Public attention was drawn to cellular automata by Martin Gardner's monthly column Mathematical Recreations, a regular feature of Scientific American for many years. The October, 1970, issue[2] featured the game of Life , which had been invented about that time by the British mathematician John Horton Conway. Sufficient interest was aroused by the game for it to be followed up in several later columns, and to support a newsletter[8] for nearly three years. Gardner's columns have now been collected into one of the compilations that are regularly published by W. H. Freeman and Company[3], while Conway's own version of the game is available in the recent Academic Press book[1] Winning Ways.
However, there had been much previous interest in cellular automata, beginning at least with the work[5] of Warren McCulloch and Walter Pitts on neural nets, later including John von Neumann's investigations[6] into self reproduction and automatic factories. Interest still continues, a recent example being Stephen Wolfram's examination[10] of one dimensional automata from the point of view of chaos in complex systems theory.
One of the fundamental expectations in the theory of automata is that the automaton will eventually settle down into a fixed cycle of states, which will then characterize its long term behavior. Some modification of this principle must be expected for infinite automata, nevertheless the search for states of low period constituted an important part of the activity inspired by the announcement of Life . Someone with a crystallographer's frame of mind might well have undertaken a classification of all such states, beginning with those of period 1, which Conway called ``still lifes.''
This article describes how such a classification can be obtained.