KGameOfLife

About John Conway

Most of the work of John Horton Conway, a mathematician at Gonville and Caius College of the University of Cambridge, has been in pure mathematics. For instance, in 1967 he discovered a new group--some call it "Conway's constellation"--that includes all but two of the then known sporadic groups. (They are called "sporadic" because they fail to fit any classification scheme.)

In addition to such serious work Conway also enjoys recreational mathematics. Although he is highly productive in this field, he seldom publishes his discoveries.Because of its analogies with the rise, fall and alternations of a society of living organisms, the Game of Life, or Life belongs to a growing class of what are called "simulation games"--games that resemble real-life processes. To play life you must have a fairly large checkerboard and a plentiful supply of flat counters of two colors. (Small checkers or poker chips do nicely.)

The basic idea is to start with a simple configuration of counters (organisms), one to a cell, then observe how it changes as you apply Conway's "genetic laws" for births, deaths, and survivals. Conway chose his rules carefully, after a long period of experimentation, to meet three desiderata:

• There should be no initial pattern for which there is a simple proof that the population can grow without limit.

• There should be initial patterns that apparently do grow without limit.

• There should be simple initial patterns that grow and change for a considerable period of time before coming to end in three possible ways: fading away completely (from overcrowding or becoming too sparse), settling into a stable configuration that remains unchanged thereafter, or entering an oscillating phase in which they repeat an endless cycle of two or more periods.

John Horton Conway's Game of Life is a cellular automaton running on a grid, where each cell can be either "alive" or "dead". A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. It consists of an infinite, regular grid of cells, each in one of a finite number of states. The grid can be in any finite number of dimensions. Time is also discrete, and the state of a cell at time t is a function of its state and the state of a finite number of neighbors at time t-1. Every cell has the same rule for updating. See http://www.wikipedia.org/wiki/Cellular_automaton for more details.

In brief, the rules should be such as to make the behavior of the population unpredictable.