Difference between revisions of "Volatility"
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{{Glossary}} | {{Glossary}} | ||
[[Image:volatile_p3.png|framed|right|A period-3 oscillator with volatility 1 discovered by [[Jason Summers]] in August | [[Image:volatile_p3.png|framed|right|A period-3 oscillator with volatility 1 discovered by [[Jason Summers]] in August {{year|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 term "volatility" is due to [[Robert Wainwright]]. | 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== | ==Oscillators with volatility 1== | ||
For many periods there are known [[:Category:Oscillators with volatility 1.00|oscillators with volatility 1]] (also called '''pure rotor | For many periods there are known [[:Category:Oscillators with volatility 1.00|oscillators with maximum volatility 1]] (also called '''pure rotor''' or '''statorless''' oscillators), such as [[Achim's p16]], [[figure eight]], [[Kok's galaxy]], [[mazing]], [[pentadecathlon]], [[phoenix 1]], [[smiley]], and [[tumbler]]. In these oscillators no cell is permanently on - that is, the stators are empty. 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]]). All oscillators with period 45+15n can be volatity 1 due to [[PD-pair reflector]] and a modified [[p15 bumper]].{{citation needed}} | ||
==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]], [[phoenix 1|2]], [[statorless p3|3]], [[statorless p5|5]], 6, [[figure eight|8]], [[ | '''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]], [[statorless p3|3]], [[statorless p5|5]], [[statorless p6#Strictly volatile variant|6]], [[figure eight|8]], [[Beluchenko's p13|13]], [[pentadecathlon|15]], [[Rob's p16|16]], [[48P22.1|22]], [[queen bee shuttle|30]], {{LinkCatagolue|xp33_yn46f01y520uc8zyo4rcy7om8zylocgyb1wogzymrggyc1m1zyl111yc13704zxgy58ck8808ooayr7e2022532wgg8gg0gsogz0a332022562y51yzy211y22zz8y2ggyzy2gy58ck8808ooaz1371011211w8ok8808esyra332022562y51zym40sogycgggzyngdgyc11rzyn13wgyb163zyq2d3y76r4zyp26f08y5g0uc4|patternname=33|format=extended|style=raw}}, and [[Karel's p177|177]], together with all periods greater than or equal to the constant V: | ||
==V== | ==V== | ||
V is the minimum value such that strictly volatile oscillators have been proved to exist for all periods greater than or equal to V. | V is the minimum value such that strictly volatile oscillators have been proved to exist for all periods greater than or equal to V. | ||
A value of 22178648 was established by [[Dave Greene]] in November 2018 using self-constructing circuitry. The following month he reduced this to 3506916. | A value of 22178648 was established by [[Dave Greene]] in November 2018 using self-constructing circuitry. The following month he reduced this to 3506916, and Goldtiger997 brought the minimum down to 3506910 a few days later by recompiling the same design.<ref name="post66216" /> There is also a known mechanism for creating strictly volatile oscillators for periods that are not multiples of eight, between 2918053 and 3506909.<ref name="post66027" /> | ||
There is also a known mechanism for creating strictly volatile oscillators for periods that are not multiples of eight, between 2918053 and | |||
==References== | ==References== | ||
<references /> | <references> | ||
<ref name="post66216">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Self-Constructing Spaceship Challenges | |||
|p = 66216 | |||
|author = Goldtiger997 | |||
|date = December 5, 2018 | |||
}}</ref> | |||
<ref name="post66027">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Self-Constructing Spaceship Challenges | |||
|p = 66027 | |||
|author = Chris Cain | |||
|date = November 30, 2018 | |||
}}</ref> | |||
</references> | |||
==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}} | ||
{{LinkLexicon|filename=lex_s.htm#statorless|patternname=Statorless}} | |||
Revision as of 03:46, 4 June 2020
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 maximum volatility 1 (also called pure rotor or statorless oscillators), such as Achim's p16, figure eight, Kok's galaxy, mazing, pentadecathlon, phoenix 1, smiley, and tumbler. In these oscillators no cell is permanently on - that is, the stators are empty. 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). All oscillators with period 45+15n can be volatity 1 due to PD-pair reflector and a modified p15 bumper.[citation needed]
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, 16, 22, 30, 33, and 177, together with all periods greater than or equal to the constant V:
V
V is the minimum value such that strictly volatile oscillators have been proved to exist for all periods greater than or equal to V. A value of 22178648 was established by Dave Greene in November 2018 using self-constructing circuitry. The following month he reduced this to 3506916, and Goldtiger997 brought the minimum down to 3506910 a few days later by recompiling the same design.[1] There is also a known mechanism for creating strictly volatile oscillators for periods that are not multiples of eight, between 2918053 and 3506909.[2]
References
- ↑ Goldtiger997 (December 5, 2018). Re: Self-Constructing Spaceship Challenges (discussion thread) at the ConwayLife.com forums
- ↑ Chris Cain (November 30, 2018). Re: Self-Constructing Spaceship Challenges (discussion thread) at the ConwayLife.com forums
External links
- Volatility at the Life Lexicon
- Statorless at the Life Lexicon