Some mathematical results for cellular automata

Many mathematical concepts from different branches of mathematics are united to study some properties of cellular automata (CA). Periodicity and chaos (in the sense of sensitive dependence on initial conditions) are studied for 1-dimensional CA. The method of the characteristic polynomial of the evolution matrix is applied. Then this study is generalized to extended (nonlocal) CA and to higher dimensions. Three-state CA and nonlinear CA are also studied. Some results for the deterministic limits of Domany–Kinzel and Bagnoli et al. models are derived.