Volatility: Difference between revisions
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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 | For many periods there are known [[:Category:Oscillators with volatility 1.00|oscillators with volatility 1]] (also called '''pure rotor''' or '''statorless''' oscillators), such as [[Achim's p16]], [[figure eight]] (p8), [[Kok's galaxy]] (p8), [[mazing]] (p4), [[pentadecathlon]] (p15), [[phoenix 1]] (p2), [[relay]] (p60+120n), [[smiley]] (p8), and [[tumbler]] (p14). In these oscillators no cell is permanently on - that is, the stators are empty. | ||
It is known that infinite families of volatility 1 oscillators can be formed either from glider shuttles such as [[relay]]<ref name="post138266" />, or from glider loops formed by no more than eight copies of a statorless 90-degree glider reflector. <ref name="post138263" /> | |||
Periods for which oscillators of volatility 1 are known are [[phoenix 1|2]], [[statorless p3|3]], [[mazing|4]], [[statorless p5|5]], [[Jason's p6|6]], [[figure eight|8]], [[Beluchenko's p13#Variants|13]], [[tumbler|14]], [[pentadecathlon|15]], [[Rob's p16|16]], [[48P22.1|22]], 24<ref name="post138516" />, [[queen bee shuttle#Variations|30]], [[68P32|32]], 33n<ref name="post138634" />, 40+8n<ref name="post138264"/>, 45+15n<ref name="post138263" /><ref name="post138266" />, [[Gabriel's p138|138]], [[Karel's p177|177n]], and all periods listed in the section V below. The smallest undecided period is 7, and prior to [[Dave Greene]]'s infinite series of strictly volatile oscillators, the largest prime period for which such an oscillator was known was 13. | |||
{{EmbedViewer | {{EmbedViewer | ||
|pname = statorlessp3 | |pname = statorlessp3 | ||
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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 | '''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 [[phoenix 1|2]], [[statorless p3|3]], [[strictly volatile p4|4]], [[statorless p5|5]], [[statorless p6#Strictly volatile variant|6]], [[figure eight|8]], [[Beluchenko's p13#Variants|13]], [[pentadecathlon|15]], [[Rob's p16|16]], [[48P22.1|22]], [[queen bee shuttle#Variations|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, defined below. | ||
==V== | ==V== | ||
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|author = Chris Cain | |author = Chris Cain | ||
|date = November 30, 2018 | |date = November 30, 2018 | ||
}}</ref> | |||
<ref name="post138263">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Self-Constructing Spaceship Challenges | |||
|p = 138263 | |||
|author = FractalFusion | |||
|date = November 30, 2021 | |||
}}</ref> | |||
<ref name="post138264">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Self-Constructing Spaceship Challenges | |||
|p = 138264 | |||
|author = Sokwe | |||
|date = November 30, 2021 | |||
}}</ref> | |||
<ref name="post138266">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Self-Constructing Spaceship Challenges | |||
|p = 138266 | |||
|author = mniemiec | |||
|date = November 30, 2021 | |||
}}</ref> | |||
<ref name="post138516">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Self-Constructing Spaceship Challenges | |||
|p = 138516 | |||
|author = FractalFusion | |||
|date = December 8, 2021 | |||
}}</ref> | }}</ref> | ||
</references> | </references> | ||
Revision as of 23:04, 11 December 2021
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, that is, the proportion of cells (as a number from 0 to 1) involved in the oscillator which change state at some point during its period. The term "volatility" is due to Robert Wainwright.
The volatility of an oscillator may be very small (for example, a large oscillator with only two rotor cells such as Boat tie spark coil which has a volatility of 0.08) or may be as large as 1 (where every cell in the oscillator is a rotor, such as Pentadecathlon).
Oscillators with volatility 1
For many periods there are known oscillators with volatility 1 (also called pure rotor or statorless oscillators), such as Achim's p16, figure eight (p8), Kok's galaxy (p8), mazing (p4), pentadecathlon (p15), phoenix 1 (p2), relay (p60+120n), smiley (p8), and tumbler (p14). In these oscillators no cell is permanently on - that is, the stators are empty.
It is known that infinite families of volatility 1 oscillators can be formed either from glider shuttles such as relay[1], or from glider loops formed by no more than eight copies of a statorless 90-degree glider reflector. [2]
Periods for which oscillators of volatility 1 are known are 2, 3, 4, 5, 6, 8, 13, 14, 15, 16, 22, 24[3], 30, 32, 33n[4], 40+8n[5], 45+15n[2][1], 138, 177n, and all periods listed in the section V below. The smallest undecided period is 7, and prior to Dave Greene's infinite series of strictly volatile oscillators, the largest prime period for which such an oscillator was known was 13.
| Statorless p3, a period-3 oscillator with volatility 1 (click above to open LifeViewer) RLE: here Plaintext: here |
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 2, 3, 4, 5, 6, 8, 13, 15, 16, 22, 30, 33, and 177, together with all periods greater than or equal to the constant V, defined below.
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.[6] 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.[7] There is also a known mechanism for creating strictly volatile oscillators for periods that are not multiples of eight, between 2918053 and 3506909.[8]
See also
References
- ↑ 1.0 1.1 mniemiec (November 30, 2021). Re: Self-Constructing Spaceship Challenges (discussion thread) at the ConwayLife.com forums
- ↑ 2.0 2.1 FractalFusion (November 30, 2021). Re: Self-Constructing Spaceship Challenges (discussion thread) at the ConwayLife.com forums
- ↑ FractalFusion (December 8, 2021). Re: Self-Constructing Spaceship Challenges (discussion thread) at the ConwayLife.com forums
- ↑ FractalFusion (December 10, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Sokwe (November 30, 2021). Re: Self-Constructing Spaceship Challenges (discussion thread) at the ConwayLife.com forums
- ↑ Dave Greene (November 21, 2018). Re: Self-Constructing Spaceship Challenges (discussion thread) at the ConwayLife.com forums
- ↑ 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