The Game of Life

In the late 1960s the English mathematician John Horton Conway introduced a game, which was best played on a computer, that was one of the first examples of a dynamic system designed for the study of complex behavior. Conway's dynamic system consisted of an infinite two-dimensional grid of square cells, and he called his game Life because each of the cells could assume one of two states: living or dead.

The game is played by following a simple rule that makes the state of each cell dependent on that of its eight neighbors (four at the corners and four at the sides). Initially a certain number of cells are alive. A clock then begins to tick. At each tick, cells either die, come alive, or stay as they are according to the following prescription: only a cell that has exactly three living neighbors will live. A living cell that has zero, one, or two living neighbors will die of loneliness, as it were, while a living cell that has four, five, six, seven, or eight living neighbors will die of overcrowding. By the same token, a cell can be born, or come alive, only if it has three living neighbors—parenting in Conway's game actually requires three people!

Conway's game of Life has shown itself to be aptly named: with the ticking of the clock, the configurations of "live" cells demonstrate an amazing range of behavior, much of it "lifelike," mimicking the process of evolution. The configurations travel across the grid, they grow, they mutate, they collide and seem to fight each other, they die.

Today little is said about catastrophe theory. More recently, the alacrity with which some of the enthusiasts of chaos theory have embraced complexity theory has prompted the more skeptical to compare these scientific theories with cultural fads.