi/5) * 2
DrawPentagon (HW, 3*tam, largo, orden-1)
Windowtitle "Hit any key to end program"
Sleep</syntaxhighlight>
=={{header|Go}}==
{{libheader|Go Graphics}}
<br>
This follows the approach of the Java entry but uses a fixed palette of 5 colors which are selected in order rather than randomly.
As output is to an external .png file, only a pentaflake of order 5 is drawn though pentaflakes of lower orders can still be drawn by setting the 'order' variable to the appropriate figure.
<syntaxhighlight lang="go">package main
import (
"github.com/fogleman/gg"
"image/color"
"math"
)
var (
red = color.RGBA{255, 0, 0, 255}
green = color.RGBA{0, 255, 0, 255}
blue = color.RGBA{0, 0, 255, 255}
magenta = color.RGBA{255, 0, 255, 255}
cyan = color.RGBA{0, 255, 255, 255}
)
var (
w, h = 640, 640
dc = gg.NewContext(w, h)
deg72 = gg.Radians(72)
scaleFactor = 1 / (2 + math.Cos(deg72)*2)
palette = [5]color.Color{red, green, blue, magenta, cyan}
colorIndex = 0
)
func drawPentagon(x, y, side float64, depth int) {
angle := 3 * deg72
if depth == 0 {
dc.MoveTo(x, y)
for i := 0; i < 5; i++ {
x += math.Cos(angle) * side
y -= math.Sin(angle) * side
dc.LineTo(x, y)
angle += deg72
}
dc.SetColor(palette[colorIndex])
dc.Fill()
colorIndex = (colorIndex + 1) % 5
} else {
side *= scaleFactor
dist := side * (1 + math.Cos(deg72)*2)
for i := 0; i < 5; i++ {
x += math.Cos(angle) * dist
y -= math.Sin(angle) * dist
drawPentagon(x, y, side, depth-1)
angle += deg72
}
}
}
func main() {
dc.SetRGB(1, 1, 1) // White background
dc.Clear()
order := 5 // Can also set this to 1, 2, 3 or 4
hw := float64(w / 2)
margin := 20.0
radius := hw - 2*margin
side := radius * math.Sin(math.Pi/5) * 2
drawPentagon(hw, 3*margin, side, order-1)
dc.SavePNG("sierpinski_pentagon.png")
}</syntaxhighlight>
{{out}}
<pre>
Image similar to Java entry but uses a fixed palette of colors.
</pre>
=={{header|Haskell}}==
For universal solution see [[Fractal tree#Haskell]]
<syntaxhighlight lang="haskell">import Graphics.Gloss
pentaflake :: Int -> Picture
pentaflake order = iterate transformation pentagon !! order
where
transformation = Scale s s . foldMap copy [0,72..288]
copy a = Rotate a . Translate 0 x
pentagon = Polygon [ (sin a, cos a) | a <- [0,2*pi/5..2*pi] ]
x = 2*cos(pi/5)
s = 1/(1+x)
main = display dc white (Color blue $ Scale 300 300 $ pentaflake 5)
where dc = InWindow "Pentaflake" (400, 400) (0, 0)</syntaxhighlight>
'''Explanation''': Since <tt>Picture</tt> forms a monoid with image overlaying as multiplication, so do functions having type <tt>Picture -> Picture</tt>:
f,g :: Picture -> Picture
f <> g = \p -> f p <> g p
Function <code>copy</code> for an angle returns transformation, which shifts and rotates given picture, therefore <code>foldMap copy</code> for a list of angles returns a transformation, which shifts and rotates initial image five times. After that the resulting image is scaled to fit the inital size, so that it is ready for next iteration.
If one wants to get all intermediate pentaflakes <code>transformation</code> shoud be changed as follows:
<syntaxhighlight lang="haskell">transformation = Scale s s . (Rotate 36 <> foldMap copy [0,72..288])</syntaxhighlight>
See also the implementation using [http://projects.haskell.org/diagrams/gallery/Pentaflake.html Diagrams]
=={{header|Java}}==
[[File:sierpinski_pentagon.png|300px|thumb|right]]
{{works with|Java|8}}
<
import java.awt.event.ActionEvent;
import java.awt.geom.Path2D;
Line 118 ⟶ 807:
return Color.getHSBColor((float) hue, 1, 1);
}
}</
=={{header|
;Notes:
* I didn't try to, but got the first of 2 possible versions according to [[wp:N-flake| WP N-flake]] article. Mine has central pentagon. All others here got second version.
* This one looks a little bit differently from the 1st version on WP. Almost like 2nd version, but with central pentagon.
* Not a Durer's pentagon either.
[[File:Pentaflakejs.png|200px|right|thumb|Output Pentaflakejs.png]]
<syntaxhighlight lang="html">
<html>
<head>
<script type="application/x-javascript">
// Globals
var cvs, ctx, scale=500, p0, ord=0, clr='blue', jc=0;
var clrs=['blue','navy','green','darkgreen','red','brown','yellow','cyan'];
function p5f() {
cvs = document.getElementById("cvsid");
ctx = cvs.getContext("2d");
cvs.onclick=iter;
pInit(); //init plot
}
function iter() {
if(ord>5) {resetf(0)};
ctx.clearRect(0,0,cvs.width,cvs.height);
p0.forEach(iter5);
p0.forEach(pIter5);
ord++; document.getElementById("p1id").innerHTML=ord;
}
function iter5(v, i, a) {
if(typeof(v[0][0]) == "object") {a[i].forEach(iter5)}
else {a[i] = meta5(v)}
}
function pIter5(v, i, a) {
if(typeof(v[0][0]) == "object") {v.forEach(pIter5)}
else {pPoly(v)}
}
function pInit() {
p0 = [make5([.5,.5], .5)];
pPoly(p0[0]);
}
function meta5(h) {
c=h[0]; p1=c; p2=h[1]; z1=p1[0]-p2[0]; z2=p1[1]-p2[1];
dist = Math.sqrt(z1*z1 + z2*z2)/2.65;
nP=[];
for(k=1; k<h.length; k++) {
p1=h[k]; p2=c; a=Math.atan2(p2[1]-p1[1], p2[0]-p1[0]);
nP[k] = make5(ppad(a, dist, h[k]), dist)
}
nP[0]=make5(c, dist);
return nP;
}
function make5(c, r) {
vs=[]; j = 1;
for(i=1/10; i<2; i+=2/5) {
vs[j]=ppad(i*Math.PI, r, c); j++;
}
vs[0] = c; return vs;
}
function pPoly(s) {
ctx.beginPath();
ctx.moveTo(s[1][0]*scale, s[1][1]*-scale+scale);
for(i=2; i<s.length; i++)
ctx.lineTo(s[i][0]*scale, s[i][1]*-scale+scale);
ctx.fillStyle=clr; ctx.fill()
}
// a - angle, d - distance, p - point
function ppad(a, d, p) {
x=p[0]; y=p[1];
x2=d*Math.cos(a)+x; y2=d*Math.sin(a)+y;
return [x2,y2]
}
function resetf(rord) {
ctx.clearRect(0,0,cvs.width,cvs.height);
ord=rord; jc++; if(jc>7){jc=0}; clr=clrs[jc];
document.getElementById("p1id").innerHTML=ord;
p5f();
}
</script>
</head>
<body onload="p5f()" style="font-family: arial, helvatica, sans-serif;">
<b>Click Pentaflake to iterate.</b> Order: <label id='p1id'>0</label>
<input type="submit" value="RESET" onclick="resetf(0);">
(Reset anytime: to start new Pentaflake and change color.)
