CALCULATING ANCESTORS IN ONE-DIMENSIONAL CELLULAR AUTOMATA

Juan Carlos Seck Tuoh Mora (), Genaro Juárez Martínez () and Harold V. McIntosh ()
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Juan Carlos Seck Tuoh Mora: Centro de Investigación Avanzada en Ingeniería Industrial, Universidad Autónoma del Estado de Hidalgo, Ciudad Universitaria, Carr. Pachuca-Tulancingo Km 4.5 Pachuca, Hidalgo 42184, México
Genaro Juárez Martínez: Departamento de Ingeniería Eléctrica, Sección Computación, CINVESTAV-IPN, Av IPN 2508, Col San Pedro Zacatenco, México D. F. 07360, México
Harold V. McIntosh: Departamento de Aplicación de Microcomputadoras, Instituto de Ciencias, Universidad Autónoma de Puebla, Apartado postal 461, 72000 Puebla, Puebla, México

International Journal of Modern Physics C (IJMPC), 2004, vol. 15, issue 08, 1151-1169

Abstract: One-dimensional cellular automata are dynamical systems characterized by discreteness (in space and time), determinism and local interaction. We present a procedure to calculate the ancestors for a given sequence of states, which is based on a special kind of graph calledsubset diagram. We use this diagram to specify subset tables for calculating ancestors which are not Garden-of-Eden sequences, hence the process is able to yield ancestors in several generations. Some examples are illustrated using the cellular automaton Rule 110 which is the most interesting automaton of two states and three neighbors.

Keywords: Garden-of-Eden sequences; de Bruijn diagrams; algorithms (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1142/S0129183104006625

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