On the evolution defined by a cellular automaton
https://doi.org/10.22405/2226-8383-2025-26-3-284-291
Abstract
This work is devoted to the study of a class of cellular automata. An automaton describes evolution on a discrete plane. Transition rules to the next state are specified. Standard questions for such evolutionary automata are investigated, including the existence of immortal
configurations and of periodic evolutions.
A criterion is found for the transition rules under which an immortal configuration exists.
It is shown that in the case of symmetric templates, periodic evolutions can have only period 2.
In perspective, a more detailed description of the various possible evolutions generated by a given fixed set of rules (template) is possible.
About the Authors
Ilya Anatolievich Ivanov-Pogodaev
Moscow Institute of Physics and Technology
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Olga Andreevna Ryzhova
Moscow Institute of Physics and Technology
Russian Federation
Russian Federation
References
1. Gardner, M. 1970, “The fantastic combinations of John Conway’s new solitaire game ’life” ’, Scientific American, vol. 223, no. 4, pp. 120–123.
2. Toffoli, T. & Margolus, N. 1991, Machines of cellular automata, Mir, Moscow. (in Russian)
3. Wolfram, S. 2002, A New Kind of Science, Wolfram Media.
4. Belov(Kanel) A.Ya, Bufetov A.I., Ivanov. I.A., Malistov A. S.Blots and templates, Summer Conference of Tournaments of Towns, 1998, MCCME, 46–49, 114–132, Math Education № 2, july-september 1997 г., 125–127(in Russian)
Review
For citations:
Ivanov-Pogodaev I.A., Ryzhova O.A. On the evolution defined by a cellular automaton. Chebyshevskii Sbornik. 2025;26(3):284-291. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-3-284-291
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