<br /><br />
<canvas id="cvsid" width=640 height=640></canvas>
</body>
</html>
</syntaxhighlight>
{{Output}}
<pre>
Page with Pentaflakejs.png
Clicking Pentaflake you can see orders 1-6 of it in different colors.
</pre>
=={{header|jq}}==
'''Adapted from [[#Julia|Julia]]'''
'''Works with jq, the C implementation of jq'''
'''Works with gojq, the Go implementation of jq'''
The following program produces an SVG image.
To produce the .svg file, use a command such as:
<pre>
jq -nr -f sierpinski-pentagon.jq > sierpinski-pentagon.svg
</pre>
where "sierpinski-pentagon.jq" is a file containing the program shown
below.
The .svg file can conveniently be viewed as a graphic using a browser,
or an editor such as Emacs or Aquamacs.
<syntaxhighlight lang="jq">
### Generic functions
def addComplex(stream): reduce stream as [$x,$y] ([0,0]; .[0] += $x | .[1] += $y);
def lpad($len; $x): tostring | ($len - length) as $l | ($x * $l) + .;
# Input: an array
def multiply($x): map(. * $x);
# Round to approx $ndec places
def round($ndec): pow(10;$ndec) as $p | . * $p | round / $p;
def power($a; $b): reduce range(0;$b) as $i (1; . * $a);
def tau: 8 * atan2(1; 1);
def tobase($b):
def digit: "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"[.:.+1];
def mod: . % $b;
def div: ((. - mod) / $b);
def digits: recurse( select(. > 0) | div) | mod ;
# For jq it would be wise to protect against `infinite` as input, but using `isinfinite` confuses gojq
select( (tostring|test("^[0-9]+$")) and 2 <= $b and $b <= 36)
| if . == 0 then "0"
else [digits | digit] | reverse[1:] | add
end;
### Sierpinski Pentagons
def svgHead($width):
"<svg height=\"\($width)\" width=\"\($width)\" style=\"fill:blue\"",
"version=\"1.1\" xmlns=\"http://www.w3.org/2000/svg\">";
def svgEnd: "</svg>";
# SVG height and width will be 2 * dim
def pentagon($dim):
def sides: 5;
def order: 5;
def scale: (3 - (order | sqrt)) / 2;
def cis: [cos, sin];
def orders:
[range(0; order) | ((1 - scale) * $dim) * power(scale ; .) ];
def vertices:
tau as $tau | [range(0; sides) | ( . * $tau / sides | cis)];
svgHead(2*$dim),
(orders as $orders
| vertices as $vertices
| range(1; 1 + power(sides; order)) as $i
| [ ($i|tobase(sides) | lpad(order; "0") | split("")[]) | $vertices[tonumber]] as $varr
| addComplex(range(0; $orders|length) as $i | $varr[$i] | multiply($orders[$i])) as $vector
| ($vertices | map( addComplex($vector, multiply($orders[-1] * (1-scale))))) as $vprod
| ($vprod | map( map(round(3)) | "\(.[0]) \(.[1])") | join(" ")) as $points
| "<polygon points=\"\($points)\" transform=\"translate(\($dim),\($dim)) rotate(-18)\" />"),
svgEnd ;
pentagon(250)
</syntaxhighlight>
{{output}}
See [[#Julia|Julia]].
