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 [[:Category:patterns_found_in_2012|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]], 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]] 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==
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]]).
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]]).
 
== Oscillators with volatility 1 ==
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), [[p60 glider shuttle]] (p60), [[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 periodic glider loops formed by no more than eight copies of a statorless 90-degree [[glider reflector]].<ref name="post138263" />
 
Periods for which non-trivial oscillators of volatility 1 are known are [[Phoenix 1|p2]], [[Statorless p3|p3]], [[Mazing|p4]], [[Statorless p5|p5]], [[Jason's p6|p6]], [[Figure eight|p8]], {{LinkCatagolue|xp12_g880anx72207xbg1m0gziaw5ky88o9p1hze5011yc680d|patternname=p12|style=raw}}{{refn|group=note|A stabilization of the [[carnival shuttle]] using {{LinkCatagolue|xp4_g880anziaw5kze5011|patternname=an unnamed statorless p4|style=raw}}.}}, [[Beluchenko's p13#Variants|p13]], [[Tumbler|p14]], [[Pentadecathlon|p15]], [[Rob's p16|p16]], [[34P20|p20]], [[48P22.1|p22]], {{LinkCatagolue|xp24_y7ah2o0goo444g0gezgy2ooc4q08i11y1u03gz3s0k111y1242y4rrrzsoo7yef0o1y0oo0gze66oy3ah2o0goo444101ey1240dczge0bxooc4q08i11z3x111y1242|patternname=p24|style=raw}}{{refn|group=note|A [[figure eight]] on [[statorless p3]].}}, [[Charity's p25|25]], [[Queen bee shuttle#Variations|p30]], [[68P32|p32]], {{LinkCatagolue|xp36_y6ca6wgy15a48zxgy62d2z4252y58m8wgg8ggy0gw356zy088k88wgg8hgxo1y011211z06acy51y0161y5ka42zyd4r4zy5125ay4653|patternname=p36|style=raw}}{{refn|group=note|A C4_4-symmetric traffic light hassler.}}, as well as 33n<ref name="post138634" />, {{nowrap|40 + 8n}}<ref name="post138264"/>, {{nowrap|45 + 15n}}<ref name="post138266" /><ref name="post138263" />, [[Twin bees shuttle|46n]]<ref name="post15656" /><ref name="post103288" /><ref name="post138263" /><ref name="post138418" />, 86n<ref name="post151283"/>, [[Karel's p177|177n]], and all periods given in the section [[#Self-constructing circuitry|Self-constructing circuitry]] below.
 
In particular, the smallest undecided period is 7, and prior to [[Dave Greene]]'s infinite series of strictly volatile oscillators, the largest [[Prime number|prime]] period for which such an oscillator was known was 13. Volatility 1 oscillators are known for all prime periods greater than or equal to 947.
 
{{EmbedViewer
|pname        = statorlessp3
|viewerconfig = #C [[ THUMBSIZE 4 WIDTH 800 HEIGHT 700 ZOOM 16 AUTOSTART GPS 2 ]]
|position    = center
|caption      = [[Statorless p3]], a period-3 oscillator with volatility 1
|style        = width:200px;
}}


==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]], 3, [[statorless p5|5]], 6, 8, [[34P13|13]], [[pentadecathlon|15]], 22, 30, 33, 92, [[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.
'''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. An oscillator is called '''strictly volatile''' if it has a strict volatility of 1, and [[trivial]] if it has a strict volatility of 0.
 
"Strictly volatile" is a very strong condition that excludes not only most patterns based on smaller-period oscillators (including glider shuttle or glider loop-based oscillators), but also some patterns that reflect or rotate on cell-centred axes or points partway through its period (such as [[twin bees shuttle]] and [[Gabriel's p138]]; related to [[kinetic symmetry]]). No infinite families of strictly volatile oscillators are known except for [[phoenix|phoenixes]] and those based on self-constructing circuitry.<!-- Does Nico Brown's design below count as 1)an infinite family that is 2)based on self-constructing circuitry? -->
 
