The Game of Life
John Horton Conway was a mathematician at Cambridge University (later at Princeton). He sought to simplify von Neumann's "universal constructor" based on cellular automata, but with fewer states and rules. "... only after the rejection of many patterns, triangular and hexagonal lattices as well as square ones, and of many other laws of birth and death, including the introduction of two and even three sexes. Acres of squared paper were covered, and he and his admiring entourage of graduate students shuffled poker chips, foreign coins, cowrie shells, Go stones or whatever came to hand, until there was a viable balance between life and death." J. J. O'Connor and E. F. Robertson, "John Horton Conway," http://wwwgroups.dcs.standrews.ac.uk/~history/Mathematicians/Conway.html 
Conway had contributed previously to the "Mathematical Recreations" column in Scientific American, written by his friend Martin Gardner. Published in Gardner's column as "The Fantastic Combinations of John Conway's New Solitaire Game 'Life'," Scientific American (1970): 12023. Conway's Prize Question: R. William Gosper (MIT) and computer Life (glider gun and puffer train) prove infinite expansion. Early communitybased game, developed and extended by programmers and players. Possibly the mostprogrammed computer game of all time. Especially popular with microcomputer enthusiasts: Byte magazine, Cromemco "Dazzler," many versions of game. 
Conway's Desired Results::  Rules: 
There should be no initial pattern for which there is a simple proof that the population can grow without limit.

Survivals. Every counter with two or three neighboring counters survives for the next generation.

The "Cheshire Cat" Sequence. Mark Alpert, "Not Just Fun and Games," Scientific American (April 1999). 
A "Glider"

A "Blinker".

A "Puffer Train."

Top 60 of GameofLife Objects: http://wwwhomes.unibielefeld.de/achim/freq_top_life.html
Java version: http://hensel.lifepatterns.net/
Java version that steps through game: http://www.bitstorm.org/gameoflife/
Life32 (best Windows version: http://psoup.math.wisc.edu/Life32.html