=={{header|Julia}}==
{{trans|Perl}}
<syntaxhighlight lang="julia">using Printf
const sides = 5
const order = 5
const dim = 250
const scale = (3 - order ^ 0.5) / 2
const τ = 8 * atan(1, 1)
const orders = map(x -> ((1 - scale) * dim) * scale ^ x, 0:order-1)
cis(x) = Complex(cos(x), sin(x))
const vertices = map(x -> cis(x * τ / sides), 0:sides-1)
fh = open("sierpinski_pentagon.svg", "w")
print(fh, """<svg height=\"$(dim*2)\" width=\"$(dim*2)\" style=\"fill:blue\" """ *
"""version=\"1.1\" xmlns=\"http://www.w3.org/2000/svg\">\n""")
for i in 1:sides^order
varr = [vertices[parse(Int, ch) + 1] for ch in split(string(i, base=sides, pad=order), "")]
vector = sum(map(x -> varr[x] * orders[x], 1:length(orders)))
vprod = map(x -> vector + orders[end] * (1-scale) * x, vertices)
points = join([@sprintf("%.3f %.3f", real(v), imag(v)) for v in vprod], " ")
print(fh, "<polygon points=\"$points\" transform=\"translate($dim,$dim) rotate(-18)\" />\n")
end
print(fh, "</svg>")
close(fh)</syntaxhighlight>
=={{header|Kotlin}}==
{{trans|Java}}
<syntaxhighlight lang="scala">// version 1.1.2
import java.awt.*
import java.awt.geom.Path2D
import java.util.Random
import javax.swing.*
class SierpinskiPentagon : JPanel() {
// exterior angle
private val degrees072 = Math.toRadians(72.0)
/* After scaling we'll have 2 sides plus a gap occupying the length
of a side before scaling. The gap is the base of an isosceles triangle
with a base angle of 72 degrees. */
private val scaleFactor = 1.0 / (2.0 + Math.cos(degrees072) * 2.0)
private val margin = 20
private var limit = 0
private val r = Random()
init {
preferredSize = Dimension(640, 640)
background = Color.white
Timer(3000) {
limit++
if (limit >= 5) limit = 0
repaint()
}.start()
}
private fun drawPentagon(g: Graphics2D, x: Double, y: Double, s: Double, depth: Int) {
var angle = 3.0 * degrees072 // starting angle
var xx = x
var yy = y
var side = s
if (depth == 0) {
val p = Path2D.Double()
p.moveTo(xx, yy)
// draw from the top
for (i in 0 until 5) {
xx += Math.cos(angle) * side
yy -= Math.sin(angle) * side
p.lineTo(xx, yy)
angle += degrees072
}
g.color = RandomHue.next()
g.fill(p)
}
else {
side *= scaleFactor
/* Starting at the top of the highest pentagon, calculate
the top vertices of the other pentagons by taking the
length of the scaled side plus the length of the gap. */
val distance = side + side * Math.cos(degrees072) * 2.0
/* The top positions form a virtual pentagon of their own,
so simply move from one to the other by changing direction. */
for (i in 0 until 5) {
xx += Math.cos(angle) * distance
yy -= Math.sin(angle) * distance
drawPentagon(g, xx, yy, side, depth - 1)
angle += degrees072
}
}
}
override fun paintComponent(gg: Graphics) {
super.paintComponent(gg)
val g = gg as Graphics2D
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
val hw = width / 2
val radius = hw - 2.0 * margin
val side = radius * Math.sin(Math.PI / 5.0) * 2.0
drawPentagon(g, hw.toDouble(), 3.0 * margin, side, limit)
}
private class RandomHue {
/* Try to avoid random color values clumping together */
companion object {
val goldenRatioConjugate = (Math.sqrt(5.0) - 1.0) / 2.0
var hue = Math.random()
fun next(): Color {
hue = (hue + goldenRatioConjugate) % 1
return Color.getHSBColor(hue.toFloat(), 1.0f, 1.0f)
}
}
}
}
fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE
f.title = "Sierpinski Pentagon"
f.isResizable = true
f.add(SierpinskiPentagon(), BorderLayout.CENTER)
f.pack()
f.setLocationRelativeTo(null)
f.isVisible = true
}
}</syntaxhighlight>
=={{header|Lua}}==
An ASCII-interpretation of the task. Uses the Bitmap class and text renderer from [[Bitmap/Bresenham's_line_algorithm#Lua|here]].
<syntaxhighlight lang="lua">Bitmap.chaosgame = function(self, n, r, niters)
local w, h, vertices = self.width, self.height, {}
for i = 1, n do
vertices[i] = {
x = w/2 + w/2 * math.cos(math.pi/2+(i-1)*math.pi*2/n),
y = h/2 - h/2 * math.sin(math.pi/2+(i-1)*math.pi*2/n)
}
end
local x, y = w/2, h/2
for i = 1, niters do
local v = math.random(n)
x = x + r * (vertices[v].x - x)
y = y + r * (vertices[v].y - y)
self:set(x,y,0xFFFFFFFF)
end
end
local bitmap = Bitmap(128, 128)
bitmap:chaosgame(5, 1/((1+math.sqrt(5))/2), 1e6)
bitmap:render({[0x000000]='..', [0xFFFFFFFF]='██'})</syntaxhighlight>
{{out}}
Shown at 25% scale:
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=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">pentaFlake[0] = RegularPolygon[5];
pentaFlake[n_] := GeometricTransformation[pentaFlake[n - 1], TranslationTransform /@ CirclePoints[{GoldenRatio^(2 n - 1), Pi/10}, 5]]
Graphics@pentaFlake[4]</syntaxhighlight>
{{out}}
https://i.imgur.com/rvXvQc0.png
=={{header|MATLAB}}==
<syntaxhighlight lang="matlab">[x, x0] = deal(exp(1i*(0.5:.4:2.1)*pi));
for k = 1 : 4
x = x(:) + x0 * (1 + sqrt(5)) * (3 + sqrt(5)) ^(k - 1) / 2 ^ k;
end
patch('Faces', reshape(1 : 5 * 5 ^ k, 5, '')', 'Vertices', [real(x(:)) imag(x(:))])
axis image off</syntaxhighlight>
{{out}}
http://i.imgur.com/8ht6HqG.png
=={{header|Nim}}==
{{trans|Go}}
{{libheader|imageman}}
<syntaxhighlight lang="nim">import math
import imageman
const
Red = ColorRGBU [byte 255, 0, 0]
Green = ColorRGBU [byte 0, 255, 0]
Blue = ColorRGBU [byte 0, 0, 255]
Magenta = ColorRGBU [byte 255, 0, 255]
Cyan = ColorRGBU [byte 0, 255, 255]
Black = ColorRGBU [byte 0, 0, 0]
(W, H) = (640, 640)
Deg72 = degToRad(72.0)
ScaleFactor = 1 / ( 2 + cos(Deg72) * 2)
Palette = [Red, Green, Blue, Magenta, Cyan]
proc drawPentagon(img: var Image; x, y, side: float; depth: int) =
var (x, y) = (x, y)
var colorIndex {.global.} = 0
var angle = 3 * Deg72
if depth == 0:
for _ in 0..4:
let (prevx, prevy) = (x, y)
x += cos(angle) * side
y -= sin(angle) * side
img.drawLine(prevx.toInt, prevy.toInt, x.toInt, y.toInt, Palette[colorIndex])
angle += Deg72
colorIndex = (colorIndex + 1) mod 5
else:
let side = side * ScaleFactor
let dist = side * (1 + cos(Deg72) * 2)
for _ in 0..4:
x += cos(angle) * dist
y -= sin(angle) * dist
img.drawPentagon(x, y, side, depth - 1)
angle += Deg72
var image = initImage[ColorRGBU](W, H)
image.fill(Black)
var order = 5
let hw = W / 2
let margin = 20.0
let radius = hw - 2 * margin
let side = radius * sin(PI / 5) * 2
image.drawPentagon(hw, 3 * margin, side, order - 1)
image.savePNG("Sierpinski_pentagon.png", compression = 9)</syntaxhighlight>
{{out}}
Same output as that of Go version except that background is black.
