# Difference between revisions of "Oscillator"

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{{Glossary}} | {{Glossary}} | ||

− | An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] and a [[stator]]. | + | An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] (the individual [[cell]]s that actually oscillate) and a [[stator]] (the cells which remain alive throughout its whole period). |

+ | |||

+ | [[Cellular automaton]] theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a [[spaceship]]. | ||

− | |||

==Important oscillators by period== | ==Important oscillators by period== | ||

− | A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one | + | A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one cell that oscillates at the full period. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed. For any period 61 or greater an oscillator can be constructed using the Herschel track method. In April, {{year|2013}} [[Mike Playle]] found a small 90-degree [[stable reflector]] that allows oscillators of all periods 43 or greater to be constructed. |

{| class="wikitable" style="margin-left:auto;margin-right:auto;" | {| class="wikitable" style="margin-left:auto;margin-right:auto;" | ||

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|- | |- | ||

! [[:Category:Oscillators with period 13|13]] | ! [[:Category:Oscillators with period 13|13]] | ||

− | | [[ | + | | [[Buckingham's p13]] |

| David Buckingham | | David Buckingham | ||

| 1976 | | 1976 | ||

| | | | ||

− | | [[ | + | | [[Beluchenko's p13]] |

| [[:Category:Patterns with 34 cells|34]] | | [[:Category:Patterns with 34 cells|34]] | ||

|- | |- | ||

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| [[:Category:Patterns found in 1997|1997]] | | [[:Category:Patterns found in 1997|1997]] | ||

| | | | ||

− | | [[ | + | | [[honey thieves]] |

| [[:Category:Patterns with 36 cells|36]] | | [[:Category:Patterns with 36 cells|36]] | ||

|- | |- | ||

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| ≤[[:Category:Patterns found in 1991|1991]] | | ≤[[:Category:Patterns found in 1991|1991]] | ||

| | | | ||

− | | [[ | + | | [[p18 bi-block hassler]] |

| [[:Category:Patterns with 43 cells|43]] | | [[:Category:Patterns with 43 cells|43]] | ||

|- | |- | ||

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| 1997 | | 1997 | ||

| | | | ||

− | | [[ | + | | [[Jason's p22]] |

| [[:Category:Patterns with 36 cells|36]] | | [[:Category:Patterns with 36 cells|36]] | ||

|- | |- | ||

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|- | |- | ||

! [[:Category:Oscillators with period 28|28]] | ! [[:Category:Oscillators with period 28|28]] | ||

− | | [[ | + | | [[newshuttle]] |

| David Buckingham | | David Buckingham | ||

| [[:Category:patterns found in 1973|1973]] | | [[:Category:patterns found in 1973|1973]] | ||

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|- | |- | ||

! [[:Category:oscillators with period 31|31]] | ! [[:Category:oscillators with period 31|31]] | ||

− | | [[ | + | | [[Merzenich's p31]] |

| [[Matthias Merzenich]] | | [[Matthias Merzenich]] | ||

| [[:Category:patterns found in 2010|2010]] | | [[:Category:patterns found in 2010|2010]] | ||

| | | | ||

− | | [[ | + | | [[Merzenich's p31]] |

| [[:Category:patterns with 48 cells|48]] | | [[:Category:patterns with 48 cells|48]] | ||

|- | |- | ||

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|- | |- | ||

! [[:Category:Oscillators with period 35|35]] | ! [[:Category:Oscillators with period 35|35]] | ||

− | | [[ | + | | [[p35 beehive hassler]] |

| Dean Hickerson | | Dean Hickerson | ||

| 1995 | | 1995 | ||

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|- | |- | ||

! [[:Category:oscillators with period 36|36]] | ! [[:Category:oscillators with period 36|36]] | ||

− | | [[ | + | | [[p36 toad hassler]] |

| Robert Wainwright | | Robert Wainwright | ||

| 1984 | | 1984 | ||

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|- | |- | ||

! [[:Category:Oscillators with period 37|37]] | ! [[:Category:Oscillators with period 37|37]] | ||

− | | [[ | + | | [[Beluchenko's p37]] |

| [[:Category:Patterns found by Nicolay Beluchenko|Nicolay Beluchenko]] | | [[:Category:Patterns found by Nicolay Beluchenko|Nicolay Beluchenko]] | ||

| [[:Category:Patterns found in 2009|2009]] | | [[:Category:Patterns found in 2009|2009]] | ||

| | | | ||

− | | [[ | + | | [[Beluchenko's p37]] |

| [[:Category:Patterns with 124 cells|124]] | | [[:Category:Patterns with 124 cells|124]] | ||

|- | |- | ||

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| [[:Category:Patterns found in 2000|2000]] | | [[:Category:Patterns found in 2000|2000]] | ||

| | | | ||

− | | [[caterer on | + | | [[caterer on Beluchenko's p13]] |

| [[:Category:Patterns with 46 cells|46]] | | [[:Category:Patterns with 46 cells|46]] | ||

|- | |- | ||

! [[:Category:oscillators with period 40|40]] | ! [[:Category:oscillators with period 40|40]] | ||

