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    • Omniperiodic

      • 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. 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.

  5. 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.

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

    Dec 13, 2023 · Back in 1970, the mathematician John Conway created a game with no players that evolves entirely from its initial state. The game is set in a kind of computational universe called a cellular automaton.

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

    Theorem. Life is omniperiodic. 1 Conway’s Game of Life. is in one of two states: alive or dead. The neighbourhood of a cell is the 8 cells that are con. ected orthogonally or diagonally to it. At each time step, or generation, the entire plane changes. If a dead cell has exactly three live neighbours, it becomes alive. three live neighbours, it .

  9. www.semanticscholar.org › paper › Conway's-Game-of[PDF] Conway's Game of Life is Omniperiodic - Semantic Scholar

    Dec 5, 2023 · 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.

  10. en.wikipedia.org › wiki › Conway's_Game_of_LifeConway's Game of Life - Wikipedia

    The Game of Life, also known as Conway's Game of Life or simply Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. [1] . It is a zero-player game, [2][3] meaning that its evolution is determined by its initial state, requiring no further input.

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