Department of Computer Science and Engineering,
University of South Carolina,
Columbia, SC 29208
In 1987, this author introduced three-dimensional (3D) versions
of the two-dimensional (2D) cellular automaton (CA) made famous by John Conway .
At that time, some criteria were given
to validate candidate 3D CA rules as "game of life" (GL) rules.
Informally, we say that a CA rule is a GL rule if
(a) when we count neighbors of a cell, we count all touching
neighbors, and they are all treated the same; (b) the rule
supports a "glider" (a translating oscillator); and (c) random
patterns exhibit bounded growth. These informal criteria
are spelled out more formally in , which also gives notation
for writing rules, namely: E1, E2, . . /F1, F2, . . . Here,
the Ei and Fi are listed in ascending order;
the Ei specify the number of touching neighbors required
to keep a living cell alive, and the Fi give the number
required to bring a nonliving cell to life. Furthermore,
when we write /F1, F2, . . we are implying that the E terms
have not been specified.
Conway's rule is thus written 2,3/3 (and not 3,2/3). The two 3D GL rules introduced in 1987 were 4,5/5 and 5,6,7/6 . There followed a series of notes in this journal wherein the discovery of two more GL rules was explored [4, 5]; the rules were 5,6/5 and 6,7,8/5. It should be noted that the rule 6,7,8/5 does not strictly adhere to the formal GL criteria given in . Nevertheless it was well behaved enough to be considered, and this slight variation was mentioned in .