Dynamical aspects in reversible one dimensional cellular automata

Juan Carlos Seck Tuoh Mora
Departamento de Ingeniería Eléctrica, Sección Computación.
CINVESTAV-IPN.
Apartado Postal 14-740, 07360, México D.F.
email: seck@computacion.cs.cinvestav.mx

Date: August, 2000

Abstract:

We shall analyze the dynamical properties that we can find in reversible one dimensional cellular automata. We take the configuration set of cellular automata as a topological space based on cylinder sets and mappings among them. We will take one dimensional cellular automata with neighborhood radius size $2$ for representing the whole set of reversible one dimensional cellular automata. Using also the characterization of reversible cellular automata with block permutations, we will expose some matricial methods for detecting the existence of fixed and periodic points; topologically transitive points; topologically ergodic sets, mixing sets and non-wandering sets. Finally, based on periodic behavior, we will be able to classify dynamical behavior of reversible one dimensional cellular automata.

Keywords: Reversible one dimensional cellular automata, cylinder set, block permutations, dynamical systems.