Dig Trig
Cellular Automaton
Conway's Game of Life
Wikipedia has quite a bit of info on Conway's Game of Life. With a very simple set of logical rules, very complex universes can be created. Test out your universe by setting your own rules for life, birth and death. The original Game of Life uses a 23/3 rule (2 or 3 neighbors stays alive, 3 neighbors creates new life, all others die) There is quite a bit of information on Cellular Automaton on Wikipedia, as well.
Rules of the Universe
All Else: Abandon All Hope Ye Who Enter Here...
10/08/08 - Universe 3/03 Mapped!
I have logged every iteration for the rule set 3/03 on a 20x20 field, starting with an empty field. There are 335,225 unique iterations before it starts to loop upon iteration 243,830. Take a look at the topology of Universe 3/03.
Try These

Hand of God

probability (0-1)

Population Timeline