Sierpinski square curve

Task

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

Go

The following uses the Lindenmayer system with the appropriate parameters from the Wikipedia article and produces a similar image (apart from the colors, yellow on blue) to the Sidef and zkl entries. <lang go>package main

import (

   "github.com/fogleman/gg"
   "github.com/trubitsyn/go-lindenmayer"
   "log"
   "math"

)

const twoPi = 2 * math.Pi

var (

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

)

var cx, cy, h, theta float64

func main() {

   dc.SetRGB(0, 0, 1) // blue background
   dc.Clear()
   cx, cy = 10, height/2+5
   h = 6
   sys := lindenmayer.Lsystem{
       Variables: []rune{'X'},
       Constants: []rune{'F', '+', '-'},
       Axiom:     "F+XF+F+XF",
       Rules: []lindenmayer.Rule{
           {"X", "XF-F+F-XF+F+XF-F+F-X"},
       },
       Angle: math.Pi / 2, // 90 degrees in radians
   }
   result := lindenmayer.Iterate(&sys, 5)
   operations := map[rune]func(){
       'F': func() {
           newX, newY := cx+h*math.Sin(theta), cy-h*math.Cos(theta)
           dc.LineTo(newX, newY)
           cx, cy = newX, newY
       },
       '+': func() {
           theta = math.Mod(theta+sys.Angle, twoPi)
       },
       '-': func() {
           theta = math.Mod(theta-sys.Angle, twoPi)
       },
   }
   if err := lindenmayer.Process(result, operations); err != nil {
       log.Fatal(err)
   }
   // needed to close the square at the extreme left
   operations['+']()
   operations['F']()

   // create the image and save it
   dc.SetRGB255(255, 255, 0) // yellow curve
   dc.SetLineWidth(2)
   dc.Stroke()
   dc.SavePNG("sierpinski_square_curve.png")

}</lang>

Julia

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

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

drawLSystem(scurve,

   forward = 3,
   turn = 90,
   startingy = -400,
   iterations = 6,
   filename = "sierpinski_square_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+F-XF+F+XF-F+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/2; }
   elsif (/\-/) { $theta -= pi/2; }

}

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

Phix

<lang Phix>constant rule = "XF-F+F-XF+F+XF-F+F-X" string s = "F+F+XF+F+XF" for n=1 to 4 do

   string next = ""
   for i=1 to length(s) do
       integer ch = s[i]
       next &= iff(ch='X'?rule:ch)
   end for
   s = next

end for

sequence X = {}, Y= {} atom x=0, y=0, theta=PI/4, r = 6 string svg = "" for i=1 to length(s) do

   integer ch = s[i]
   switch ch do
       case 'F':   X &= x; x += r*cos(theta)
                   Y &= y; y += r*sin(theta)
       case '+':   theta += PI/2
       case '-':   theta -= PI/2
   end switch

end for constant svgfmt = """ <svg xmlns="http://www.w3.org/2000/svg" height="%d" width="%d">

<rect height="100%%" width="100%%" style="fill:black" />
<polyline points="%s" style="stroke: orange; stroke-width: 1" transform="translate(%d,%d)" />

</svg>""" string points = "" for i=1 to length(X) do

   points &= sprintf("%.2f,%.2f ",{X[i],Y[i]})

end for integer fn = open("sierpinski_square_curve.svg","w") atom xt = -min(X)+10,

    yt = -min(Y)+10

printf(fn,svgfmt,{max(X)+xt+10,max(Y)+yt+10,points,xt,yt}) close(fn)</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 = 'X' but Lindenmayer( { X => 'XF-F+F-XF+F+XF-F+F-X' } );

$sierpinski++ xx 5;

my $dim = 600; my $scale = 6;

my @points = (-80, 298);

for $sierpinski.comb {

   state ($x, $y) = @points[0,1];
   state $d = $scale + 0i;
   when 'F' { @points.append: ($x += $d.re).round(1), ($y += $d.im).round(1) }
   when /< + - >/ { $d *= "{$_}1i" }
   default { }

}

my @t = @points.tail(2).clone;

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

$out.spurt: SVG.serialize(

   svg => [
       :width($dim), :height($dim),
       :rect[:width<100%>, :height<100%>, :fill<black>],
       :polyline[
         :points((@points, map {(@t »+=» $_).clone}, ($scale,0), (0,$scale), (-$scale,0)).join: ','),
         :fill<black>, :transform("rotate(45, 300, 300)"), :style<stroke:#61D4FF>,
       ],
       :polyline[
         :points(@points.map( -> $x,$y { $x, $dim - $y + 1 }).join: ','),
         :fill<black>, :transform("rotate(45, 300, 300)"), :style<stroke:#61D4FF>,
       ],
   ],

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

Sidef

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

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

)

var lsys = LSystem(

   width:  510,
   height: 510,

   xoff: -505,
   yoff: -254,

   len:   4,
   angle: 90,
   color: 'dark green',

)

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

zkl

Uses Image Magick and the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl <lang zkl>sierpinskiSquareCurve(4) : turtle(_);

fcn sierpinskiSquareCurve(n){ // Lindenmayer system --> Data of As

  var [const] A="AF-F+F-AF+F+AF-F+F-A", B="";  // Production rules
  var [const] Axiom="F+AF+F+AF";
  buf1,buf2 := Data(Void,Axiom).howza(3), Data().howza(3);  // characters
  do(n){
     buf1.pump(buf2.clear(),fcn(c){ if(c=="A") A else if(c=="B") B else c });
     t:=buf1; buf1=buf2; buf2=t;	// swap buffers
  }
  buf1		// n=4 --> 3,239 characters

}

fcn turtle(curve){ // a "square" turtle, directions are +-90*

  const D=10;
  ds,dir := T( T(D,0), T(0,-D), T(-D,0), T(0,D) ), 2; // turtle offsets
  dx,dy := ds[dir];
  img,color := PPM(650,650), 0x00ff00;  // green on black
  x,y := img.w/2, 10;
  curve.replace("A","").replace("B","");  // A & B are no-op during drawing
  foreach c in (curve){
     switch(c){

case("F"){ img.line(x,y, (x+=dx),(y+=dy), color) } // draw forward case("+"){ dir=(dir+1)%4; dx,dy = ds[dir] } // turn right 90* case("-"){ dir=(dir-1)%4; dx,dy = ds[dir] } // turn left 90*

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

}</lang>

Output:

Offsite image at Sierpinski square curve of order 4