wiredrat, you got me thinking about what I was really after and are right about me wanting the total population. Up in Re^2: A script with a loop is running my computer Out of memory I was talking about the number 250 billion. Well, that is the total population I am trying to get without something clunking out on me. So, I did a little finagling and came up with the following which returns the amount born into a generation and the total population which include the previous two generations. So, while I am still storing every generation generated, the current code is faster even with the new addition of total population.

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

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 => {
    children => $generation,
    total_population => $generation,
  }
);

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

for my $gen (2..$generations) {
  my $children = 0;
  for (1..$generation) {
    $children += $distribution[rand(@distribution)];
  }
  $generation = $children;
  last if ($children == 0);
  $generations{$gen}{children} = $generation;
  my $total_population = $generations{$gen}{children};
    $total_population += $generations{$gen - 1}{children} if $generati
+ons{$gen - 1};
    $total_population += $generations{$gen - 2}{children} if $generati
+ons{$gen - 2};
  $generations{$gen}{total_population} = $total_population;
}

my @children;
my @population;
for (1..$generations) {
  push @children, $generations{$_}{children};
  push @population, $generations{$_}{total_population};
}

my $max_length_generation = length(commify(max(keys %generations)));
my $max_length_children = length(commify(max(@children)));
my $max_length_population = length(commify(max(@population)));

for (sort {$a <=> $b} keys %generations) {
  printf "%${max_length_generation}s: %${max_length_children}s %${max_
+length_population}s\n",
  $_,commify($generations{$_}{children}),commify($generations{$_}{tota
+l_population});
}
[download]

Thanks again for the idea!