Reference Work Entry

Handbook of Natural Computing

pp 25-75

Cellular Automata Dynamical Systems

  • Alberto DennunzioAffiliated withDipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca
  • , Enrico FormentiAffiliated withDépartement d'Informatique, Université de Nice-Sophia Antipolis
  • , Petr KůrkaAffiliated withCenter for Theoretical Studies, Academy of Sciences and Charles University in Prague


We present recent studies on cellular automata (CAs) viewed as discrete dynamical systems. In the first part, we illustrate the relations between two important notions: subshift attractors and signal subshifts, measure attractors and particle weight functions. The second part of the chapter considers some operations on the space of one-dimensional CA configurations, namely, shifting and lifting, showing that they conserve many dynamical properties while reducing complexity. The final part reports recent investigations on two-dimensional CA. In particular, we report a construction (slicing construction) that allows us to see a two-dimensional CA as a one-dimensional one and to lift some one-dimensional results to the two-dimensional case.