Difference between revisions of "Volatility"

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==Oscillators with volatility 1==
 
==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]]).
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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. 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]]).
  
 
==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 periods greater than or equal to 22178648. The latter was established by [[Dave Greene]] in November 2018 using self-constructing circuitry.
+
'''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]], [[phoenix 1|2]], 3, [[statorless p5|5]], 6, 8, [[34P13|13]], [[pentadecathlon|15]], 22, 30, 33, [[Karel's p177|177]], and all periods greater than or equal to 22178648. The latter was established by [[Dave Greene]] in November 2018 using self-constructing circuitry.
  
 
==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 02:54, 24 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. 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).

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 periods greater than or equal to 22178648. The latter was established by Dave Greene in November 2018 using self-constructing circuitry.

External links