Complex Systems

The Discovery of a New Glider for the Game of Three-Dimensional Life Download PDF

Carter Bays
University of South Carolina, Columbia, SC 29208 USA


The two cubic forms of the three-dimensional cellular automaton popularly called Life are denoted "Life 4555'' and "Life 5766,'' where the first two numbers give the acceptable number of live neighbor cells required to sustain a (currently) live cell for the next generation, and the second pair of numbers specifies the number of live neighbor cells required to give birth to a currently non-living cell. Life 5766 has been shown to be a three-dimensional analog to Conway's popular two-dimensional version, whose rule can be written "Life 2333.'' In fact, the entire two-dimensional Conway universe can be simulated in Life 5766 with reasonable efficiency (see reference [1]). It has further been noted that Life 5766 was of interest mainly because of this analogy and that the glider (as well as many other interesting forms) were similar to their two-dimensional Conway counterparts.