On December 2, {{year|2022}}, [[Nico Brown]] published a script which can construct a strictly volatile oscillator for any period greater than or equal to 949.<ref name="post154361" /> The resulting patterns are extremely large, with the p1024 case (the only one run to completion so far) having a population of over 594 million cells. Further modifications to the script allowed for periods 943, 945, 946, 947, and 948 to be constructed.<ref name="post154407" /> Below this, the only periods for which strictly volatile oscillators are known are [[Phoenix 1|p2]], [[Statorless p3|p3]], [[Strictly volatile p4|p4]], [[Statorless p5|p5]], [[Statorless p6#Strictly volatile variant|p6]], [[Figure eight|p8]], [[Beluchenko's p13#Variants|p13]], [[Pentadecathlon|p15]], [[Rob's p16|p16]], [[48P22.1|p22]], [[Charity's p25|p25]], [[queen bee shuttle#Variations|p30]], {{LinkCatagolue|xp33_yn46f01y520uc8zyo4rcy7om8zylocgyb1wogzymrggyc1m1zyl111yc13704zxgy58ck8808ooayr7e2022532wgg8gg0gsogz0a332022562y51yzy211y22zz8y2ggyzy2gy58ck8808ooaz1371011211w8ok8808esyra332022562y51zym40sogycgggzyngdgyc11rzyn13wgyb163zyq2d3y76r4zyp26f08y5g0uc4|patternname=p33|format=extended|style=raw}}{{refn|group=note|An eightfold version of [[Jason's p33]].}}, [[P86 R-pentomino hassler#Statorless p86|p86]], and [[Karel's p177|p177]].
 
==Self-constructing circuitry==
In November 2018, [[Dave Greene]] established using self-constructing circuitry that strictly volatile oscillators exist for all periods greater than or equal to 22178648.<ref name="post65835" /> 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 using this method for creating strictly volatile oscillators for periods that are not multiples of eight, between 2918053 and 3506909.<ref name="post66027" />
 
==See also==
{{CatRel|Highly volatile oscillators|Oscillators with specific volatility|Oscillators with specific strict volatility}}
* [[Phoenix]]
* [[Oscillizer]]
* [["volmatchstrict" stamp collection]] -- a collection of composite-period oscillators where volatility matches strict volatility
 
==Notes==
<references group=note />
 
==References==
<references>
<ref name="post138266">{{LinkForumThread
|format = ref
|title  = Re: Oscillator Discussion Thread
|p      = 138266
|author = mniemiec
|date  = December 1, 2021
}}</ref>
<ref name="post138263">{{LinkForumThread
|format = ref
|title  = Re: Oscillator Discussion Thread
|p      = 138263
|author = FractalFusion
|date  = December 1, 2021
}}</ref>
<ref name="post138634">{{LinkForumThread
|format = ref
|title  = Re: Oscillator Discussion Thread
|p      = 138634
|author = FractalFusion
|date  = December 10, 2021
}}</ref>
<ref name="post138264">{{LinkForumThread
|format = ref
|title  = Re: Oscillator Discussion Thread
|p      = 138264
|author = Sokwe
|date  = December 1, 2021
}}</ref>
<ref name="post15656">{{LinkForumThread
|format = ref
|title  = Re: Thread for your unsure discoveries
|p      = 15656
|author = Ivan Fomichev
|date  = January 4, 2015
}}</ref>
<ref name="post103288">{{LinkForumThread
|format = ref
|title  = Re: Oscillator Discussion Thread
|p      = 103288
|author = James Pascua
|date  = August 31, 2020
}}</ref>
<ref name="post138418">{{LinkForumThread
|format = ref
|title  = Re: Oscillator Discussion Thread
|p      = 138418
|author = Martin Grant
|date  = December 6, 2021
}}</ref>
<ref name="post154361">{{LinkForumThread
|format = ref
|title  = Re: Oscillator Discussion Thread
|p      = 154361
|author = Nico Brown
|date  = December 2, 2022
}}</ref>
<ref name="post154407">{{LinkForumThread
|format = ref
|title  = Re: Oscillator Discussion Thread
|p      = 154407
|author = Nico Brown
|date  = December 3, 2022
}}</ref>
<ref name="post65835">{{LinkForumThread
|format = ref
|title  = Re: Self-Constructing Spaceship Challenges
|p      = 65835
|author = Dave Greene
|date  = November 21, 2018
}}</ref>
<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>
<ref name="post151283">{{LinkForumThread
|format = ref
|title  = Re: Oscillator Discussion Thread
|p      = 151283
|author = Matthias Merzenich
|date  = September 23, 2022
}}</ref>
</references>


==External links==
==External links==
{{LinkWeisstein|StrictVolatility.html|patternname=Strict volatility}}
* {{LinkLexicon|lex_v.htm#volatility}}
{{LinkLexicon|lex_v.htm#volatility}}
* {{LinkLexicon|filename=lex_s.htm#statorless|patternname=Statorless}}
 