=={{header|Perl}}==
{{libheader|ntheory}}
{{trans|Raku}}
<syntaxhighlight lang="perl">use ntheory qw(todigits);
use Math::Complex;
$sides = 5;
$order = 5;
$dim = 250;
$scale = ( 3 - 5**.5 ) / 2;
push @orders, ((1 - $scale) * $dim) * $scale ** $_ for 0..$order-1;
open $fh, '>', 'sierpinski_pentagon.svg';
print $fh qq|<svg height="@{[$dim*2]}" width="@{[$dim*2]}" style="fill:blue" version="1.1" xmlns="http://www.w3.org/2000/svg">\n|;
$tau = 2 * 4*atan2(1, 1);
push @vertices, cis( $_ * $tau / $sides ) for 0..$sides-1;
for $i (0 .. -1+$sides**$order) {
@base5 = todigits($i,5);
@i = ( ((0)x(-1+$sides-$#base5) ), @base5);
@v = @vertices[@i];
$vector = 0;
$vector += $v[$_] * $orders[$_] for 0..$#orders;
my @points;
for (@vertices) {
$v = $vector + $orders[-1] * (1 - $scale) * $_;
push @points, sprintf '%.3f %.3f', $v->Re, $v->Im;
}
print $fh pgon(@points);
}
sub cis { Math::Complex->make(cos($_[0]), sin($_[0])) }
sub pgon { my(@q)=@_; qq|<polygon points="@q" transform="translate($dim,$dim) rotate(-18)"/>\n| }
print $fh '</svg>';
close $fh;</syntaxhighlight>
[https://github.com/SqrtNegInf/Rosettacode-Perl5-Smoke/blob/master/ref/sierpinski_pentagon.svg Sierpinski pentagon] (offsite image)
=={{header|Phix}}==
{{libheader|Phix/pGUI}}
{{libheader|Phix/online}}
You can run this online [http://phix.x10.mx/p2js/SierpinskyPentagon.htm here]. Use +/- to change the level, 0..5.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #000080;font-style:italic;">--
-- demo\rosetta\SierpinskyPentagon.exw
-- ===================================
--</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">include</span> <span style="color: #000000;">pGUI</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">canvas</span>
<span style="color: #004080;">cdCanvas</span> <span style="color: #000000;">cddbuffer</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">title</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"Sierpinski Pentagon"</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">scale_factor</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">/(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">+</span><span style="color: #7060A8;">cos</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">side_factor</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">+</span><span style="color: #7060A8;">cos</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">angles</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)),</span>
<span style="color: #000000;">cosangles</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">angles</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">cos</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">sinangles</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">angles</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sin</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">level</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">3</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">drawPentagon</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">side</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">depth</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">depth</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">cdCanvasBegin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span><span style="color: #004600;">CD_FILL</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">5</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">x</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">cosangles</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">side</span>
<span style="color: #000000;">y</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">sinangles</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">side</span>
<span style="color: #7060A8;">cdCanvasVertex</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">+</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">-</span><span style="color: #000000;">y</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">cdCanvasEnd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">side</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">scale_factor</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">distance</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">side</span><span style="color: #0000FF;">*</span><span style="color: #000000;">side_factor</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">5</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">x</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">cosangles</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">distance</span>
<span style="color: #000000;">y</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">sinangles</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">distance</span>
<span style="color: #000000;">drawPentagon</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">side</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">depth</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">redraw_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000080;font-style:italic;">/*ih*/</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000080;font-style:italic;">/*posx*/</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">/*posy*/</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupGetIntInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"DRAWSIZE"</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">hw</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">h</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">margin</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">20</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">radius</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">hw</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">margin</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">side</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">radius</span> <span style="color: #0000FF;">*</span> <span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">2</span>
<span style="color: #7060A8;">cdCanvasActivate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasClear</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">drawPentagon</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hw</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">*</span><span style="color: #000000;">margin</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">side</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">-</span><span style="color: #000000;">radius</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">margin</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasFlush</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">IUP_DEFAULT</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">map_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000000;">ih</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">cdCanvas</span> <span style="color: #000000;">cdcanvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cdCreateCanvas</span><span style="color: #0000FF;">(</span><span style="color: #004600;">CD_IUP</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ih</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">cddbuffer</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cdCreateCanvas</span><span style="color: #0000FF;">(</span><span style="color: #004600;">CD_DBUFFER</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasSetBackground</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">CD_PARCHMENT</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasSetForeground</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">CD_BLUE</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">IUP_DEFAULT</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">set_dlg_title</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupSetStrAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"TITLE"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"%s (level %d)"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">title</span><span style="color: #0000FF;">,</span><span style="color: #000000;">level</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">key_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000080;font-style:italic;">/*ih*/</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #004600;">K_ESC</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">IUP_CLOSE</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+-"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #008000;">'+'</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">level</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">level</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #008000;">'-'</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">level</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">level</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">set_dlg_title</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupRedraw</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">IUP_CONTINUE</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupOpen</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">canvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupCanvas</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"RASTERSIZE=640x640"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetCallbacks</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"MAP_CB"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"map_cb"</span><span style="color: #0000FF;">),</span>
<span style="color: #008000;">"ACTION"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"redraw_cb"</span><span style="color: #0000FF;">)})</span>
<span style="color: #000000;">dlg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupDialog</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetCallback</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"KEY_CB"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"key_cb"</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">set_dlg_title</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupShow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"RASTERSIZE"</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">NULL</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">IupMainLoop</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
=={{header|Processing}}==
<syntaxhighlight lang="java">
float s_angle, scale, margin = 25, total = 4;
float p_size = 700;
float radius = p_size/2-2*margin;
float side = radius * sin(PI/5)*2;
void setup() {
float temp = width/2;
size(590, 590);
background(0, 0, 200);
stroke(255);
s_angle = 72*PI/180;
scale = 1/(2+cos(s_angle)*2);
for (int i = 0; i < total; i++) {
background(0, 0, 200);
drawPentagon(width/2, (height-p_size)/2 + 3*margin, side, total);
}
}
void drawPentagon(float x, float y, float side, float depth) {
float angle = 3*s_angle;
if (depth == 0) {
for (int i = 0; i < 5; i++) {
float px = x;
float py = y;
x = x+cos(angle)*side;
y = y-sin(angle)*side;
line(x, y, px, py);
angle += s_angle;
}
} else {
side *= scale;
float distance = side+side*cos(s_angle)*2;
for (int j = 0; j < 5; j++) {
x = x+cos(angle)*distance;
y = y-sin(angle)*distance;
drawPentagon(x, y, side, depth-1);
angle += s_angle;
}
}
}</syntaxhighlight>'''The sketch can be run online''' :<BR> [https://www.openprocessing.org/sketch/955331 here.]
