Difference between revisions of "Volatility"

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(add self-constructing strictly volatile periods)
m (It's not completely clear that the half-metatick superstructure of the 0E0P will all be volatility-1 for every simulated pattern -- but meta^N 0E0Ps definitely seem safe.)
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==Strict volatility==
 
==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 [[still_life|1]], 2, 3, 5, 6, 8, 13, 15, 22, 30, 33, 177, and all multiples of 68719476736.  The last period is due to the ability of the [[0E0P metacell]] to simulate [[omniperiodic]] rules.  Much lower periods are possible using [[single-channel]] destruction and construction, but as of November 2018 no working examples have been constructed.
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'''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 [[still_life|1]], 2, 3, 5, 6, 8, 13, 15, 22, 30, 33, 177, and all powers of 68719476736.  The last period is due to the ability of the [[0E0P metacell]] to simulate [[omniperiodic]] rules.  Much lower periods are possible using [[single-channel]] destruction and construction, but as of November 2018 no working examples have been constructed.
  
 
==External links==
 
==External links==
 
{{LinkWeisstein|StrictVolatility.html|patternname=Strict volatility}}
 
{{LinkWeisstein|StrictVolatility.html|patternname=Strict volatility}}
 
{{LinkLexicon|lex_v.htm#volatility}}
 
{{LinkLexicon|lex_v.htm#volatility}}

Revision as of 17:31, 19 November 2018

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. 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, 177, and all powers of 68719476736. The last period is due to the ability of the 0E0P metacell to simulate omniperiodic rules. Much lower periods are possible using single-channel destruction and construction, but as of November 2018 no working examples have been constructed.

External links