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A period-3 oscillator with volatility 1 discovered by Jason Summers in August 2012

The volatility of an oscillator is the size (in cells) of its rotor divided by the sum of the sizes of its rotor and its stator. In other words, it is the proportion of cells involved in the oscillator which actually oscillate. The term "volatility" is due to Robert Wainwright.

Oscillators with volatility 1

For many periods there are known oscillators with volatility 1 (also called pure rotor oscillators), such as Achim's p16, figure eight, Kok's galaxy, mazing, pentadecathlon, phoenix 1, smiley, and tumbler. The smallest period for which the existence of such statorless oscillators is undecided is 7, although there are no known strictly volatile period-4 oscillators. Prior to Dave Greene's infinite series of strictly volatile oscillators, the largest prime period for which such an oscillator was known is 13 (see 34P13).

Strict volatility

Strict volatility is a term that was suggested by Noam Elkies in August 1998 for the proportion of cells involved in a period n oscillator that themselves oscillate with period n. For prime n this is the same as the ordinary volatility. The only periods for which strictly volatile oscillators are known are 1, 2, 3, 5, 6, 8, 13, 15, 22, 30, 33, 177, and all periods greater than or equal to 22178648. The latter was established by Dave Greene in November 2018 using self-constructing circuitry.

External links