Here is last (hopefully) instalment in this thread; it only concerns faster, compared to the PDL CPAN tutorial, "Game of Life" implementation. But maybe some features used are too advanced for a tutorial. Improvement comes from:

• To achieve wrap around, the ugly glueing in parent node is replaced with dicing along each axis. Very convenient function.
• Horrible expression to compute next generation (requires 8 operations on whole arrays) is replaced with shorter version (just 4).

use strict;
use warnings;
use feature 'say';
use Time::HiRes 'time';

use PDL;
use PDL::NiceSlice;
use Test::PDL 'eq_pdl';

use constant {
    WIDTH  => 20,
    HEIGHT => 20,
    STEPS  => 1000,
};
my $x = zeroes long, WIDTH, HEIGHT;

# Put in a simple glider.
$x(1:3,1:3) .= pdl ( [1,1,1],
                     [0,0,1],
                     [0,1,0] );
my $backup = $x-> copy;

printf "Game of Life!\nMatrix: %s, %d generations\n", 
    $x-> info, STEPS;

# Tutorial
my $t = time;
for ( 1 .. STEPS ) {
    my $t_ = time;
    # Calculate the number of neighbours per cell.
    my $n = $x->range(ndcoords($x)-1,3,"periodic")->reorder(2,3,0,1);
    $n = $n->sumover->sumover - $x;

    # Calculate the next generation.
    $x = ((($n == 2) + ($n == 3))* $x) + (($n == 3) * !$x);
}
printf "Tutorial: %0.3f s\n", time - $t;

# Faster
my $m = $backup-> copy;
$t = time;
my $wrap_w = pdl [ reverse WIDTH - 1, ( 0 .. WIDTH - 1 ), 0 ];
my $wrap_h = pdl [ reverse HEIGHT - 1, ( 0 .. HEIGHT - 1 ), 0 ];
for ( 1 .. STEPS ) {
    my $n = $m
        -> dice_axis( 0, $wrap_w )
        -> lags( 0, 1, WIDTH )
        -> sumover
        -> dice_axis( 1, $wrap_h )
        -> lags( 1, 1, HEIGHT )
        -> xchg( 0, 1 )
        -> sumover;
    $n -= $m;
    $m = ( $n == 3 ) | $m & ( $n == 2 )
}
printf "Faster:   %0.3f s\n", time - $t;

die unless eq_pdl( $x, $m );

__END__

Game of Life!
Matrix: PDL: Long D [20,20], 1000 generations
Tutorial: 0.341 s
Faster:   0.111 s

Matrix: PDL: Long D [200,200], 100 generations
Tutorial: 0.845 s
Faster:   0.086 s

Matrix: PDL: Long D [1000,1000], 20 generations
Tutorial: 4.422 s
Faster:   0.443 s

Matrix: PDL: Long D [2000,2000], 10 generations
Tutorial: 8.878 s
Faster:   0.872 s
[download]

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