SimpleLife
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!

Love the Life App. Do you have a widget for the Mac?
Hi Dennis. Glad you like the app! I don’t have plans to create a Mac version of SimpleLife (widget or otherwise) at the moment, but perhaps I will one day. In the meantime, I recommend the excellent “Golly” project as a very powerful and fully-featured “Life” client that runs on OS X. You can download it here.
Will this run on my blackberry?