#!/usr/bin/perl6

given new life(dimension => 20)
{
    for 1..Inf -> $count
    {
        .display();
        print "TURN $count, press enter for next turn, ctl-c to quit";
        <$*STDIN>;
        .calculate();
    }
}

class life
{
    has int $.dimension;

    has @.grid is dim($.dimension, $.dimension)
               is base_index($.dimension/2, $.dimension/2)
           of bit is default(0)
                  is str {<< - + >>[$_]};

    method BUILD($.dimension)
    {
        for (-1, 0), (-1, 1), (0, 0), (0, -1), (1, 0) -> $x, $y
        {
            @.grid[$y][$x] = 1;
        }
    }

    method will_live(int $y, int $x) returns bool is private
    {
        my $neighborhood = @.grid[$y+(-1|0|+1)][$x+(-1|0|+1)];
        my $alive = sum($neighborhood.elems);

        @.grid[$y][$x] ?? 1 < $alive-1 < 4 :: $alive == 3;
    }

    method calculate
    {
        my @new_grid is like @.grid;
        for @new_grid.kv -> $y, @new_row is rw
        {
            for @row.kv -> $x, $new_cell is rw
            {
                $new_cell = .will_live($y,$x) ?? 1 :: 0;
            }
        }
        @.grid = @new_grid;
    }

    method display
    {
        for @.grid -> @row
        {
            print @row, "\n";
        }
    }
}
[download]

Update: I'm pretty sure the junction I gave for the neighborhood won't work: here's an improved will_live method:

    method will_live(int $y, int $x) returns bool
    {
        my $offsets = [-1|0|+1 , -1|0|+1] & none([0,0]);
        my @neighbors = ($offsets >>+<< [$y,$x]).states;
        my @cells = @neighbors.map {@.grid[$_[0]][$_[1]]};
        my $alive = @cells.sum;

        @.grid[$y][$x] ?? $alive == 2|3 :: $alive == 3;
    }
[download]