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

The two cubic forms of the three-dimensional cellular automato n popularly called Life are denoted "Life 4555" and "Life 5766," where th e first two numb ers give th e acceptable number of live neighbor cells required to sustain a (cur rently) live cell for th e next generation , and the second pai r of numb ers specifies the number oflive neighbor cells required to give birth to a current ly non-li ving cell. Life 5766 has been shown to be a th ree-dimensional analog to Conway's popular two-dimension al version, whose rule can be written "Life 2333." In fact , the ent ire two-dimensional Conway universe can be simulated in Life 5766 with reasonable efficiency (see reference [1]). It has fur th er been not ed th at Life 5766 was of interest mainly because of thi s analogy and th at th e glider (as well as many oth er interesting forms) were similar to th eir two-dimension al Conway counterparts. Until now, only two gliders (which are merely oscillating forms tha t tr anslate through the universe) had been discovered one each for Life 4555 and Life 5766 (see figure 1). Now, however, an entirely new glider has been discovered for Life 5766 that has no count erpart in th e two-dimensional Conway analog and thu s is an ent ity in its own right . This object is quite rare (details below), yet does occur "na turally"; th at is, one can conduct random experim ents and event ually (within a reason able time) th e object shows up. The new glider has a period of 8, at which tim e it has moved a distance of two uni ts in a direction parallel to one of the coordinate axes. The eight states are shown in figure 2; note that generations 4-7 repeat generations 0-3 bu t are reflecti ons. The signature (see [2]) for each st ate is given direct ly above th e appropriate state. Nat urally the signat ures for generations 4-7 repeat thos e for 0-3. T he object was found using a DEC 3100 RISC workst ation in the following mann er (det ails omitted) . First , a 23 x 23 x 23 "universe" was set to all zero (all cells dead) . Then th e center 7 x 7 x 7 portion was ini tialized randomly to a 20% density of live cells. This defined the initial condit ions for an experiment, which was run unt il one of three things happened: (a) all living cells died out or st abilized (t his happ ened most of the time, and after approximat ely 16 generat ions); (b) an oscillat ing form app ear ed (this happ ened