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1. • 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

2. People also ask

   How many oscillators are there in Conway's game of life?

   • 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.

   [2312.02799] Conway's Game of Life is Omniperiodic - arXiv.org

   arxiv.org/abs/2312.02799

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   Is life omniperiodic?

   • 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.

   [2312.02799] Conway's Game of Life is Omniperiodic - arXiv.org

   arxiv.org/abs/2312.02799

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   What is Conway's game of life?

   • This universe consists of an infinite grid of squares that can be alive or dead and that, at each time step, can flip from one state to the other according to the states of the squares around it. This cellular automaton has since become known as Conway’s Game of Life and famous for the extraordinary complexity that emerges within it.

   Mathematicians Prove the "Omniperiodicity" of Conway's Game of Life

   www.discovermagazine.com/the-sciences/mathematicians-prove-the-omniperiodicity-of-conways-game-of-life

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   Is the game of life omniperiodic?

   • The final piece of Life's omniperiodic puzzle (source: arxiv.org/abs/2312.02799) Now Mitchell and co announce the work is done. “The search has finally ended, with the discovery of oscillators having the final two periods,” they say. This proves once and for all that the Game of Life is indeed omniperiodic.

   Mathematicians Prove the "Omniperiodicity" of Conway's Game of Life

   www.discovermagazine.com/the-sciences/mathematicians-prove-the-omniperiodicity-of-conways-game-of-life

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   Did John Conway create a game of life?

   • A problem that has long been a focal point of research for the famous Game of Life, has finally been solved. (Credit: NicoElNino/Shutterstock) Sign up for our email newsletter for the latest science news Back in 1970, the mathematician John Conway created a game with no players that evolves entirely from its initial state.

   Mathematicians Prove the "Omniperiodicity" of Conway's Game of Life

   www.discovermagazine.com/the-sciences/mathematicians-prove-the-omniperiodicity-of-conways-game-of-life

   See all results for this question

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

   arxiv.org › abs › 2312

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

   www.discovermagazine.com › the-sciences

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   Dec 13, 2023 · This proves once and for all that the Game of Life is indeed omniperiodic. Mitchell and co’s paper describes all 43 of these oscillators along with the techniques that computer scientists and mathematicians have developed to find them and build ever more capable oscillators.

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

   www.quantamagazine.org › maths-game-of-life

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   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.

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

   arxiv.org › html › 2312

   • Cached

   Conway’s Game of Life is by far the most famous cellular automaton. David Buckingham first established a finite bound above which oscillators of every period could be built by running a signal around a specially constructed track.

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

   arxiv.org › pdf › 2312

   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.

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

   ui.adsabs.harvard.edu › abs › 2023arXiv231202799B

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

    www.semanticscholar.org › paper › Conway's-Game-of

    Dec 5, 2023 · TLDR. Three explicit methods are presented to construct oscillators in Conway's Life while guaranteeing certain complexity bounds, leading to the existence of an infinite sequence of oscillators of periods n = 58, 59, 60, … and uniformly bounded population. Expand.