Sierpinski curve

From Rosetta Code
Revision as of 15:23, 15 August 2020 by Chunes (talk | contribs) (Add Factor)
Sierpinski curve is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.


Task

Produce a graphical or ASCII-art representation of a Sierpinski curve of at least order 3.

C++

Output is a file in SVG format. The curve is generated using the Lindenmayer system method. <lang cpp>// See https://en.wikipedia.org/wiki/Sierpi%C5%84ski_curve#Representation_as_Lindenmayer_system

  1. include <cmath>
  2. include <fstream>
  3. include <iostream>
  4. include <string>

std::string rewrite(const std::string& s) { 

   std::string t;
   for (char c : s) {
       if (c == 'X')
           t += "XF+G+XF--F--XF+G+X";
       else
           t += c;
   }
   return t;

}

void line(std::ostream& out, double& x, double& y, double length, int angle) { 

   constexpr double pi = 3.14159265359;
   double theta = (pi * angle)/180.0;
   x += length * std::cos(theta);
   y -= length * std::sin(theta);
   out << 'L' << x << ',' << y << '\n';

}

void execute(std::ostream& out, const std::string& s, double x, double y, 

            double length, int angle) {
   out << 'M' << x << ',' << y << '\n';
   for (char c : s) {
       if (c == 'F' || c == 'G')
           line(out, x, y, length, angle);
       else if (c == '+')
           angle = (angle + 45) % 360;
       else if (c == '-')
           angle = (angle - 45) % 360;
   }

}

int main() { 

   const int size = 545;
   const int order = 5;
   const double x = 5, y = 10, length = 7;
   std::ofstream out("sierpinski_curve.svg");
   if (!out) {
       std::cerr << "Cannot open output file\n";
       return 1;
   }
   out << "<svg xmlns='http://www.w3.org/2000/svg' width='"
       << size << "' height='" << size << "'>\n";
   out << "<rect width='100%' height='100%' fill='white'/>\n";
   out << "<path stroke-width='1' stroke='black' fill='none' d='";
   std::string s = "F--XF--F--XF";
   for (int i = 0; i < order; ++i)
       s = rewrite(s);
   execute(out, s, x, y, length, 45);
   out << "'/>\n</svg>\n";
   return 0;

}</lang>

Output:

See: sierpinski_curve.svg (offsite SVG image)

Factor

Works with: Factor version 0.99 2020-08-14

<lang factor>USING: accessors kernel L-system sequences ui ;

curve ( L-system -- L-system )
   L-parser-dialect
   { "G" [ dup length>> draw-forward ] } suffix >>commands
   [ 45 >>angle ] >>turtle-values
   "F--XF--F--XF" >>axiom
   {
       { "X" "XF+G+XF--F--XF+G+X" }
   } >>rules ;

[ <L-system> curve "Sierpinski curve" open-window ] with-ui</lang>


When using the L-system visualizer, the following controls apply:

Camera controls
Button Command
a zoom in
z zoom out
left arrow turn left
right arrow turn right
up arrow pitch down
down arrow pitch up
q roll left
w roll right
Other controls
Button Command
x iterate L-system

Go

Library: Go Graphics
Translation of: Phix

A partial translation anyway which produces a static image of a SC of level 5, yellow on blue, which can be viewed with a utility such as EOG. <lang go>package main

import ( 

   "github.com/fogleman/gg"
   "math"

)

var ( 

   width  = 770.0
   height = 770.0
   dc     = gg.NewContext(int(width), int(height))

)

var cx, cy, h float64

func lineTo(newX, newY float64) { 

   dc.LineTo(newX-width/2+h, height-newY+2*h)
   cx, cy = newX, newY

}

func lineN() { lineTo(cx, cy-2*h) } func lineS() { lineTo(cx, cy+2*h) } func lineE() { lineTo(cx+2*h, cy) } func lineW() { lineTo(cx-2*h, cy) }

func lineNW() { lineTo(cx-h, cy-h) } func lineNE() { lineTo(cx+h, cy-h) } func lineSE() { lineTo(cx+h, cy+h) } func lineSW() { lineTo(cx-h, cy+h) }

func sierN(level int) { 

   if level == 1 {
       lineNE()
       lineN()
       lineNW()
   } else {
       sierN(level - 1)
       lineNE()
       sierE(level - 1)
       lineN()
       sierW(level - 1)
       lineNW()
       sierN(level - 1)
   }

}

func sierE(level int) { 

   if level == 1 {
       lineSE()
       lineE()
       lineNE()
   } else {
       sierE(level - 1)
       lineSE()
       sierS(level - 1)
       lineE()
       sierN(level - 1)
       lineNE()
       sierE(level - 1)
   }

