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  • Periodic solutions of one-dimensional cellularautomata with uniformly chosen random rules [Elektronski vir]
    Gravner, Janko ; Liu, Xiaochen
    We study cellular automata whose rules are selected uniformly at random. Our setting are two-neighbor one-dimensional rules with a large number n of states. The main quantity we analyze is the ... asymptotic distribution, as n → ∞ , of the number of different periodic solutions with given spatial and temporal periods. The main tool we use is the Chen-Stein method for Poisson approximation, which establishes that the number of periodic solutions, with their spatial and temporal periods confined to a finite range, converges to a Poisson random variable with an explicitly given parameter. The limiting probability distribution of the smallest temporal period for a given spatial period is deduced as a corollary and relevant empirical simulations are presented.
    Vir: The Electronic journal of combinatorics [Elektronski vir]. - ISSN 1077-8926 (Vol. 4, iss. 18, art. P4.51, 2021, str. 1-19)
    Vrsta gradiva - e-članek ; neleposlovje za odrasle
    Leto - 2021
    Jezik - angleški
    COBISS.SI-ID - 128178435

    Povezava(-e):

    https://www.combinatorics.org/ojs/index.php/eljc/article/view/v28i4p51
    https://doi.org/10.37236/10114
    DOI

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