John Conway’s Game of Life is a well-known cellular automaton. In Life, “cells” live on a two-dimensional grid and survive, reproduce, and die based on four simple rules:
Start with a random configuration or input your own starting configuration with touch controls.
Wikipedia has a good introduction to the game, including several interesting patterns that you can try in SimpleLife.
SimpleLife supports iOS devices with iOS 3.0 or higher. It is available for free download on the iTunes Store.
Special thanks to Devin Waterman and his dad Rob for helping me out with testing on the iPod touch. Thanks, guys!