Thanks for that tip, JavaFan. I used it, and you are so right. It is much faster and my memory doesn't run out! Unfortunately, I did come against another error "Range iterator outside integer range". I haven't quite got that figured just yet.

I didn't use your exact fragment, but I think it is close enough.

#!/usr/bin/perl -l
use strict;
use warnings;
use feature qw(say);
use List::Util qw(sum max);

use lib 'lib';
use Base::Nifty qw(commify);

say "How many children are in the first generation?";
my $generation = <>;
say "How many generations do you want to generate?";
my $generations = <>;
chomp($generation,$generations);

my %generations = (
  1 => $generation,
);

my @distribution = (0,0,0,1,1,1,2,2,2,3,3,4,5,6);

for my $gen (1..$generations) {
  my $children = 0;
  for (1..$generation) {
    $children += $distribution[rand(@distribution)];
  }
  $generation = $children;
  last if ($children == 0);
  $generations{$gen + 1} = $generation;
}

my $max_length_generation = length(commify(max(keys %generations)));
my $max_length_children = length(commify(max(values %generations)));

for (sort {$a <=> $b} keys %generations) {
  printf "%${max_length_generation}s: %${max_length_children}s\n",$_,c
+ommify($generations{$_});
}
[download]

The += did a whole lot of good! I haven't used that construction much in the past, so I don't automatically think of it. Hopefully one day it will sink in.