The 256 rules in table 1 are stated as functions of three site values . Of these, 48 depend only on two of the site values. Some other rules can be formed from compositions of these simpler rules. This table lists rules which can be formed by compositions according to
where indicates that the value is irrelevant. Only minimal representative rules from table 1 are included. In each case, all possible compositions are listed. Note that most of the compositions do not commute.
Table by Erica Jen (Los Alamos National Laboratory).