Cellular Automata Dynamical Systems

Alberto Dennunzio (1) , Enrico Formenti (2, 3) , Petr Kurka (4)

1 DISCo - Dipartimento di Informatica Sistemistica e Comunicazione
2 Laboratoire I3S - MDSC - Modèles Discrets pour les Systèmes Complexes
3 I3S - Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis
4 UK - Univerzita Karlova [Praha, Česká republika] = Charles University [Prague, Czech Republic]

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.

Domaines: Informatique [cs]; Complexité [cs.CC]; Mathématique discrète [cs.DM]; Combinatoire [math.CO]; Systèmes dynamiques [math.DS]; Dynamique Chaotique [nlin.CD]; Automates cellulaires et gaz sur réseau [nlin.CG]; Adaptation et Systèmes auto-organisés [nlin.AO]

Alberto Dennunzio, Enrico Formenti, Petr Kurka. Cellular Automata Dynamical Systems. Grzegorz Rozenberg; Thomas Bäck; Joost N. Kok. Handbook of Natural Computing, Springer, pp.25--75, 2012, 978-3-540-92909-3. ⟨10.1007/978-3-540-92910-9_2⟩. ⟨hal-01312493⟩