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      • Conway's Game of Life is omniperiodic, since there are oscillators of every period, with the last found period being p41 in July 2023.
      conwaylife.com/wiki/Omniperiodic

      Omniperiodic - LifeWiki

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  3. arxiv.org › abs › 2312[2312.02799] Conway's Game of Life is Omniperiodic - arXiv.org

    Dec 5, 2023 · 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.

  4. arxiv.org › html › 2312Conway’s Game of Life is Omniperiodic - arXiv.org

    Conway’s Game of Life is a cellular automaton occurring on an infinite plane of square grid cells, each of which is in one of two states: alive or dead. The neighbourhood of a cell is the 8 cells that are connected orthogonally or diagonally to it.

  5. www.quantamagazine.org › maths-game-of-lifeMath’s ‘Game of Life’ Reveals Long-Sought Repeating Patterns

    Jan 18, 2024 · John Conway’s Game of Life, a famous cellular automaton, has been found to have periodic patterns of every possible length. This pattern in the Game of Life repeats itself after 41 steps. Its recent discovery ends a decades-long quest to show that Life is omniperiodic. DVDP for Quanta Magazine.

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  7. www.discovermagazine.com › the-sciencesMathematicians Prove the "Omniperiodicity" of Conway's Game ...

    Dec 13, 2023 · In other words, is the Game of Life omniperiodic? Given the proof above, this boils down to the problem of finding oscillating patterns that repeat for every period from 1 to 43. The first few were relatively easy to find.

  8. www.semanticscholar.org › paper › Conway's-Game-ofConway's Game of Life is Omniperiodic - Semantic Scholar

    Dec 5, 2023 · 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.

  9. arxiv.org › pdf › 2312arXiv:2312.02799v1 [math.CO] 5 Dec 2023

    Theorem. Life is omniperiodic. 1 Conway’s Game of Life Conway’s Game of Life [14] is a cellular automaton occurring on an infinite plane of square grid cells, each of which is in one of two states: alive or dead. The neighbourhood of a cell is the 8 cells that are connected orthogonally or diagonally to it.

  10. ui.adsabs.harvard.edu › abs › 2023arXiv231202799BConway's Game of Life is Omniperiodic - NASA/ADS

    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.

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