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Mathematics > Combinatorics

arXiv:2312.02799 (math)
[Submitted on 5 Dec 2023]

Title:Conway's Game of Life is Omniperiodic

Authors:Nico Brown, Carson Cheng, Tanner Jacobi, Maia Karpovich,
Matthias Merzenich, David Raucci, Mitchell Riley
Download a PDF of the paper titled Conway's Game of Life is
Omniperiodic, by Nico Brown and 5 other authors
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    Abstract:In the theory of cellular automata, an oscillator is a
    pattern that repeats itself after a fixed number of generations;
    that number is called its period. A cellular automaton is called
    omniperiodic if there exist oscillators of all periods. At the
    turn of the millennium, only twelve oscillator periods remained
    to be found in Conway's Game of Life. The search has finally
    ended, with the discovery of oscillators having the final two
    periods, 19 and 41, proving that Life is omniperiodic. Besides
    filling in the missing periods, we give a detailed history of the
    omniperiodicity problem and the strategies used to solve it,
    summarising the work of a large number of people in the decades
    since the creation of Life.

Comments: 32 pages, numerous figures
Subjects: Combinatorics (math.CO); Cellular Automata and Lattice
          Gases (nlin.CG)
Cite as:  arXiv:2312.02799 [math.CO]
          (or arXiv:2312.02799v1 [math.CO] for this version)
          https://doi.org/10.48550/arXiv.2312.02799
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Mitchell Riley [view email]
[v1] Tue, 5 Dec 2023 14:35:28 UTC (327 KB)
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