=={{header|Prolog}}==
{{works with|SWI Prolog}}
This code is based on the Java solution. The output is an SVG file.
<syntaxhighlight lang="prolog">main:-
write_sierpinski_pentagon('sierpinski_pentagon.svg', 600, 5).
write_sierpinski_pentagon(File, Size, Order):-
open(File, write, Stream),
format(Stream, "<svg xmlns='http://www.w3.org/2000/svg' width='~d' height='~d'>\n",
[Size, Size]),
write(Stream, "<rect width='100%' height='100%' fill='white'/>\n"),
Margin = 5,
Radius is Size/2 - 2 * Margin,
Side is Radius * sin(pi/5) * 2,
Height is Side * (sin(pi/5) + sin(2 * pi/5)),
X is Size/2,
Y is (Size - Height)/2,
Scale_factor is 1/(2 + cos(2 * pi/5) * 2),
sierpinski_pentagon(Stream, X, Y, Scale_factor, Side, Order),
write(Stream, "</svg>\n"),
close(Stream).
sierpinski_pentagon(Stream, X, Y, _, Side, 1):-
!,
write(Stream, "<polygon stroke-width='1' stroke='black' fill='blue' points='"),
format(Stream, '~g,~g', [X, Y]),
Angle is 6 * pi/5,
write_pentagon_points(Stream, Side, Angle, X, Y, 5),
write(Stream, "'/>\n").
sierpinski_pentagon(Stream, X, Y, Scale_factor, Side, N):-
Side1 is Side * Scale_factor,
N1 is N - 1,
Angle is 6 * pi/5,
sierpinski_pentagons(Stream, X, Y, Scale_factor, Side1, Angle, N1, 5).
write_pentagon_points(_, _, _, _, _, 0):-!.
write_pentagon_points(Stream, Side, Angle, X, Y, N):-
N1 is N - 1,
X1 is X + cos(Angle) * Side,
Y1 is Y - sin(Angle) * Side,
Angle1 is Angle + 2 * pi/5,
format(Stream, ' ~g,~g', [X1, Y1]),
write_pentagon_points(Stream, Side, Angle1, X1, Y1, N1).
sierpinski_pentagons(_, _, _, _, _, _, _, 0):-!.
sierpinski_pentagons(Stream, X, Y, Scale_factor, Side, Angle, N, I):-
I1 is I - 1,
Distance is Side + Side * cos(2 * pi/5) * 2,
X1 is X + cos(Angle) * Distance,
Y1 is Y - sin(Angle) * Distance,
Angle1 is Angle + 2 * pi/5,
sierpinski_pentagon(Stream, X1, Y1, Scale_factor, Side, N),
sierpinski_pentagons(Stream, X1, Y1, Scale_factor, Side, Angle1, N, I1).</syntaxhighlight>
{{out}}
[[Media:Sierpinski_pentagon_prolog.svg]]
=={{header|Python}}==
Draws the result on a canvas. Runs pretty slowly.
<syntaxhighlight lang="python">from turtle import *
import math
speed(0) # 0 is the fastest speed. Otherwise, 1 (slow) to 10 (fast)
hideturtle() # hide the default turtle
part_ratio = 2 * math.cos(math.radians(72))
side_ratio = 1 / (part_ratio + 2)
hide_turtles = True # show/hide turtles as they draw
path_color = "black" # path color
fill_color = "black" # fill color
# turtle, size
def pentagon(t, s):
t.color(path_color, fill_color)
t.pendown()
t.right(36)
t.begin_fill()
for i in range(5):
t.forward(s)
t.right(72)
t.end_fill()
# iteration, turtle, size
def sierpinski(i, t, s):
t.setheading(0)
new_size = s * side_ratio
if i > 1:
i -= 1
# create four more turtles
for j in range(4):
t.right(36)
short = s * side_ratio / part_ratio
dist = [short, s, s, short][j]
# spawn a turtle
spawn = Turtle()
if hide_turtles:spawn.hideturtle()
spawn.penup()
spawn.setposition(t.position())
spawn.setheading(t.heading())
spawn.forward(dist)
# recurse for spawned turtles
sierpinski(i, spawn, new_size)
# recurse for parent turtle
sierpinski(i, t, new_size)
else:
# draw a pentagon
pentagon(t, s)
# delete turtle
del t
def main():
t = Turtle()
t.hideturtle()
t.penup()
screen = t.getscreen()
y = screen.window_height()
t.goto(0, y/2-20)
i = 5 # depth. i >= 1
size = 300 # side length
# so the spawned turtles move only the distance to an inner pentagon
size *= part_ratio
# begin recursion
sierpinski(i, t, size)
main()</syntaxhighlight>
See [https://trinket.io/python/5137ae2b92 online implementation]. See [http://i.imgur.com/96D0c7i.png completed output].
=={{header|Quackery}}==
<syntaxhighlight lang="quackery">[ $ "turtleduck.qky" loadfile ] now!
