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    4 => { # Dragon curve: distance=10, theta=90
        axiom => 'FX',
        X => 'X+YF+',
        Y => '-FX-Y',
    },
    5 => { # Sierpiński arrowhead curve: distance=1, theta=60
        axiom => 'F',
        F => 'G-F-G',
        G => 'F+G+F',
    },
    6 => { # Sierpiński triangle: distance=4, theta=120
        axiom => 'F-G-G',
        F => 'F-G+F+G-F',
        G => 'GG',
    },
    7 => { # Koch snowflake: distance=3, theta=60
        axiom => 'F++F++F',
        F => 'F-F++F-F',
        X => 'FF',
    },
    8 => { # Sierpiński carpet: distance=4, theta=90
        axiom => 'F',
        F => 'F+F-F-F-G+F+F+F-F',
        G => 'GGG',
    },
    9 => { # Koch island: distance=5, theta=90
        axiom => 'F-F-F-F',
        F => 'F-F+F+FF-F-F+F',
    },
    10 => { # Koch islands and lakes: distance=5, theta=90
        axiom => 'F+F+F+F',
        F => 'F+f-FF+F+FF+Ff+FF-f+FF-F-FF-Ff-FFF',
        f => 'ffffff',
    },
    11 => { # Grid: distance=5, theta=90
        axiom => 'F-F-F-F',
        F => 'FF-F-F-F-FF',
    },
    12 => { # Terndrils: distance=5, theta=90
        axiom => 'F-F-F-F',
        F => 'FF-F--F-F',
    },
);

my $string = $rule{ $opts{rule} }{axiom};

my $turtle = Data::Turtle->new(
    width  => $opts{width},
    height => $opts{height},
    x      => $opts{width} / 2,
    y      => $opts{center} ? $opts{height} / 2 : $opts{height},
);

my $img = GD::Image->new( $opts{width}, $opts{height} );

my %color = (
    white => $img->colorAllocate( 255, 255, 255 ),
    black => $img->colorAllocate( 0, 0, 0 ),
);

$img->transparent( $color{white} );
$img->interlaced('true');

my @statestack;

my %translate = (
    'f' => sub { $turtle->forward( $opts{distance} ) },
    'F' => \&forward,
    'G' => \&forward,
    '-' => sub { $turtle->turn( - $opts{theta} ) },
    '+' => sub { $turtle->turn( $opts{theta} ) },
    'M' => sub { $turtle->mirror },
    '[' => sub { push @statestack, [ $turtle->get_state ] },
    ']' => sub { $turtle->set_state( @{ pop @statestack } ) },
);

for ( 1 .. $opts{repeat} ) {
    $string =~ s/(.)/defined($rule{ $opts{rule} }{$1}) ? $rule{ $opts{rule} }{$1} : $1/eg;
}
warn "$string\n";

for my $command ( split //, $string ) {
    $translate{$command}->() if exists $translate{$command};
}

print $img->png;

sub forward {
    my @line = $turtle->forward( $opts{distance} );
    if ( $turtle->pen_down ) {
        $img->setThickness( $line[5] );
        $img->line( @line[ 0 .. 3 ], $color{ $line[4] } );
    }
}