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Calculating Ancestors In One-Dimensional Cellular Automata

Author

Listed:
  • 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)

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.

Suggested Citation

  • Juan Carlos Seck Tuoh Mora & Genaro Juárez Martínez & Harold V. Mcintosh, 2004. "Calculating Ancestors In One-Dimensional Cellular Automata," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1151-1169.
    • Handle: RePEc:wsi:ijmpcx:v:15:y:2004:i:08:n:s0129183104006625
    DOI: 10.1142/S0129183104006625
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