The Game of Life (or sometimes just called “Life”) is not a game at all in the traditional sense – there are no opposing players or teams. Rather, it’s an example of something called a “cellular automaton:” a simulation of lifelike processes in which “cells” – the squares on a two-dimensional square grid – contend with each other to stay alive and to create new live cells. It was originally created by John Horton Conway, a Cambridge mathematician.
The way that you play is by drawing an initial configuration of cells, applying the rules below to every cell in the original drawing simultaneously, and then watching it evolve and change over time. When you click “play,” the simulation will quickly go through generations of cells, which live and die by four very simple rules:
1. Loneliness: Any live cell with fewer than 2 live neighbors dies
2. Stasis: Any live cell with 2 or 3 live neighbors survives to the next generation
3. Overcrowding: Any live cell with more than 3 live neighbors dies.
4. Reproduction: Any dead cell with exactly 3 live neighbors becomes a live cell.
Our fascination with Life is that it’s a wonderfully concise yet lucid demonstration of the principle that simple processes, given enough time to operate, can have far-reaching and surprising consequences.
The process doesn’t need or bear much description. Just get in there and play with it. Try some of the pre-defined patterns and some of your own. Combine them. See how even a small change in the initial configuration can create very different outcomes.
[from page 62 of Trillions, in the section "The King and the Mathematician"]
Learn more about Conway’s Life at its wikipedia page.