# Difference between revisions of "Volatility"

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− | 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. For many periods there are known oscillators with volatility 1, 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 3, although [[Dean Hickerson]] showed in 1994 that there are period 3 oscillators with volatility arbitrarily close to 1 (as the possibility of feeding the [[glider]]s from a [[gun]] into an [[eater]] shows to be the case for all but finitely many periods). The largest prime period for which such an oscillator is known is 13 (see [[34P13]]). | + | 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. For many periods there are known [[:Category:Oscillators_with_volatility_1.00|oscillators with volatility 1]], 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 3, although [[Dean Hickerson]] showed in 1994 that there are period 3 oscillators with volatility arbitrarily close to 1 (as the possibility of feeding the [[glider]]s from a [[gun]] into an [[eater]] shows to be the case for all but finitely many periods). The largest prime period for which such an oscillator is known is 13 (see [[34P13]]). |

The term "volatility" is due to [[Robert Wainwright]]. | The term "volatility" is due to [[Robert Wainwright]]. |

## Revision as of 09:53, 15 September 2011

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. For many periods there are known oscillators with volatility 1, 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 3, although Dean Hickerson showed in 1994 that there are period 3 oscillators with volatility arbitrarily close to 1 (as the possibility of feeding the gliders from a gun into an eater shows to be the case for all but finitely many periods). The largest prime period for which such an oscillator is known is 13 (see 34P13).

The term "volatility" is due to Robert Wainwright.

## 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.

## External links

- Volatility at the Life Lexicon