[ [ 1 1
30 times
[ tuck + ]
swap join ] constant
do ] is phi ( --> n/d )
[ 5 times
[ 2dup walk
1 5 turn ]
2drop ] is pentagon ( n/d n --> )
forward is pentaflake
[ dup 0 = iff
[ drop
' [ 79 126 229 ] fill
pentagon ] done
1 - temp put
5 times
[ 2dup 2 1 phi v- v*
temp share pentaflake
2dup fly
1 5 turn ]
temp release
2drop ] resolves pentaflake ( n/d n --> )
turtle
0 frames
3 10 turn
300 1 fly
2 5 turn
' [ 79 126 229 ] colour
400 1 5 pentaflake
1 frames</syntaxhighlight>
{{output}}
[[File:Quackery Sierpinski pentaflake.png]]
=={{header|Racket}}==
{{trans|Java}}
<
(require racket/draw pict racket/math racket/class)
Line 208 ⟶ 1,780:
(dc-draw-pentagon 3 120 120)
(dc-draw-pentagon 4 120 120)
(dc-draw-pentagon 5 640 640)</
=={{header|Raku}}==
(formerly Perl 6)
{{works with|rakudo|2018-10}}
[[File:Perl6 pentaflake.svg|300x300px|thumb|right|5th order pentaflake]]
<syntaxhighlight lang="raku" line>constant $sides = 5;
constant order = 5;
constant $dim = 250;
constant scaling-factor = ( 3 - 5**.5 ) / 2;
my @orders = ((1 - scaling-factor) * $dim) «*» scaling-factor «**» (^order);
my $fh = open('sierpinski_pentagon.svg', :w);
$fh.say: qq|<svg height="{$dim*2}" width="{$dim*2}" style="fill:blue" version="1.1" xmlns="http://www.w3.org/2000/svg">|;
my @vertices = map { cis( $_ * τ / $sides ) }, ^$sides;
for 0 ..^ $sides ** order -> $i {
my $vector = [+] @vertices[$i.base($sides).fmt("%{order}d").comb] «*» @orders;
$fh.say: pgon ((@orders[*-1] * (1 - scaling-factor)) «*» @vertices «+» $vector)».reals».fmt("%0.3f");
};
sub pgon (@q) { qq|<polygon points="{@q}" transform="translate({$dim},{$dim}) rotate(-18)"/>| }
$fh.say: '</svg>';
$fh.close;</syntaxhighlight>
=={{header|Ruby}}==
{{libheader|RubyGems}}
{{libheader|JRubyArt}}
JRubyArt is a port of processing to ruby
<syntaxhighlight lang="ruby">
THETA = Math::PI * 2 / 5
SCALE_FACTOR = (3 - Math.sqrt(5)) / 2
MARGIN = 20
attr_reader :pentagons, :renderer
def settings
size(400, 400)
end
def setup
sketch_title 'Pentaflake'
radius = width / 2 - 2 * MARGIN
center = Vec2D.new(radius - 2 * MARGIN, 3 * MARGIN)
pentaflake = Pentaflake.new(center, radius, 5)
@pentagons = pentaflake.pentagons
end
def draw
background(255)
stroke(0)
pentagons.each do |penta|
draw_pentagon(penta)
end
no_loop
end
def draw_pentagon(pent)
points = pent.vertices
begin_shape
points.each do |pnt|
pnt.to_vertex(renderer)
end
end_shape(CLOSE)
end
def renderer
@renderer ||= GfxRender.new(self.g)
end
class Pentaflake
attr_reader :pentagons
def initialize(center, radius, depth)
@pentagons = []
create_pentagons(center, radius, depth)
end
def create_pentagons(center, radius, depth)
if depth.zero?
pentagons << Pentagon.new(center, radius)
else
radius *= SCALE_FACTOR
distance = radius * Math.sin(THETA) * 2
(0..4).each do |idx|
x = center.x + Math.cos(idx * THETA) * distance
y = center.y + Math.sin(idx * THETA) * distance
center = Vec2D.new(x, y)
create_pentagons(center, radius, depth - 1)
end
end
end
end
class Pentagon
attr_reader :center, :radius
def initialize(center, radius)
@center = center
@radius = radius
end
def vertices
(0..4).map do |idx|
center + Vec2D.new(radius * Math.sin(THETA * idx), radius * Math.cos(THETA * idx))
end
end
end
</syntaxhighlight>
=={{header|Rust}}==
This code is based on the Java solution. The output is a file in SVG format.
<syntaxhighlight lang="rust">// [dependencies]
// svg = "0.8.0"
fn sierpinski_pentagon(
mut document: svg::Document,
mut x: f64,
mut y: f64,
mut side: f64,
order: usize,
) -> svg::Document {
use std::f64::consts::PI;
use svg::node::element::Polygon;
let degrees72 = 0.4 * PI;
let mut angle = 3.0 * degrees72;
let scale_factor = 1.0 / (2.0 + degrees72.cos() * 2.0);
if order == 1 {
let mut points = Vec::new();
points.push((x, y));
for _ in 0..5 {
x += angle.cos() * side;
y -= angle.sin() * side;
angle += degrees72;
points.push((x, y));
}
let polygon = Polygon::new()
.set("fill", "blue")
.set("stroke", "black")
.set("stroke-width", "1")
.set("points", points);
document = document.add(polygon);
} else {
side *= scale_factor;
let distance = side + side * degrees72.cos() * 2.0;
for _ in 0..5 {
x += angle.cos() * distance;
y -= angle.sin() * distance;
angle += degrees72;
document = sierpinski_pentagon(document, x, y, side, order - 1);
}
}
document
}
fn write_sierpinski_pentagon(file: &str, size: usize, order: usize) -> std::io::Result<()> {
use std::f64::consts::PI;
use svg::node::element::Rectangle;
let margin = 5.0;
let radius = (size as f64) / 2.0 - 2.0 * margin;
let side = radius * (0.2 * PI).sin() * 2.0;
let height = side * ((0.2 * PI).sin() + (0.4 * PI).sin());
let x = (size as f64) / 2.0;
let y = (size as f64 - height) / 2.0;
let rect = Rectangle::new()
.set("width", "100%")
.set("height", "100%")
.set("fill", "white");
let mut document = svg::Document::new()
.set("width", size)
.set("height", size)
.add(rect);
document = sierpinski_pentagon(document, x, y, side, order);
svg::save(file, &document)
}
fn main() {
write_sierpinski_pentagon("sierpinski_pentagon.svg", 600, 5).unwrap();
}</syntaxhighlight>
{{out}}
[[Media:Sierpinski_pentagon_rust.svg]]
=={{header|Scala}}==
===Java Swing Interoperability===
<syntaxhighlight lang="scala">import java.awt._
import java.awt.event.ActionEvent
import java.awt.geom.Path2D
import javax.swing._
import scala.annotation.tailrec
