TRANSITIVE BEHAVIOR IN REVERSIBLE ONE-DIMENSIONAL CELLULAR AUTOMATA WITH A WELCH INDEX 1

Juan Carlos Seck Tuoh Mora ()
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Juan Carlos Seck Tuoh Mora: Departamento de Ingeniería Eléctrica, Sección Computación, CINVESTAV-IPN, Av. IPN 2508, Col. San Pedro Zacatenco, México 07360 D.F., México

International Journal of Modern Physics C (IJMPC), 2002, vol. 13, issue 06, 837-855

Abstract: The problem of knowing and characterizing the transitive behavior of a given cellular automaton is a very interesting topic. This paper provides a matrix representation of the global dynamics in reversible one-dimensional cellular automata with a Welch index 1, i.e., those where the ancestors differ just at one end. We prove that the transitive closure of this matrix shows diverse types of transitive behaviors in these systems. Part of the theorems in this paper are reductions of well-known results in symbolic dynamics. This matrix and its transitive closure were computationally implemented, and some examples are presented.

Keywords: Cellular automata; dynamical systems; matrix methods (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1142/S0129183102003607

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