Towards the classification of all Boolean cellular automata

A classification scheme for all Boolean cellular automata models involving an arbitrary number of inputs is proposed. The scheme is based upon counting the number of stable points for a given rule, i.e., points whose time development is stable with respect to small perturbations. When applied to all cellular automata with 2, 3, 4, or 5 Boolean inputs (the latter involving more than 4000 million cases), it yields, in each case, a nontrivial classification (i.e., there is no single class in which nearly all the rules lie). In addition, it is shown how rules satisfying a given Boolean differential equation can easily be obtained.