  An "odd-rule" cellular automaton (CA) is defined by specifying a neighborhood
for each cell, with the rule that a cell turns ON if it is in the neighborhood
of an odd number of ON cells at the previous generation, and otherwise turns
OFF. We classify all the odd-rule CAs defined by neighborhoods which are
subsets of a 3 X 3 grid of square cells. There are 86 different CAs modulo
trivial symmetries. When we consider only the different sequences giving the
number of ON cells after n generations, the number drops to 48, two of which
are the Moore and von Neumann CAs. This classification is carried out by using
the "meta-algorithm" described in an earlier paper to derive the generating
functions for the 86 sequences, and then removing duplicates. The
fastest-growing of these CAs is neither the Fredkin nor von Neumann
neighborhood, but instead is one defined by "Odd-rule" 365, which turns ON
almost 75% of all possible cells.
