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Jul 21, 2023 · Does Sparse Life or Dense Life ever reach a positive density? Can we build a border from which no information can escape? And there's another open problem that occurs to me now that omnipediodicity is solved, which is to look at the group of symmetries of Life (including time-shift symmetries) and classify exactly which subgroups are achieved ...
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.
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 · Conway's Game of Life is Omniperiodic. 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.
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In October 1996, David Buckingham wrote the article My Experience with B-heptominos in Oscillators that describes his discovery of Herschel conduits, including sufficient stable conduits to enable, for the first time, the construction of period n oscillators for every n ≥ 58, and true period n guns for every n≥ 62. The discovery of the Snark by Mik...
By running Dean Hickerson's drifter searcher to find signals that can be manipulated like Herschels, it is possible to prove that a variety of Life-like cellular automata are omniperiodic. However, these signals are more like the 2c/3 signal, in that they operate on a dense background and can closely follow each other. There is a significant possib...
Nico Brown, Carson Cheng, Tanner Jacobi, Maia Karpovich, Matthias Merzenich, David Raucci, Mitchell Riley (December 5, 2023). "Conway's Game of Life is Omniperiodic". arXiv.My Experience with B-heptominos in Oscillators at the Life LexiconOmniperiodic at the Life LexiconIs Life omniperiodic? at Game of Life News. Posted by Adam P. Goucher on January 16, 2011.Yesterday, Nico Brown has discovered a pattern with period 41, effectively answer a 50-year-long question: Life is indeed omniperiodic, meaning that oscillators of any period are possible. You can find an updated list of oscillators here!
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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.
