# Turtle as in LOGO's Turtle
{package turtle;
	use constant PI => 3.14159265359;
	sub new {return bless({h=>0,xy=>[[0],[0]]});}
	sub rt {$_[0]->{h}=$_[0]->{h}+$_[1];} # right turn by x degrees
	sub fd {			      # forward by x points
		my ($h, $xy, $d) = ($_[0]->{h}, $_[0]->{xy}, $_[1]);
		$xy->[0][scalar(@{$xy->[0]})] = $d*sin(PI*$h/180) + $xy->[0][$#{@{$xy->[0]}}]; 
		$xy->[1][scalar(@{$xy->[1]})] = $d*cos(PI*$h/180) + $xy->[1][$#{@{$xy->[1]}}]; 
		$_[0]->{xy} = $xy; return $xy;
	}
}


# -----------------------------------------------------------
# Koch Snowflake
sub koch {
	my ($turtle, $d, $level) = @_ ;
	if ($level==0) {$turtle->fd($d); return 1;} 
	$turtle->rt(  0); koch($turtle, $d/3,$level-1);
	$turtle->rt(-60); koch($turtle, $d/3,$level-1);
	$turtle->rt(120); koch($turtle, $d/3,$level-1);
	$turtle->rt(-60); koch($turtle, $d/3,$level-1);
}
# -----------------------------------------------------------
my $turtle = turtle->new();
map {$turtle->rt(120); koch($turtle, 170, 4);} 0..2;
# -----------------------------------------------------------
plotxy($turtle->{xy}, 'koch.jpg');


# -----------------------------------------------------------
# Minkowski Island
sub minkowski {
	my ($turtle, $d, $level) = @_ ;
	if ($level==0) {$turtle->fd($d); return 1;} 
	minkowski($turtle,$d/4,$level-1);
	$turtle->rt(-90); minkowski($turtle,$d/4,$level-1);
	$turtle->rt( 90); minkowski($turtle,$d/4,$level-1);
	$turtle->rt( 90); minkowski($turtle,$d/4,$level-1);
	minkowski($turtle,$d/4,$level-1);
	$turtle->rt(-90); minkowski($turtle,$d/4,$level-1);
	$turtle->rt(-90); minkowski($turtle,$d/4,$level-1);
	$turtle->rt( 90); minkowski($turtle,$d/4,$level-1);
}
# -----------------------------------------------------------
$turtle = turtle->new();
map {$turtle->rt(90); minkowski($turtle, 150, 3);} 0..3;
# -----------------------------------------------------------
plotxy($turtle->{xy}, 'minkowski.jpg');
# -----------------------------------------------------------


# -----------------------------------------------------------
# Dragon Curve
sub dragon1 {
	my ($turtle, $d, $level) = @_ ;
	if ($level==0) {$turtle->fd($d); return 1;} 
	dragon($turtle,$d*0.707,$level-1);
	$turtle->rt(-90); dragon1($turtle,$d*0.707,$level-1);
}
sub dragon {
	my ($turtle, $d, $level) = @_ ;
	if ($level==0) {$turtle->fd($d); return 1;} 
	dragon($turtle,$d*0.707,$level-1);
	$turtle->rt(90); dragon1($turtle,$d*0.707,$level-1);
}
# -----------------------------------------------------------
$turtle = turtle->new();
dragon($turtle, 150, 12);
# -----------------------------------------------------------
plotxy($turtle->{xy}, 'dragon.jpg');