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Mean-Field Analysis with Random Perturbations to Detect Gliders in Cellular Automata

Author

Listed:
  • Juan Carlos Seck-Tuoh-Mora

    (Área Académica de Ingeniería, Instituto de Ciencias Básicas e Ingeniería, Universidad Autónoma del Estado de Hidalgo, Pachuca 42184, Hidalgo, Mexico
    These authors contributed equally to this work.)

  • Joselito Medina-Marin

    (Área Académica de Ingeniería, Instituto de Ciencias Básicas e Ingeniería, Universidad Autónoma del Estado de Hidalgo, Pachuca 42184, Hidalgo, Mexico
    These authors contributed equally to this work.)

  • Norberto Hernández-Romero

    (Área Académica de Ingeniería, Instituto de Ciencias Básicas e Ingeniería, Universidad Autónoma del Estado de Hidalgo, Pachuca 42184, Hidalgo, Mexico
    These authors contributed equally to this work.)

  • Genaro J. Martínez

    (Artificial Life Robotics Laboratory, Escuela Superior de Computo, Instituto Politecnico Nacional, Mexico City 07738, Mexico
    Unconventional Computing Laboratory, University of the West of England, Bristol BS16 1QY, UK
    These authors contributed equally to this work.)

Abstract

Cellular automata are mathematical models that represent systems with complex behavior through simple interactions between their individual elements. These models can be used to study unconventional computational systems and complexity. One notable aspect of cellular automata is their ability to create structures known as gliders, which move in a regular pattern to represent the manipulation of information. This paper introduces the modification of mean-field theory applied to cellular automata, using random perturbations based on the system’s evolution rule. The original aspect of this approach is that the perturbation factor is tailored to the nature of the rule, altering the behavior of the mean-field polynomials. By combining the properties of both the original and perturbed polynomials, it is possible to detect when a cellular automaton is more likely to generate gliders without having to run evolutions of the system. This methodology is a useful approach to finding more examples of cellular automata that exhibit complex behavior. We start by examining elementary cellular automata, then move on to examples of automata that can generate gliders with more states. To illustrate the results of this methodology, we provide evolution examples of the detected automata.

Suggested Citation

  • Juan Carlos Seck-Tuoh-Mora & Joselito Medina-Marin & Norberto Hernández-Romero & Genaro J. Martínez, 2023. "Mean-Field Analysis with Random Perturbations to Detect Gliders in Cellular Automata," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4319-:d:1261430
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    References listed on IDEAS

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    1. Jianguo Tan & Wenjuan Wang & Jianfeng Feng, 2022. "Transient Dynamics Analysis of a Predator-Prey System with Square Root Functional Responses and Random Perturbation," Mathematics, MDPI, vol. 10(21), pages 1-12, November.
    2. Lin Sun & Suisui Chen & Jiucheng Xu & Yun Tian, 2019. "Improved Monarch Butterfly Optimization Algorithm Based on Opposition-Based Learning and Random Local Perturbation," Complexity, Hindawi, vol. 2019, pages 1-20, February.
    3. Cerruti, Umberto & Dutto, Simone & Murru, Nadir, 2020. "A symbiosis between cellular automata and genetic algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Taras Lukashiv & Yuliia Litvinchuk & Igor V. Malyk & Anna Golebiewska & Petr V. Nazarov, 2023. "Stabilization of Stochastic Dynamical Systems of a Random Structure with Markov Switches and Poisson Perturbations," Mathematics, MDPI, vol. 11(3), pages 1-22, January.
    5. Martínez, Genaro Juárez & Adamatzky, Andrew & McIntosh, Harold V., 2006. "Phenomenology of glider collisions in cellular automaton Rule 54 and associated logical gates," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 100-111.
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