#! perl -slw
use strict;

$|++;

our $DEPTH ||= 3;

sub fract2D {
    use integer;
    my( $x, $y, $depth ) = @_;

    if( $x < 16 and $y <  ) {        ## A block on the major diagonal
        return $x == $y ? $depth : $depth -1;
    }
    elsif( $depth > 1 ) {
        return fract2D( $x % 4**$depth, $y % 4**$depth, $depth -1 );
    }
    else {
        return fract2D( $x % 4**$depth, $y % 4**$depth, $depth );
    }
}

for my $depth ( $DEPTH ) {
    for my $y ( 0 .. 4**$depth-1 ) {
        my $c = 0;
        for my $x ( 0 .. 4 ** $depth -1 ) {
            printf +( ( ++$c % 4 ) == 0 ? " %2d " : " %2d" ),
                fract2D( $x, $y, $depth );
        }
        print +( $y % 4 ) == 3 ? "\n" : '';
    }
    print '';
}