}

func sierS(level int) { 

   if level == 1 {
       lineSW()
       lineS()
       lineSE()
   } else {
       sierS(level - 1)
       lineSW()
       sierW(level - 1)
       lineS()
       sierE(level - 1)
       lineSE()
       sierS(level - 1)
   }

}

func sierW(level int) { 

   if level == 1 {
       lineNW()
       lineW()
       lineSW()
   } else {
       sierW(level - 1)
       lineNW()
       sierN(level - 1)
       lineW()
       sierS(level - 1)
       lineSW()
       sierW(level - 1)
   }

}

func squareCurve(level int) { 

   sierN(level)
   lineNE()
   sierE(level)
   lineSE()
   sierS(level)
   lineSW()
   sierW(level)
   lineNW()
   lineNE() // needed to close the square in the top left hand corner

}

func main() { 

   dc.SetRGB(0, 0, 1) // blue background
   dc.Clear()
   level := 5
   cx, cy = width/2, height
   h = cx / math.Pow(2, float64(level+1))
   squareCurve(level)
   dc.SetRGB255(255, 255, 0) // yellow curve
   dc.SetLineWidth(2)
   dc.Stroke()
   dc.SavePNG("sierpinski_curve.png")

}</lang>

Java

Translation of: C++

<lang java>import java.io.*;

public class SierpinskiCurve { 

   public static void main(final String[] args) {
       try (Writer writer = new BufferedWriter(new FileWriter("sierpinski_curve.svg"))) {
           SierpinskiCurve s = new SierpinskiCurve(writer);
           s.currentAngle = 45;
           s.currentX = 5;
           s.currentY = 10;
           s.lineLength = 7;
           s.begin(545);
           s.execute(rewrite(5));
           s.end();
       } catch (final Exception ex) {
           ex.printStackTrace();
       }
   }

   private SierpinskiCurve(final Writer writer) {
       this.writer = writer;
   }

   private void begin(final int size) throws IOException {
       write("<svg xmlns='http://www.w3.org/2000/svg' width='%d' height='%d'>\n", size, size);
       write("<rect width='100%%' height='100%%' fill='white'/>\n");
       write("<path stroke-width='1' stroke='black' fill='none' d='");
   }

   private void end() throws IOException {
       write("'/>\n</svg>\n");
   }

   private void execute(final String s) throws IOException {
       write("M%g,%g\n", currentX, currentY);
       for (int i = 0, n = s.length(); i < n; ++i) {
           switch (s.charAt(i)) {
               case 'F':
               case 'G':
                   line(lineLength);
                   break;
               case '+':
                   turn(ANGLE);
                   break;
               case '-':
                   turn(-ANGLE);
                   break;
           }
       }
   }

   private void line(final double length) throws IOException {
       final double theta = (Math.PI * currentAngle) / 180.0;
       currentX += length * Math.cos(theta);
       currentY -= length * Math.sin(theta);
       write("L%g,%g\n", currentX, currentY);
   }

   private void turn(final int angle) {
       currentAngle = (currentAngle + angle) % 360;
   }

   private void write(final String format, final Object... args) throws IOException {
       writer.write(String.format(format, args));
   }

   private static String rewrite(final int order) {
       String s = AXIOM;
       for (int i = 0; i < order; ++i) {
           final StringBuilder sb = new StringBuilder();
           for (int j = 0, n = s.length(); j < n; ++j) {
               final char ch = s.charAt(j);
               if (ch == 'X')
                   sb.append(PRODUCTION);
               else
                   sb.append(ch);
           }
           s = sb.toString();
       }
       return s;
   }

   private final Writer writer;
   private double lineLength;
   private double currentX;
   private double currentY;
   private int currentAngle;

   private static final String AXIOM = "F--XF--F--XF";
   private static final String PRODUCTION = "XF+G+XF--F--XF+G+X";
   private static final int ANGLE = 45;

}</lang>

Output:

See: sierpinski_curve.svg (offsite SVG image)

