From: Harold V. McIntosh (MCINTOSH@unamvm1.dgsca.unam.mx)
Date: Tue Apr 13 1993 - 23:29:46 UTC
Ergin Guney <eg23+(at)ANDREW.CMU.EDU> asks: Does anybody there know the rules for 3 dimensional game of life? and Richard Ottolini <stgprao(at)ST.UNOCAL.COM> replies: There was a Scientific American mathematical recreations column circa 1989 with interesting rules. - He no doubt means: A. K. Dewdney, Computer Recreations - the game Life acquires some successors in three dimensiona, Scientific American, February 1987, pp 8-13. Also see: A. K. Dewdney, The Armchair Universe, W. H. Freeman and Company, New York, 1988 (ISBN 0-7167-1939-8 pbk), which may still be in print and easier to get than old Scientific Americans. - That article featured work of Carter Bays, which was reported in more detail in a series of articles in Complex Systems, also around 1987. Bays offered some programs for the Macintosh and a newsletter, but after two issues, little more has been heard from him. - Basically, his rules were semitotalistic, which means that according to whether a cell is dead or alive, you add up the number of live neighbors. The symbol w/x/y/z means that a cell is born with between w and x neighbors; a live cell will curvive when the number lies between y and z. Conway's Life was a 2/3/3/3 Life, according to this. Bays found several noteworthy ranges for three dimensional rules. - The sad truth seems to be, that there IS no three-dimensional Life, nor for that matter, any other than the original. Of course, that does not mean that one should not keep on looking, nor that there aren't any. - Since he invented the game, one would have to ask Conway what constitutes a legitimate Life. According to Martin Gardner, his criteria were that small populations could exist in isolation, neither dying out completely, nor growing without bound. There are various ways to foresee whether an automaton will meet this criterion, among which, totalistic and semitotalistic rules lying within certain ranges seem to work as required. - However, soon after its discovery, Life complicated itself (yes, the pun is intended. People who work with Life are used to puns). In succession, gliders were discovered, then glider guns, then logical circuitry based on glider streams, and finally universal computers and constructors. Nowadays one expects a 'Life' to exhibit all this superstructure (or at least something equivalent); but unfortunately neither Stephen Wolfram (who worked intensively with automata) not Bays have gotten much beyond the glider stage. - There are so many automaton rules lying around, that surely there must be some interesting ones amongst them. Working in higher dimensions is asking for trouble, since they are so hard to visualize (although effective three dimensional displays are marginally possible). It is ironical that, at the theoretical level, the universe of any automaton is teeming with glider-like structures. Capturing, taming, and putting them to productive use is an entirely different story. - Harold V. McIntosh |Depto. de Aplicaci'on de Microcomputadoras MCINTOSH@UNAMVM1.BITNET |Instituto de Ciencias/UAP mcintosh@unamvm1.dgsca.unam.mx |Apdo. Postal 461 (+52+22)43-6330 |72000 Puebla, Pue., MEXICO
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