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
Dennunzio, A., Formenti, E., Kůrka, P. (2012). Cellular Automata Dynamical Systems. In G. Rozenberg, T. Bäck, J.N. Kok (a cura di), Handbook of Natural Computing (pp. 25-75). Berlin : Springer [10.1007/978-3-540-92910-9_2].
Cellular Automata Dynamical Systems
DENNUNZIO, ALBERTO;
2012
Abstract
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
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