Julia

Turtle procedural (lineto) version

Modified from Craft of Coding blog, Processing version <lang Julia>using Luxor

function sierpinski_curve(x0, y0, h, level) 

   x1, y1 = x0, y0
   lineto(x, y) = begin line(Point(x1, y1), Point(x, y), :stroke); x1, y1 = x, y end
   lineN() = lineto(x1,y1-2*h)
   lineS() = lineto(x1,y1+2*h)
   lineE() = lineto(x1+2*h,y1)
   lineW() = lineto(x1-2*h,y1)
   lineNW() = lineto(x1-h,y1-h)
   lineNE() = lineto(x1+h,y1-h)
   lineSE() = lineto(x1+h,y1+h)
   lineSW() = lineto(x1-h,y1+h)
   function drawN(i)
       if i == 1
           lineNE(); lineN(); lineNW()
       else
           drawN(i-1); lineNE(); drawE(i-1); lineN(); drawW(i-1); lineNW(); drawN(i-1)
       end
   end
   function drawE(i)
       if i == 1
           lineSE(); lineE(); lineNE()
       else
           drawE(i-1); lineSE(); drawS(i-1); lineE(); drawN(i-1); lineNE(); drawE(i-1)
       end
   end
   function drawS(i)
       if i == 1
           lineSW(); lineS(); lineSE()
       else
           drawS(i-1); lineSW(); drawW(i-1); lineS(); drawE(i-1); lineSE(); drawS(i-1)
       end
   end
   function drawW(i)
       if i == 1
           lineNW(); lineW(); lineSW()
       else
           drawW(i-1); lineNW(); drawN(i-1); lineW(); drawS(i-1); lineSW(); drawW(i-1)
       end
   end
   function draw_curve(levl)
       drawN(levl); lineNE(); drawE(levl); lineSE()
       drawS(levl); lineSW(); drawW(levl); lineNW()
   end
   draw_curve(level)

end

Drawing(800, 800) sierpinski_curve(10, 790, 3, 6) finish() preview() </lang>

LSystem version

<lang julia>using Lindenmayer # https://github.com/cormullion/Lindenmayer.jl

sierpcurve = LSystem(Dict("X" => "XF+G+XF--F--XF+G+X"), "F--XF--F--XF")

drawLSystem(sierpcurve, 

   forward = 10,
   turn = 45,
   startingpen= (0.2, 0.8, 0.8),
   startingx = -380,
   startingy = 380,
   startingorientation = π/4,
   iterations = 5,
   filename = "sierpinski_curve.png",
   showpreview = true

) </lang>

Perl

<lang perl>use strict; use warnings; use SVG; use List::Util qw(max min);

use constant pi => 2 * atan2(1, 0);

my $rule = 'XF+F+XF--F--XF+F+X'; my $S = 'F--F--XF--F--XF'; $S =~ s/X/$rule/g for 1..5;

my (@X, @Y); my ($x, $y) = (0, 0); my $theta = pi/4; my $r = 6;

for (split //, $S) { 

   if (/F/) {
       push @X, sprintf "%.0f", $x;
       push @Y, sprintf "%.0f", $y;
       $x += $r * cos($theta);
       $y += $r * sin($theta);
   }
   elsif (/\+/) { $theta += pi/4; }
   elsif (/\-/) { $theta -= pi/4; }

}

my ($xrng, $yrng) = ( max(@X) - min(@X), max(@Y) - min(@Y)); my ($xt, $yt) = (-min(@X) + 10, -min(@Y) + 10);

my $svg = SVG->new(width=>$xrng+20, height=>$yrng+20); my $points = $svg->get_path(x=>\@X, y=>\@Y, -type=>'polyline'); $svg->rect(width=>"100%", height=>"100%", style=>{'fill'=>'black'}); $svg->polyline(%$points, style=>{'stroke'=>'orange', 'stroke-width'=>1}, transform=>"translate($xt,$yt)");

open my $fh, '>', 'sierpinski-curve.svg'; print $fh $svg->xmlify(-namespace=>'svg'); close $fh;</lang> See: sierpinski-curve.svg (offsite SVG image)

Phix

Library: Phix/pGUI

<lang Phix>-- demo\rosetta\Sierpinski_curve.exw -- -- Draws curves lo to hi (simultaneously), initially {1,1}, max {8,8} -- Press +/- to change hi, shift +/- to change lo. -- ("=_" are also mapped to "+-", for the non-numpad +/-) -- include pGUI.e

Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas

integer width, height, 

       lo = 1, hi = 1

atom cx, cy, h

procedure lineTo(atom newX, newY) 

   cdCanvasVertex(cddbuffer, newX-width/2+h, height-newY+2*h)
   cx = newX
   cy = newY

end procedure

procedure lineN() lineTo(cx,cy-2*h) end procedure procedure lineS() lineTo(cx,cy+2*h) end procedure procedure lineE() lineTo(cx+2*h,cy) end procedure procedure lineW() lineTo(cx-2*h,cy) end procedure

procedure lineNW() lineTo(cx-h,cy-h) end procedure procedure lineNE() lineTo(cx+h,cy-h) end procedure procedure lineSE() lineTo(cx+h,cy+h) end procedure procedure lineSW() lineTo(cx-h,cy+h) end procedure

procedure sierN(integer level) 

  if level=1 then
     lineNE()  lineN()
     lineNW()
  else
     sierN(level-1)  lineNE()
     sierE(level-1)  lineN()
     sierW(level-1)  lineNW()
     sierN(level-1) 
  end if

end procedure

procedure sierE(integer level) 

  if level=1 then
     lineSE()  lineE()
     lineNE() 
  else
     sierE(level-1)  lineSE()
     sierS(level-1)  lineE()
     sierN(level-1)  lineNE()
     sierE(level-1) 
  end if

end procedure

procedure sierS(integer level) 

  if level=1 then
     lineSW()  lineS()
     lineSE() 
  else
     sierS(level-1)  lineSW()
     sierW(level-1)  lineS()
     sierE(level-1)  lineSE()
     sierS(level-1) 
  end if

end procedure

procedure sierW(integer level) 

  if level=1 then
     lineNW()  lineW()
     lineSW() 
  else
     sierW(level-1)  lineNW()
     sierN(level-1)  lineW()
     sierS(level-1)  lineSW()
     sierW(level-1) 
  end if

end procedure

procedure sierpinskiCurve(integer level) 

  sierN(level)     lineNE()
  sierE(level)     lineSE()
  sierS(level)     lineSW()
  sierW(level)     lineNW()

end procedure

function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/) 

   {width, height} = IupGetIntInt(canvas, "DRAWSIZE")
   cdCanvasActivate(cddbuffer)
   for level=lo to hi do
       cx = width/2
       cy = height
       h = cx/power(2,level+1)
       cdCanvasBegin(cddbuffer, CD_CLOSED_LINES)
       sierpinskiCurve(level)
       cdCanvasEnd(cddbuffer)
   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_BLUE)
   return IUP_DEFAULT

end function

function key_cb(Ihandle /*ih*/, atom c) 

   if c=K_ESC then return IUP_CLOSE end if
   if find(c,"+=-_") then
       bool bShift = IupGetInt(NULL,"SHIFTKEY")
       if c='+' or c='=' then
           if bShift then
               lo = min(lo+1,hi)
           else
               hi = min(8,hi+1)
           end if
       elsif c='-' or c='_' then
           if bShift then
               lo = max(1,lo-1)
           else
               hi = max(lo,hi-1)
           end if
       end if
       IupSetStrAttribute(dlg, "TITLE", "Sierpinski curve (%d..%d)",{lo,hi})
       cdCanvasClear(cddbuffer)
       IupUpdate(canvas)
   end if
   return IUP_CONTINUE

end function

procedure main() 

   IupOpen()
   
   canvas = IupCanvas(NULL)
   IupSetAttribute(canvas, "RASTERSIZE", "770x770")
   IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
   IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))

   dlg = IupDialog(canvas)
   IupSetAttribute(dlg, "TITLE", "Sierpinski curve (1..1)")
   IupSetCallback(dlg, "K_ANY", Icallback("key_cb"))

   IupMap(dlg)
   IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
   IupMainLoop()
   IupClose()

end procedure

main()</lang>

Raku

(formerly Perl 6)

Works with: Rakudo version 2020.02

<lang perl6>use SVG;

role Lindenmayer { 

   has %.rules;
   method succ {
       self.comb.map( { %!rules{$^c} // $c } ).join but Lindenmayer(%!rules)
   }

}

my $sierpinski = 'F--XF--F--XF' but Lindenmayer( { X => 'XF+G+XF--F--XF+G+X' } );

$sierpinski++ xx 5;

my $dim = 640; my $scale = 8; my $dir = pi/4; my @points = (316, -108);

for $sierpinski.comb { 

   state ($x, $y) = @points[0,1];
   state $d = 0;
   when 'F'|'G' { @points.append: ($x += $scale * $d.cos).round(1), ($y += $scale * $d.sin).round(1) }
   when '+' { $d -= $dir }
   when '-' { $d += $dir }
   default { }

}

my $out = './sierpinski-curve-perl6.svg'.IO;

$out.spurt: SVG.serialize( 

   svg => [
       :width($dim), :height($dim),
       :rect[:width<100%>, :height<100%>, :fill<black>],
       :polyline[
         :points(@points.join: ','), :fill<black>,
         :transform("rotate(45, 320, 320)"), :style<stroke:#F7DF1E>,
       ],
   ],

);</lang> See: Sierpinski-curve-perl6.svg (offsite SVG image)