import scala.math.{Pi, cos, sin, sqrt}
object SierpinskiPentagon extends App {
SwingUtilities.invokeLater(() => {
class SierpinskiPentagon extends JPanel {
/* Try to avoid random color values clumping together */
private var hue = math.random
// exterior angle
private val deg072 = 2 * Pi / 5d //toRadians(72)
/* After scaling we'll have 2 sides plus a gap occupying the length
of a side before scaling. The gap is the base of an isosceles triangle
with a base angle of 72 degrees. */
//private val scaleFactor = 1 / (2 + cos(deg072) * 2)
private var limit = 0
private def drawPentagon(g: Graphics2D, x: Double, y: Double, side: Double, depth: Int): Unit = {
val scaleFactor = 1 / (2 + cos(deg072) * 2)
if (depth == 0) {
// draw from the top
@tailrec
def iter0(i: Int, x: Double, y: Double, angle: Double, p: Path2D.Double): Path2D.Double = {
if (i < 0) p
else {
p.lineTo(x, y)
iter0(i - 1, x + cos(angle) * side, y - sin(angle) * side, angle + deg072, p)
}
}
def p1: Path2D.Double = iter0(4, x, y, 3 * deg072, {
val p = new Path2D.Double
p.moveTo(x, y)
p
})
def p: Path2D.Double = iter0(4, x, y, 3 * deg072, p1)
def next: Color = {
hue = (hue + (sqrt(5) - 1) / 2) % 1
Color.getHSBColor(hue.toFloat, 1, 1)
}
g.setColor(next)
g.fill(p)
}
else {
val _side = side * scaleFactor
/* Starting at the top of the highest pentagon, calculate
the top vertices of the other pentagons by taking the
length of the scaled side plus the length of the gap. */
val distance = _side + _side * cos(deg072) * 2
/* The top positions form a virtual pentagon of their own,
so simply move from one to the other by changing direction. */
def iter1(i: Int, x: Double, y: Double, angle: Double): Unit = {
if (i < 0) ()
else {
drawPentagon(g, x, y, _side, depth - 1)
iter1(i - 1, x + cos(angle) * distance, y - sin(angle) * distance, angle + deg072)
}
}
iter1(4, x + cos(3 * deg072) * distance, y - sin(3 * deg072) * distance, 4 * deg072)
}
}
override def paintComponent(gg: Graphics): Unit = {
val (g, margin) = (gg.asInstanceOf[Graphics2D], 20)
val side = (getWidth / 2 - 2 * margin) * sin(Pi / 5) * 2
super.paintComponent(gg)
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
drawPentagon(g, getWidth / 2, 3 * margin, side, limit)
}
new Timer(3000, (_: ActionEvent) => {
limit += 1
if (limit >= 5) limit = 0
repaint()
}).start()
setPreferredSize(new Dimension(640, 640))
setBackground(Color.white)
}
val f = new JFrame("Sierpinski Pentagon") {
setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE)
setResizable(true)
add(new SierpinskiPentagon, BorderLayout.CENTER)
pack()
setLocationRelativeTo(null)
setVisible(true)
}
})
}</syntaxhighlight>
=={{header|Sidef}}==
{{trans|Raku}}
Generates a SVG image to STDOUT. Redirect to a file to capture and display it.
<syntaxhighlight lang="ruby">define order = 5
define sides = 5
define dim = 500
define scaling_factor = ((3 - 5**0.5) / 2)
var orders = order.of {|i| ((1-scaling_factor) * dim) * scaling_factor**i }
say <<"STOP";
<?xml version="1.0" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg height="#{dim*2}" width="#{dim*2}"
style="fill:blue" transform="translate(#{dim},#{dim}) rotate(-18)"
version="1.1" xmlns="http://www.w3.org/2000/svg">
STOP
var vertices = sides.of {|i| Complex(0, i * Number.tau / sides).exp }
for i in ^(sides**order) {
var vector = ([vertices["%#{order}d" % i.base(sides) -> chars]] »*« orders «+»)
var points = (vertices »*» orders[-1]*(1-scaling_factor) »+» vector »reals()» «%« '%0.3f')
say ('<polygon points="' + points.join(' ') + '"/>')
}
say '</svg>'</syntaxhighlight>
=={{header|VBA}}==
Using Excel
<syntaxhighlight lang="vb">Private Sub sierpinski(Order_ As Integer, Side As Double)
Dim Circumradius As Double, Inradius As Double
Dim Height As Double, Diagonal As Double, HeightDiagonal As Double
Dim Pi As Double, p(5) As String, Shp As Shape
Circumradius = Sqr(50 + 10 * Sqr(5)) / 10
Inradius = Sqr(25 + 10 * Sqr(5)) / 10
Height = Circumradius + Inradius
Diagonal = (1 + Sqr(5)) / 2
HeightDiagonal = Sqr(10 + 2 * Sqr(5)) / 4
Pi = WorksheetFunction.Pi
Ratio = Height / (2 * Height + HeightDiagonal)
'Get a base figure
Set Shp = ThisWorkbook.Worksheets(1).Shapes.AddShape(msoShapeRegularPentagon, _
2 * Side, 3 * Side / 2 + (Circumradius - Inradius) * Side, Diagonal * Side, Height * Side)
p(0) = Shp.Name
Shp.Rotation = 180
Shp.Line.Weight = 0
For j = 1 To Order_
'Place 5 copies of the figure in a circle around it
For i = 0 To 4
'Copy the figure
Set Shp = Shp.Duplicate
p(i + 1) = Shp.Name
If i = 0 Then Shp.Rotation = 0
'Place around in a circle
Shp.Left = 2 * Side + Side * Inradius * 2 * Cos(2 * Pi * (i - 1 / 4) / 5)
Shp.Top = 3 * Side / 2 + Side * Inradius * 2 * Sin(2 * Pi * (i - 1 / 4) / 5)
Shp.Visible = msoTrue
Next i
'Group the 5 figures
Set Shp = ThisWorkbook.Worksheets(1).Shapes.Range(p()).Group
p(0) = Shp.Name
If j < Order_ Then
'Shrink the figure
Shp.ScaleHeight Ratio, False
Shp.ScaleWidth Ratio, False
'Flip vertical and place in the center
Shp.Rotation = 180
Shp.Left = 2 * Side
Shp.Top = 3 * Side / 2 + (Circumradius - Inradius) * Side
End If
Next j
End Sub
Public Sub main()
sierpinski Order_:=5, Side:=200
End Sub</syntaxhighlight>
=={{header|Wren}}==
{{trans|Go}}
{{libheader|DOME}}
Black backgound and slightly different palette to Go. Also pentagons are unfilled.
