!Converted with LaTeX2HTML 95.1 (Fri Jan 20 1995) by Nikos Drakos (email@example.com), CBLU, University of Leeds >
To watch the evolution of an arbitrary linear automaton from a random initial configuration is to see a great deal of confusion. Gradually -- in some cases quite quickly -- it becomes apparent that each rule of evolution has its own personality, and that as rules and types of automata are varied, similarities are as apparent as differences. Presumably this led Conway to seek out rules for which random configurations eventually settled down to simple activity rather than disappearing entirely, remaining motionless, or filling up the entire space. However, there seem to be automata for practically every taste.
Wolfram laid down a serviceable classification into four categories
A good starting point, having selected a specific rule, is to work out a table of periods (time repetition) and cycles (space repetition) in which a given row shows the number of cycles of given period in rings of length given by the columns. It may be a bit disappointing that so few rows can be obtained within the limits of computer memory and running time that presently exist. The exponential growth of resources required ensures that rows or columns will only be added one at a time, and gradually at that, as computer power increases. Still, the first few rows and columns can actually be done; the information obtained can be quite informative.