; Koch Snowflake

to KochIsland :size :level
	repeat 3 [KSide :size :level rt 120]
end 

to KSide :size :level
	if :level = 0 [fd :size stop]
	KSide :size / 3 :level - 1
	lt 60 KSide :size / 3 :level - 1
	rt 120 KSide :size / 3 :level - 1
	lt 60 KSide :size / 3 :level - 1
end

##</code><code>##

#! /usr/local/bin/perl -w
use strict;
use GD;
# -----------------------------------------------------------
use constant PI => 3.14159265359;
# -----------------------------------------------------------
# turtle as in LOGO's turtle
# Usage: $turtle = turtle();
#        $turtle->($turn_right_x_degree, $forward_x_points);
#        $xy = $turtle->();
sub turtle {
	my ($h, $xy) = (0, [[0],[0]]); 	# h = heading (0 - north, 90 - east, etc)
	return sub { 
		$h = $h + (shift || 0);	# accumulative turns in degree
		my $d = shift || 0;	# distance
		$xy->[0][scalar(@{$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]}}]; 
		return $xy;
	};
}
# -----------------------------------------------------------
# Koch Snowflake
sub koch {
	my ($turtle, $d, $level) = @_ ;
	if ($level==0) {$turtle->(0,$d); return 1;} 
	$turtle->(  0,0); koch($turtle,$d/3,$level-1);
	$turtle->(-60,0); koch($turtle,$d/3,$level-1);
	$turtle->(120,0); koch($turtle,$d/3,$level-1);
	$turtle->(-60,0); koch($turtle,$d/3,$level-1);
}
# -----------------------------------------------------------
my $turtle = turtle();
map {$turtle->(120, 0); koch($turtle, 170, 4);} 0..2;
# -----------------------------------------------------------
plotxy($turtle->(), 'koch.jpg');
# -----------------------------------------------------------


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


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


# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # 
# Sub for Plotting
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # 
sub min {(sort {$a<=>$b} @_ )[0];}
# ----------------------------------------------------------------
sub max {(sort {$a<=>$b} @_ )[-1];}
# ----------------------------------------------------------------
sub plotxy {
	my $xy = shift;
	my $file = shift;
	my $scale = shift || 1;
	# -------------------------------------------------------
	my @x = @{$xy->[0]};
	my @y = @{$xy->[1]};
	my $x_min = min(@x);
	my $y_min = min(@y);
	map {$x[$_]=$scale*($x[$_]-$x_min)} 0..$#x;
	map {$y[$_]=$scale*($y[$_]-$y_min)} 0..$#y;
	my $x_width = max(@x) - 0;
	my $y_width = max(@y) - 0;
	# -------------------------------------------------------
	my $image = new GD::Image($x_width,$y_width);
	my $white = $image->colorAllocate(255,255,255);
	my $black = $image->colorAllocate(0,0,0);   
	$image->transparent($white);
	$image->interlaced('true'); 
	$image->line($x[$_-1],$y[$_-1],$x[$_],$y[$_],$black) for 1..$#x;
	$image = $image->copyFlipVertical() ;
	open(IMG, ">$file");
	binmode IMG;
	print IMG $image->jpeg;
}

##</code><code>##

# 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');

##</code><code>##

use constant PI => 3.14159265359;
# -----------------------------------------------------------
# Turtle Graph
my $h=0; my @x=(0); my @y=(0);
sub rt {$h = $h + shift;}
sub fd {
	$x[scalar @x] = $_[0]*sin(PI*$h/180) + $x[$#x]; 
	$y[scalar @y] = $_[0]*cos(PI*$h/180) + $y[$#y]; 
}
sub reset_xy {$h=0; @x=(0); @y=(0);}
# -----------------------------------------------------------


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


# -----------------------------------------------------------
# Minkowski Island
sub minkowski {
	my ($d, $level) = @_ ;
	if ($level==0) {fd($d); return 1;} 
	minkowski($d/4,$level-1);
	rt(-90); minkowski($d/4,$level-1);
	rt( 90); minkowski($d/4,$level-1);
	rt( 90); minkowski($d/4,$level-1);
	minkowski($d/4,$level-1);
	rt(-90); minkowski($d/4,$level-1);
	rt(-90); minkowski($d/4,$level-1);
	rt( 90); minkowski($d/4,$level-1);
}
# -----------------------------------------------------------
reset_xy();	# if necessary
map {rt(90); minkowski(150, 3);} 0..3;
# -----------------------------------------------------------
plotxy([\@x,\@y], 'minkowski.jpg');
# -----------------------------------------------------------


# -----------------------------------------------------------
# Dragon Curve
sub dragon1 {
	my ($d, $level) = @_ ;
	if ($level==0) {fd($d); return 1;} 
	dragon($d*0.707,$level-1);
	rt(-90); dragon1($d*0.707,$level-1);
}
sub dragon {
	my ($d, $level) = @_ ;
	if ($level==0) {fd($d); return 1;} 
	dragon($d*0.707,$level-1);
	rt(90); dragon1($d*0.707,$level-1);
}
# -----------------------------------------------------------
reset_xy();	# if necessary
dragon(150, 12);
# -----------------------------------------------------------
plotxy([\@x,\@y], 'dragon.jpg');