A Note on  \alpha -Asynchronous Life-Like Cellular Automata (original) (raw)

Abstract

This note shows the dynamics of Life-like cellular automata under \(\alpha \)-asynchronous perturbation where each cell is updated with \(\alpha \) probability. Here, we explore the possibility of phase transition dynamics during evolution of both low and high density Life-like games. Hereafter, we compare Game of Life (Life) and Life-like games with the effect of perturbation. This study also displays a beautiful gallery (natural patterns) of extended Life games with the effect of perturbation. Finally, we explore random games and their connection with second-order phase transition and first-order irreversible phase transition.

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Notes

    1. For fully asynchronous updating, one cell is chosen uniformly at random and updated at each time step, and the other cells are left unchanged [28, 31].
    1. Note that, here, high (resp. low) perturbation rate means low (resp. high) \(\alpha \)-value.
    1. Following the naming Bp/Sq, we can write \(p = [p_1,p_2]\) and \(q = [q_1,q_2]\) where the parameters take the number of live neighbours within the interval \(p_1\) and \(p_2\); resp. \(q_1\) and \(q_2\). Considering parameters \(p_1\), \(p_2\), \(q_1\), \(q_2\), one can take integer values from 1 to 8, and there are 1296 games. Here, we call those games as extended Life games [13].

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Authors and Affiliations

  1. Ahmedabad University, Ahmedabad, Gujarat, India
    Souvik Roy
  2. Indian Institute of Engineering Science and Technology, Shibpur, India
    Subrata Paul
  3. Technical University of Denmark, Kongens Lyngby, Denmark
    Sumit Adak

Authors

  1. Souvik Roy
  2. Subrata Paul
  3. Sumit Adak

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Correspondence toSouvik Roy .

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Editors and Affiliations

  1. National Institute of Technology Durgapur, Durgapur, West Bengal, India
    Mamata Dalui
  2. Indian Institute of Engineering Science, Shibpur, Howrah, West Bengal, India
    Sukanta Das
  3. Université Côte d’Azur, Sophia Antipolis, France
    Enrico Formenti

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Roy, S., Paul, S., Adak, S. (2024). A Note on \(\alpha \)-Asynchronous Life-Like Cellular Automata. In: Dalui, M., Das, S., Formenti, E. (eds) Cellular Automata Technology. ASCAT 2024. Communications in Computer and Information Science, vol 2021. Springer, Cham. https://doi.org/10.1007/978-3-031-56943-2\_15

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