It's definitely a fractal curve. It's just so long since I did fractal things, I don't remember what people were calling these them.

String rewriting is all in The Science of Fractal Images, ed Peitgen & Saupe (Springer-Verlag, 1991, ISBN: 0387966080). Of course, they were using an awkward Pascal-like pseudocode language with no regular expressions ...

Here's at least part of the famous snowflake. I think I changed three lines:

#!/usr/bin/perl -w
use strict;
use integer;

my $depth   = 4;
my $start   = '_/_\_/_';    # _ = forward, / = left, \ = right
my $fractal = $start;

$fractal =~ s/_/$start/og for ( 0 .. $depth );

$fractal =~ s/_/0 0.8 rlineto /g;
$fractal =~ s,/,60 rotate ,g;
$fractal =~ s,\\,240 rotate ,g;
print '%!', "\n", '0.1 setlinewidth 500 100 moveto ', $fractal,
  'stroke showpage', "\n";
[download]

Now what would be really cool would be a Perl routine that would parse ASCII-art axioms and production rules, and generate the fractal. My free time is not that copious.

--
bowling trophy thieves, die!