Sierpinski square curve: Difference between revisions
(→{{header|Julia}}: mark as incorrect, since it does not generate the Sierpinski square curve) |
(Go/Julia moved, Phix replaced, see talk page) |
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Produce a graphical or ASCII-art representation of a [[wp:Sierpiński_curve|Sierpinski square curve]] of at least order 3.
=={{header|Perl}}==
Line 276 ⟶ 95:
=={{header|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>
=={{header|Sidef}}==
|
Revision as of 16:51, 5 March 2020
- Task
Produce a graphical or ASCII-art representation of a Sierpinski square curve of at least order 3.
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 $fh;</lang> See: sierpinski-square-curve.svg (offsite SVG image)
Perl 6
<lang perl6>use SVG;
role Lindenmayer {
has %.rules; method succ { self.comb.map( { %!rules{$^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)
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>
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