Complex Systems

Cellular Automata and Nonperiodic Orbits Download PDF

Luciano Margara
Computer Science Department,
University of Bologna,
Piazza di Porta S. Donato 5,
40127 Bologna, Italy


The periodic behavior of a particular class of dynamical systems, the cellular automata (CA), is studied. A large class of CAs is defined, (containing both additive and nonadditive CAs) in terms of the sensitivity of the local rule on which the CA is based. For this class, the set of configurations which enter a cycle after a finite number of iterations is completely characterized and it is proved that this set has measure zero according to every probability measure that assigns measure zero to single configurations.