Complex Systems

Further Notes on the Game of Three-Dimensional Life Download PDF

Carter Bays
Department of Computer Science,
University of South Carolina, Columbia, SC 29208, USA


The game of three-dimensional Life, a cellular automaton that exhibits in three dimensions properties similar to John Conway's famous two-dimensional game, was discovered in 1986. Four "life supporting'' rules in the cubic universe have been found. These are Life 4555, Life 5766, Life 5655, and Life 6855. The first two numbers give the range of living neighbor cells permitted for a currently live cell to remain so; the second pair gives the range of the number of neighbor cells required to bring a currently dead cell to life. Thus, 4555 means that a living cell must touch 4 or 5 live cells to remain alive and a dead cell must touch exactly 5 to become alive. Conway's rule is 2333.

Each of these rules supports one or more gliders (translating oscillators), some of which are easy to discover and others which are quite rare, turning up only after a considerable number of random "primordial soup'' experiments have been performed. Here we present four newly discovered gliders---two for Life 5655 and two for Life 4555. The discovery of more gliders for Life 5655 is particularly surprising because this rule appears just barely to sustain life; that is, almost all primordial soup experiments tend to thin out quite rapidly and leave little or no residue (see [5]). The discovery of new gliders for Life 4555 is rather gratifying because this was the first three-dimensional life rule found and in many ways is still the most fascinating.