Difference between revisions of "Volatility"

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{{Glossary}}
 
{{Glossary}}
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]]).
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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]]]]
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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 [[: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 5, 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]]).
  
 
The term "volatility" is due to [[Robert Wainwright]].
 
The term "volatility" is due to [[Robert Wainwright]].
  
 
==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.
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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, 6, 8, 13, 15, 22, 30, 33, and 177.
  
 
==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 05:46, 29 December 2012

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. 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 5, 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).

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. The only periods for which strictly volatile oscillators are known are 1, 2, 3, 6, 8, 13, 15, 22, 30, 33, and 177.

External links