Topological Entropy and Complexity of One Class of Cellular Automata Rules

In this paper, some complex dynamics of one equivalence class of elementary cellular automata are characterized via symbolic dynamics on the space of bi-infinite symbolic sequences. By establishing a topologically conjugate relationship with a 2-order subshift of finite type of symbolic dynamical systems, it is rigorously proved that the four rules N=119, 63, 17, and 3 are topologically mixing on their global attractors. Meanwhile, it is shown that they are chaotic both in the sense of Li-Yorke and Devaney on their global attractors. Furthermore, the topological entropies of these rules on Sigma₂ are computed.