Cellular Automata and Nonperiodic Orbits

A bstract. T he periodic behavior of a particu lar class of dynamical sys tems , the cellular automata (CA) , is studied . A lar ge class of CAs is defined , (containing both addit ive and nonadditive CAs) in terms of the sensi tivity of t he local rule on which the CA is based . For this class , the set of configurations which ente r a cycle afte r a finit e number of it erat ions is complete ly characte rized and it is pr oved that this set has measure zero according to every pr obab ility measure that ass igns measure zero to single configurations .