Further Notes on the Game of Three-Dimensional Life
Carter Bays · Complex Systems · 1994
The game of three-dim ensional Life, a cellula r automaton th at exhibit s in t hree dimensions properties simila r t o J ohn Conway 's famous two-dimen siona l game, was discovered in 1986. Four life supporting rul es in th e cubic universe have been found. T hese are Life 4555, Life 5766, Life 5655, and Life 6855. T he first two numbers give t he range of living neighb or cells perm itted for a currentl y live cell t o rem ain so; t he second pair gives t he range of t he number of neighbor cells required to bring a cur rent ly dead cell to life. Thus, 4555 mean s t hat a living cell must to uch 4 or 5 live cells to remain alive and a dead cell must to uch exact ly 5 to become alive. Conway's rul e is 2333. Each of t hese rul es support s one or more gliders (t ra nslating oscillato rs), some of which are easy t o discover and ot hers which are quit e ra re, t urning up only aft er a consider able number of random primord ial experiments have been performed . Here we pr esent four newly discovered gliders- two for Life 5655 an d t wo for Life 4555. The discovery of more gliders for Life 5655 is par t icularly surprising b ecause t his ru le appears ju st barely t o sustain life; t hat is, almost all primordial soup experiment s t end to t hin out quit e rapidly and leave little or no residue (see [5]). T he discovery of new gliders for Life