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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 maximum volatility 1 (also called pure rotor or statorless oscillators), such as Achim's p16, figure eight, Kok's galaxy, mazing, pentadecathlon, phoenix 1, smiley, and tumbler. In these oscillators no cell is permanently on - that is, the stators are empty. 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). All oscillators with period 45+15n can be volatity 1 due to PD-pair reflector and a modified p15 bumper.[citation needed]

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, 16, 22, 30, 33, and 177, together with all periods greater than or equal to the constant V:


V is the minimum value such that strictly volatile oscillators have been proved to exist for all periods greater than or equal to V. A value of 22178648 was established by Dave Greene in November 2018 using self-constructing circuitry. The following month he reduced this to 3506916, and Goldtiger997 brought the minimum down to 3506910 a few days later by recompiling the same design.[1] There is also a known mechanism for creating strictly volatile oscillators for periods that are not multiples of eight, between 2918053 and 3506909.[2]


  1. Goldtiger997 (December 5, 2018). Re: Self-Constructing Spaceship Challenges (discussion thread) at the ConwayLife.com forums
  2. Chris Cain (November 30, 2018). Re: Self-Constructing Spaceship Challenges (discussion thread) at the ConwayLife.com forums

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