On One-Sided, D-Chaotic Cellular Automata, Having Continuum of Fixed Points and Topological Entropy log (p) for any Prime p>3
Wit Forys and Janusz Matyja
In a metric Cantor space of right infinite words BN over an alphabet B containing at least 2 elements, for any positive integer n ∈ N3 = N \ {3i : i ∈ N ∪ {0}} we present a method of construction of a one-sided cellular automaton which has radius r = 1, is chaotic in the Devaney’s sense, non-injective, has continuum of fixed points and topological entropy equal to log (n). The method is based on the properties of the introduced one sided cellular automaton F with radius r = 1, defined over an alphabet with exactly 2p elements, for any prime number p > 3.We prove, and it is crucial for the mentioned construction, that for any prime number p > 3 the automaton F is itself chaotic in the Devaney’s sense, non-injective, has continuum of fixed points and has topological entropy equal to log (p).
Keywords: one-sided cellular automata, D-chaotic, E-chaotic, fixed points, topological entropy.