CHARACTERISTIC REPRESENTATION OF ELEMENTARY CELLULAR-AUTOMATA

We propose a characteristic representation of one-dimensional and two- state, three-neighbor cellular automaton rules, which can be interpret ed as a numerical description of Wolfram's classification scheme. Each rule can be considered to behave, in many situations, like some other rules. The similarity of behavior is quantified. The quantification i s done by creating a function designed to give an average weight of co nfigurations after many time steps, and then comparing this function, in a precise way, to some other rules by the value of coefficients exp anded by the rule functions. We call such an expansion form of the fun ction characteristic representation. The simulation result of the repr esentation shows that Class IV rules are distinguished from Class III rules by the similarity to Class Il rules. Criticality of Class IV rul es is displayed by functions linearly combining typical Class II and I II rule functions.