Further Notes on the Game of Three-Dimensional Life

The game of three-dim ensional Life, a cellular automaton th at exhibits in t hree dimensions properties similar t o J ohn Conway 's famo us two-dimen-siona l game, was discovered in 1986. Four "life supporting" rules 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 remain 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 supports one or more gliders (t ra nslating oscillato rs), some of which are easy t o discover and ot hers which are quit e rare, t urning up only aft er a consider able number of random "primord ial soup" experiments have been performed. Here we pr esent four newly discovered gliders-two for Life 5655 an d two for Life 4555. The discovery of more gliders for Life 5655 is par t icularly surprising because t his ru le appears ju st barely t o sustain life; t hat is, almost all primordial soup experiments 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 4555 is rather gratifying because t his was t he first t hree-dimensiona l life ru le found an d in many ways is still the most fascinating. T he discovery of t hese four new gliders would probab ly not have occurred wit hout th e use of "symmet ric pri mordial soup ." Figur e 1 shows t he various typ es of symmet ry t hat have been imposed up on sma ll, ot herwise rando m initial cell configurations (roughly 8 x 10 x 10 in volum e), which were placed in the cent er of a lar ge, ot herwise empty uni verse (about 45 x 45 x 45). Glid ers were discovered by perform ing experiments until some configur at …