Rust

Program output is a file in SVG format. <lang rust>// [dependencies] // svg = "0.8.0"

use svg::node::element::path::Data; use svg::node::element::Path;

struct SierpinskiCurve { 

   current_x: f64,
   current_y: f64,
   current_angle: i32,
   line_length: f64,

}

impl SierpinskiCurve { 

   fn new(x: f64, y: f64, length: f64, angle: i32) -> SierpinskiCurve {
       SierpinskiCurve {
           current_x: x,
           current_y: y,
           current_angle: angle,
           line_length: length,
       }
   }
   fn rewrite(order: usize) -> String {
       let mut str = String::from("F--XF--F--XF");
       for _ in 0..order {
           let mut tmp = String::new();
           for ch in str.chars() {
               match ch {
                   'X' => tmp.push_str("XF+G+XF--F--XF+G+X"),
                   _ => tmp.push(ch),
               }
           }
           str = tmp;
       }
       str
   }
   fn execute(&mut self, order: usize) -> Path {
       let mut data = Data::new().move_to((self.current_x, self.current_y));
       for ch in SierpinskiCurve::rewrite(order).chars() {
           match ch {
               'F' => data = self.draw_line(data),
               'G' => data = self.draw_line(data),
               '+' => self.turn(45),
               '-' => self.turn(-45),
               _ => {}
           }
       }
       Path::new()
           .set("fill", "none")
           .set("stroke", "black")
           .set("stroke-width", "1")
           .set("d", data)
   }
   fn draw_line(&mut self, data: Data) -> Data {
       let theta = (self.current_angle as f64).to_radians();
       self.current_x += self.line_length * theta.cos();
       self.current_y -= self.line_length * theta.sin();
       data.line_to((self.current_x, self.current_y))
   }
   fn turn(&mut self, angle: i32) {
       self.current_angle = (self.current_angle + angle) % 360;
   }
   fn save(file: &str, size: usize, order: usize) -> std::io::Result<()> {
       use svg::node::element::Rectangle;
       let x = 5.0;
       let y = 10.0;
       let rect = Rectangle::new()
           .set("width", "100%")
           .set("height", "100%")
           .set("fill", "white");
       let mut s = SierpinskiCurve::new(x, y, 7.0, 45);
       let document = svg::Document::new()
           .set("width", size)
           .set("height", size)
           .add(rect)
           .add(s.execute(order));
       svg::save(file, &document)
   }

}

fn main() { 

   SierpinskiCurve::save("sierpinski_curve.svg", 545, 5).unwrap();

}</lang>

Output:

See: sierpinski_curve.svg (offsite SVG image)

Sidef

Uses the LSystem() class from Hilbert curve. <lang ruby>var rules = Hash( 

   x => 'xF+G+xF--F--xF+G+x',

)

var lsys = LSystem( 

   width:  550,
   height: 550,

   xoff: -9,
   yoff: -271,

   len:   5,
   angle: 45,
   color: 'dark green',

)

lsys.execute('F--xF--F--xF', 5, "sierpiński_curve.png", rules)</lang> Output image: Sierpiński curve

zkl

Uses Image Magick and the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl <lang zkl>sierpinskiCurve(5) : turtle(_,45,45); // n=5 --> 11,606 characters

fcn sierpinskiCurve(order){ 

  LSystem("F--XF--F--XF",Dictionary("X","XF+G+XF--F--XF+G+X"), order)

} fcn LSystem(axiom,rules,order){ // Lindenmayer system 

  buf1,buf2 := Data(Void,axiom).howza(3), Data().howza(3);  // characters
  do(order){
     buf1.pump(buf2.clear(),'wrap(c){ rules.find(c,c) });   // change if rule
     t:=buf1; buf1=buf2; buf2=t;	// swap buffers
  }
  buf1

}

fcn turtle(curve,angle,startAngle){ // angles in degrees 

  const D=10.0;
  dir:=startAngle;
  img,color := PPM(800,800), 0x00ff00;  // green on black
  x,y := 15, img.h - x;
  foreach c in (curve){
     switch(c){

case("F","G"){ // draw forward a,b := D.toRectangular(dir.toFloat().toRad()); img.line(x,y, (x+=a.round()),(y+=b.round()), color) } case("+"){ dir=(dir + angle)%360; } // turn left angle case("-"){ dir=(dir - angle)%360; } // turn right angle 

     }
  }
  img.writeJPGFile("sierpinskiCurve.zkl.jpg");

}</lang>

Output:

Offsite image at Sierpinski curve order 5

Retrieved from "https://rosettacode.org/wiki/Sierpinski_curve?oldid=298926"