I was waiting for another one of these posts ;-) Rule 90 will generate Sierpinski's sieve (but then, you can in turn generate that from Pascal's triangle (mod 2)).
#!/usr/bin/perl -w
use strict;
my ($file, %rules, $string, $rewrite, $angle, $i);
$file = "gosper";
# Peano-Gosper curve.
$rules{"X"} = "X+YF++YF-FX--FXFX-YF+";
$rules{"Y"} = "-FX+YFYF++YF+FX--FX-Y";
$string = "FX"; $angle = 60; $i = 4;
foreach (1..$i) {
$rewrite = "";
for (split //,$string) {
$rewrite .= $rules{$_} || $_;
}
$string = $rewrite;
}
open PS,">$file.ps";
print PS "%#\n\n";
print PS "306 396 moveto\n";
for my $ch (split //,$string) {
if ($ch eq 'f') {
print PS "0 1 rlineto\n";
} elsif ($ch eq 'F') {
print PS "0 1 rmoveto\n";
} elsif ($ch eq '+') {
print PS "360 $angle rotate\n";
} elsif ($ch eq '-') {
print PS "360 $angle neg rotate\n";
} elsif ($ch eq '!') {
print PS "-1 1 scale\n";
} elsif ($ch eq '[') {
print PS "gsave\n";
} elsif ($ch eq ']') {
print PS "stroke\ngrestore\n";
}
}
print PS "stroke\nshowpage";
close PS;
Note that you need to replace uppercase F with lowercase f to turn on the 'pen'.