__NOTOC__

Latest revision as of 03:59, 14 January 2024

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), p60 glider shuttle (p60), 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 periodic glider loops formed by no more than eight copies of a statorless 90-degree glider reflector.[2]

Periods for which non-trivial oscillators of volatility 1 are known are p2, p3, p4, p5, p6, p8, p12[note 1], p13, p14, p15, p16, p20, p22, p24[note 2], 25, p30, p32, p36[note 3], as well as 33n[3], 40 + 8n[4], 45 + 15n[1][2], 46n[5][6][2][7], 86n[8], 177n, and all periods given in the section Self-constructing circuitry below.

In particular, 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. Volatility 1 oscillators are known for all prime periods greater than or equal to 947.

x = 31, y = 28, rule = B3/S23 9bobo5bo3bo5bobo$8bo3bo4bo3bo4bo3bo$9bo7bo3bo7bo$11b2ob2obo3bob2ob2o$ 17bo3bo$10bo3bo9bo3bo$8bobo17bobo2$8bo19bo$7b2o18b2o$7bo19bo$5bo2bo16b o2bo$o4bo14bo4bo$4ob2ob3o9b4ob2ob3o$3ob2ob4o9b3ob2ob4o$5bo4bo14bo4bo$ 2bo2bo16bo2bo$3bo19bo$2b2o18b2o$2bo19bo2$obo17bobo$2bo3bo9bo3bo$9bo3bo $3b2ob2obo3bob2ob2o$bo7bo3bo7bo$o3bo4bo3bo4bo3bo$bobo5bo3bo5bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 WIDTH 800 HEIGHT 700 ZOOM 16 AUTOSTART GPS 2 ]]
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. An oscillator is called strictly volatile if it has a strict volatility of 1, and trivial if it has a strict volatility of 0.

"Strictly volatile" is a very strong condition that excludes not only most patterns based on smaller-period oscillators (including glider shuttle or glider loop-based oscillators), but also some patterns that reflect or rotate on cell-centred axes or points partway through its period (such as twin bees shuttle and Gabriel's p138; related to kinetic symmetry). No infinite families of strictly volatile oscillators are known except for phoenixes and those based on self-constructing circuitry.

On December 2, 2022, Nico Brown published a script which can construct a strictly volatile oscillator for any period greater than or equal to 949.[9] The resulting patterns are extremely large, with the p1024 case (the only one run to completion so far) having a population of over 594 million cells. Further modifications to the script allowed for periods 943, 945, 946, 947, and 948 to be constructed.[10] Below this, the only periods for which strictly volatile oscillators are known are p2, p3, p4, p5, p6, p8, p13, p15, p16, p22, p25, p30, p33[note 4], p86, and p177.

Self-constructing circuitry

In November 2018, Dave Greene established using self-constructing circuitry that strictly volatile oscillators exist for all periods greater than or equal to 22178648.[11] 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.[12] There is also a known mechanism using this method for creating strictly volatile oscillators for periods that are not multiples of eight, between 2918053 and 3506909.[13]

See also

See also categories Highly volatile oscillators, Oscillators with specific volatility and Oscillators with specific strict volatility

Notes

  1. A stabilization of the carnival shuttle using an unnamed statorless p4.
  2. A figure eight on statorless p3.
  3. A C4_4-symmetric traffic light hassler.
  4. An eightfold version of Jason's p33.

References

  1. 1.0 1.1 mniemiec (December 1, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  2. 2.0 2.1 2.2 FractalFusion (December 1, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  3. FractalFusion (December 10, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  4. Sokwe (December 1, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  5. Ivan Fomichev (January 4, 2015). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
  6. James Pascua (August 31, 2020). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  7. Martin Grant (December 6, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  8. Matthias Merzenich (September 23, 2022). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  9. Nico Brown (December 2, 2022). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  10. Nico Brown (December 3, 2022). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  11. Dave Greene (November 21, 2018). Re: Self-Constructing Spaceship Challenges (discussion thread) at the ConwayLife.com forums
  12. Goldtiger997 (December 5, 2018). Re: Self-Constructing Spaceship Challenges (discussion thread) at the ConwayLife.com forums
  13. Chris Cain (November 30, 2018). Re: Self-Constructing Spaceship Challenges (discussion thread) at the ConwayLife.com forums

External links