<syntaxhighlight lang="wren">import "graphics" for Canvas, Color
import "dome" for Window
import "math" for Math
var Deg72 = 72 * Num.pi / 180 // 72 degrees in radians
var ScaleFactor = 1 / (2 + Math.cos(Deg72) * 2)
var Palette = [Color.red, Color.blue, Color.green, Color.indigo, Color.brown]
var ColorIndex = 0
var OldX = 0
var OldY = 0
class SierpinskiPentagon {
construct new(width, height) {
Window.title = "Sierpinksi Pentagon"
Window.resize(width, height)
Canvas.resize(width, height)
_w = width
_h = height
}
init() {
var order = 5 // can also set this to 1, 2, 3, or 4
var hw = _w / 2
var margin = 20
var radius = hw - 2 * margin
var side = radius * Math.sin(Num.pi/5) * 2
drawPentagon(hw, 3 * margin, side, order - 1)
}
drawPentagon(x, y, side, depth) {
var angle = 3 * Deg72
if (depth == 0) {
var col = Palette[ColorIndex]
OldX = x
OldY = y
for (i in 0..4) {
x = x + Math.cos(angle) * side
y = y - Math.sin(angle) * side
Canvas.line(OldX, OldY, x, y, col, 2)
OldX = x
OldY = y
angle = angle + Deg72
}
ColorIndex = (ColorIndex + 1) % 5
} else {
side = side * ScaleFactor
var dist = side * (1 + Math.cos(Deg72) * 2)
for (i in 0..4) {
x = x + Math.cos(angle) * dist
y = y - Math.sin(angle) * dist
drawPentagon(x, y, side, depth-1)
angle = angle + Deg72
}
}
}
update() {}
draw(alpha) {}
}
var Game = SierpinskiPentagon.new(640, 640)</syntaxhighlight>
{{out}}
[[File:Wren-Sierpinski_pentagon.png|400px]]
=={{header|XPL0}}==
{{trans|Wren}}
[[File:SierXPL0.gif|200px|thumb|right]]
<syntaxhighlight lang "XPL0">def Order = 5; \can also set this to 1, 2, 3, or 4
def Width=640, Height=640;
def Pi = 3.14159265358979323846;
def Deg72 = 72.*Pi/180.; \72 degrees in radians
def HW = Width/2;
def Margin = 20;
def Radius = HW - 2*Margin;
real ScaleFactor;
int ColorIndex;
proc DrawPentagon(X, Y, Side, Depth);
real X, Y, Side; int Depth;
real Angle, Dist;
int I;
[Angle:= 3. * Deg72;
if Depth = 0 then
[Move(fix(X), fix(Y));
for I:= 0 to 4 do
[X:= X + Cos(Angle) * Side;
Y:= Y - Sin(Angle) * Side;
Line(fix(X), fix(Y), ColorIndex+9);
Angle:= Angle + Deg72;
];
ColorIndex:= ColorIndex+1;
if ColorIndex >= 5 then ColorIndex:= 0;
]
else [Side:= Side * ScaleFactor;
Dist:= Side * (1. + Cos(Deg72) * 2.);
for I:= 0 to 4 do
[X:= X + Cos(Angle) * Dist;
Y:= Y - Sin(Angle) * Dist;
DrawPentagon(X, Y, Side, Depth-1);
Angle:= Angle + Deg72;
];
];
];
real Side;
[SetFB(Width, Height, 8);
ScaleFactor:= 1. / (2. + Cos(Deg72) * 2.);
ColorIndex:= 0;
Side:= float(Radius) * Sin(Pi/5.) * 2.;
DrawPentagon(float(HW), float(3*Margin), Side, Order-1);
]</syntaxhighlight>
=={{header|zkl}}==
{{trans|Raku}}
<syntaxhighlight lang="zkl">const order=5, sides=5, dim=250, scaleFactor=((3.0 - (5.0).pow(0.5))/2);
const tau=(0.0).pi*2; // 2*pi*r
orders:=order.pump(List,fcn(n){ (1.0 - scaleFactor)*dim*scaleFactor.pow(n) });
println(
#<<<
0'|<?xml version="1.0" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg height="%d" width="%d" style="fill:blue" transform="translate(%d,%d) rotate(-18)"
version="1.1" xmlns="http://www.w3.org/2000/svg">|
#<<<
.fmt(dim*2,dim*2,dim,dim));
vertices:=sides.pump(List,fcn(s){ (1.0).toRectangular(tau*s/sides) }); // points on unit circle
vx:=vertices.apply('wrap([(a,b)]v,x){ return(a*x,b*x) }, // scaled points
orders[-1]*(1.0 - scaleFactor));
fmt:="%%0%d.%dB".fmt(sides,order).fmt; //-->%05.5B (leading zeros, 5 places, base 5)
sides.pow(order).pump(Console.println,'wrap(i){
vector:=fmt(i).pump(List,vertices.get) // "00012"-->(vertices[0],..,vertices[2])
.zipWith(fcn([(a,b)]v,x){ return(a*x,b*x) },orders) // ((a,b)...)*x -->((ax,bx)...)
.reduce(fcn(vsum,v){ vsum[0]+=v[0]; vsum[1]+=v[1]; vsum },L(0.0, 0.0)); //-->(x,y)
pgon(vx.apply(fcn([(a,b)]v,c,d){ return(a+c,b+d) },vector.xplode()));
});
println("</svg>"); // 3,131 lines
fcn pgon(vertices){ // eg ( ((250,0),(248.595,1.93317),...), len 5
0'|<polygon points="%s"/>|.fmt(
vertices.pump(String,fcn(v){ "%.3f %.3f ".fmt(v.xplode()) }) )
}</syntaxhighlight>
{{out}}
See [http://www.zenkinetic.com/Images/RosettaCode/sierpinskiPentagon.zkl.svg this image].
Displays fine in FireFox, in Chrome, it doesn't appear to be transformed so you only see part of the image.
<pre>
zkl bbb > sierpinskiPentagon.zkl.svg
$ wc sierpinskiPentagon.zkl.svg
3131 37519 314183 sierpinskiPentagon.zkl.svg
</pre>
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