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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
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.
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.
Dec 5, 2023 · 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.
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.
generations; that number is called its period. A cellular automaton is omniperiodic if there exist oscillators of all periods. 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
Dec 5, 2023 · In a groundbreaking discovery, Nico Brown, Carson Cheng, Tanner Jacobi, Maia Karpovich, Matthias Merzenich, David Raucci, and Mitchell Riley have proven that Conway's Game of Life is omniperiodic by finding oscillators with periods 19 and 41.
The Physics arXiv Blog, Mathematicians Prove the “Omniperiodicity” of Conway’s Game of Life (Dec 2024) Last revised on January 14, 2024 at 05:35:47. See the history of this page for a list of all contributions to it.
