Okay, here's my take on this...

#!/usr/bin/perl
package main; # We're Perl 6 we are

use warnings;
use strict;

given Life.new(20) {
  while 1 {
    .display_on($*OUT);
    .calculate;
  }
}

class Life {
  has Int $.generations;
  has Int $.max;
  has @.grid;
  has @.neighbourhoods;

  method BUILD(Int $dim) {
    $.generations = 0;

    my @grid of Bit is dim(2, $dim, $dim) is default(0);
    
    @grid[0][$dim / 2 - 1][$dim / 2    ] = 1;
    @grid[0][$dim / 2 - 1][$dim / 2 + 1] = 1;
    @grid[0][$dim / 2    ][$dim / 2    ] = 1;
    @grid[0][$dim / 2    ][$dim / 2 - 1] = 1;
    @grid[0][$dim / 2 + 1][$dim / 2    ] = 1;
    @.grid := @grid;

    # Set up our neighbourhoods and cell count
    $.max = $dim - 1;

    for 0..$.max -> $i {
      for 0..$.max -> $j {
        my @hood is dim(2,3,3);
        @hood[0..1][0..2][0..2] >>:=<< 
          @.grid[0..1][map $_%($.max+1), $i-1..$i+1]
                     .[map $_ % ($.max+1),$j-1..$j+1];
        push @.neighbourhoods, @hood;
      }
    }
  }
  
  method calculate {
    for @.neighbourhoods -> @hood {
      my @old := @hood[$.generations % 2];
      my $new := @hood[($.generations + 1) % 2];
      
      my $live = sum(*@old) - @old[1][1];
      $new = $live == 2 && @old[1][1] ||
             $live == 3;
    }
    $.generations++;
  }

  method display_on($fh) {
    for 0 .. $.max -> $i {
      for 0 .. $.max -> $j {
        $fh.print($.grid[$generation][$i][$j] ?? '+' :: '.');
        LAST { $fh.print("\n") }
      }
    }

    print "Turn $.generation, press enter for next turn, ctl-c to quit
+";
    <STDIN>
  }
}
[download]

Of course, all this presupposes that I actually understand what I'm doing with :=, which isn't necessarily a good assumption. The trick is that we're precalculating (and binding) all our neighbourhoods, and setting up the old/new grids at initialization time as well, which enables us to simplify the calculation somewhat.

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