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A cellular automaton is said to be omniperiodic if it has oscillators of all periods.

It is not known whether Conway's Game of Life is omniperiodic, since oscillators have not been constructed for every period. The only periods for which no oscillator is known are 19 and 41. The most recently achieved periods are p39 in July 2000, p27 in November 2002, p51 in March 2009, p37 in April 2009, p31 in November 2010, p43 and p53 in April 2013, p23 in November 2019, p38 in January 2022, and p34 (the first non-trivial example) in July 2022.

Note that if infinite oscillators are allowed, then all periods are possible because any period of 14 or more can be obtained using a stream of gliders or lightweight spaceships.

Large-period oscillators

In October 1996, David Buckingham wrote the article My Experience with B-heptominos in Oscillators[1] 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 Mike Playle in April 2013 allowed the construction of oscillators of all periods greater than or equal to 43.

Other rules

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.[2][3] 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 possibility that such a signal turner exists for Conway's Game of Life, but no explicit examples have been found.

See also


  1. Buckingham on B-heptomino/Herschel oscillators at Paul Callahan's Page of Conway's Life Miscellany
  2. Matthias Merzenich (June 4, 2010). Re: B3/S234 (discussion thread) at the forums
  3. Dave Greene (December 26, 2021). Re: Suggested LifeWiki edits (discussion thread) at the forums

External links