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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
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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.
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.
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.
The discovery of 208P41 proved Conway's Game of Life to be omniperiodic because no period-41 oscillator had been discovered before! Oscillators of all other periods had either been discovered, of proven to be possible. For periods 62 and above, oscillators can be constructed using the Herschel loop. Which is basically a stream of gliders being ...
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.
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.
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.
