http://qs1969.pair.com?node_id=175820

in reply to 1-D Cellular Automata

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;