Omniperiodic

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

Conway's Game of Life is omniperiodic, since there are oscillators of every period, with the last found period being p41 in July 2023. The last periods to be found are as follows:

• p39 (the first non-trivial example) in July 2000
• p27 in November 2002
• p51 (the first non-trivial example) 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
• p34 (the first non-trivial example) in July 2022
• p19 and p41 in July 2023

Large-period oscillators

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 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. 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

• Emu
• Herschel loop

External links

• My Experience with B-heptominos in Oscillators at the Life Lexicon
• Omniperiodic at the Life Lexicon
• Is Life omniperiodic? at Game of Life News. Posted by Adam P. Goucher on January 16, 2011.
• Which Life-like CA have been proven omniperiodic? (discussion thread) at the ConwayLife.com forums