Thank you for the idea of distribution, I toyed with the idea while writing it, but thought int(rand(6)) was easier. You are right though, it should be weighted towards fewer children per person of the previous generation. However, I found a situation where I have had to stop the loop. In the first few iterations of the main loop, a generation could end up with 0 children in it. At that point, going any further would be pointless. So while I could still push the generation with 0 children to an array instead of adding another key to the hash, max(keys %generations) != $generations. I am still working the array versus hash idea, I still have to figure out everything I would have to change. I am just more comfortable dealing with hashes than arrays. Meanwhile, here is the updated script.

#!/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 (1..$generations) {
  my @generation;
  for (1..$generation) {
    my $children = $distribution[rand(@distribution)];
    push @generation, $children;
  }
  $generation = sum(@generation);
  last if sum(@generation == 0);
  $generations{$_ + 1} = $generation;
  @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($generations{$_});
}
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