# Difference between revisions of "Volatility"

m (p5 strictly volatile oscillator found by Josh Ball) |
Apple Bottom (Talk | contribs) (copyedit; v=1 oscs are also called "pure rotor oscillators", as per 34P13.) |
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[[Image:volatile_p3.png|framed|right|A period-3 oscillator with volatility 1 discovered by [[Jason Summers]] in August [[:Category:patterns_found_in_2012|2012]]]] | [[Image:volatile_p3.png|framed|right|A period-3 oscillator with volatility 1 discovered by [[Jason Summers]] in August [[:Category:patterns_found_in_2012|2012]]]] | ||

− | The '''volatility''' of an [[oscillator]] is the size (in [[cell]]s) 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 '''volatility''' of an [[oscillator]] is the size (in [[cell]]s) 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 [[:Category:Oscillators with volatility 1.00|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. The largest prime period for which such an oscillator is known is 13 (see [[34P13]]). | ||

==Strict volatility== | ==Strict volatility== |

## Revision as of 11:10, 24 August 2017

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. The largest prime period for which such an oscillator is 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, and 177.

## External links

- Volatility at the Life Lexicon