− | | [[ | + | | [[p40 B-heptomino shuttle]] |

| David Buckingham | | David Buckingham | ||

| ≤1991 | | ≤1991 | ||

| | | | ||

− | | [[ | + | | [[Beluchenko's p40]] |

| [[:Category:patterns with 26 cells|26]] | | [[:Category:patterns with 26 cells|26]] | ||

|- | |- | ||

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|- | |- | ||

! [[:Category:oscillators with period 42|42]] | ! [[:Category:oscillators with period 42|42]] | ||

− | | [[ | + | | [[p42 glider shuttle]] |

| Noam Elkies | | Noam Elkies | ||

| 1994 | | 1994 | ||

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|- | |- | ||

! [[:Category:oscillators with period 43|43]] | ! [[:Category:oscillators with period 43|43]] | ||

− | | [[ | + | | [[p43 glider loop]] |

| [[Mike Playle]] | | [[Mike Playle]] | ||

| [[:Category:patterns found in 2013|2013]] | | [[:Category:patterns found in 2013|2013]] | ||

| | | | ||

− | | [[ | + | | [[p43 glider loop]] |

| [[:Category:patterns with 228 cells|228]] | | [[:Category:patterns with 228 cells|228]] | ||

|- | |- | ||

! [[:Category:oscillators with period 44|44]] | ! [[:Category:oscillators with period 44|44]] | ||

− | | [[ | + | | [[p44 pi-heptomino hassler]] |

| David Buckingham | | David Buckingham | ||

| 1992 | | 1992 | ||

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|- | |- | ||

! [[:Category:oscillators with period 48|48]] | ! [[:Category:oscillators with period 48|48]] | ||

− | | [[ | + | | [[p48 toad hassler]] |

| Bill Gosper | | Bill Gosper | ||

| 1994 | | 1994 | ||

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|- | |- | ||

! [[:Category:oscillators with period 50|50]] | ! [[:Category:oscillators with period 50|50]] | ||

− | | [[ | + | | [[p50 glider shuttle]] |

| Dean Hickerson | | Dean Hickerson | ||

| 1992 | | 1992 | ||

| | | | ||

− | | [[ | + | | [[p50 traffic jam]] |

| [[:Category:patterns with 92 cells|92]] | | [[:Category:patterns with 92 cells|92]] | ||

|- | |- | ||

! [[:Category:Oscillators with period 51|51]] | ! [[:Category:Oscillators with period 51|51]] | ||

− | | [[ | + | | [[Beluchenko's p51]] |

| Nicolay Beluchenko | | Nicolay Beluchenko | ||

| 2009 | | 2009 | ||

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|- | |- | ||

! [[:Category:Oscillators with period 52|52]] | ! [[:Category:Oscillators with period 52|52]] | ||

− | | [[ | + | | [[Four eaters hassling lumps of muck]] |

| David Buckingham | | David Buckingham | ||

| 1977 | | 1977 | ||

| | | | ||

− | | [[ | + | | [[Four eaters hassling lumps of muck]] |

| [[:Category:Patterns with 35 cells|35]] | | [[:Category:Patterns with 35 cells|35]] | ||

|- | |- | ||

! [[:Category:oscillators with period 53|53]] | ! [[:Category:oscillators with period 53|53]] | ||

− | | [[ | + | | [[p53 glider loop]] |

| [[Mike Playle]] | | [[Mike Playle]] | ||

| [[:Category:patterns found in 2013|2013]] | | [[:Category:patterns found in 2013|2013]] | ||

| | | | ||

− | | [[ | + | | [[p53 glider loop]] |

| [[:Category:patterns with 228 cells|228]] | | [[:Category:patterns with 228 cells|228]] | ||

|- | |- | ||

! [[:Category:Oscillators with period 54|54]] | ! [[:Category:Oscillators with period 54|54]] | ||

− | | [[ | + | | [[p54 shuttle]] |

| David Buckingham | | David Buckingham | ||

− | | [[:Category:patterns found in | + | | [[:Category:patterns found in 1973|1973]] |

| | | | ||

− | | [[ | + | | [[p54 shuttle]] |

| [[:Category:Patterns with 48 cells|48]] | | [[:Category:Patterns with 48 cells|48]] | ||

|- | |- | ||

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|- | |- | ||

! [[:Category:oscillators with period 56|56]] | ! [[:Category:oscillators with period 56|56]] | ||

− | | [[ | + | | [[p56 B-heptomino shuttle]] |

| David Buckingham | | David Buckingham | ||

| ≤1991 | | ≤1991 | ||

| | | | ||

− | | [[ | + | | [[p56 B-heptomino shuttle]] |

| [[:Category:patterns with 45 cells|45]] | | [[:Category:patterns with 45 cells|45]] | ||

|- | |- | ||

! [[:Category:Oscillators with period 57|57]] | ! [[:Category:Oscillators with period 57|57]] | ||

− | | [[ | + | | [[p57 Herschel loop 1]] |

| [[:Category:patterns found by Dietrich Leithner|Dietrich Leithner]] | | [[:Category:patterns found by Dietrich Leithner|Dietrich Leithner]] | ||

| 1997 | | 1997 | ||

| | | | ||

− | | [[ | + | | [[p57 bumper loop]] |

| [[:Category:patterns with 152 cells|152]] | | [[:Category:patterns with 152 cells|152]] | ||

|- | |- | ||

! [[:Category:oscillators with period 58|58]] | ! [[:Category:oscillators with period 58|58]] | ||

− | | [[ | + | | [[p58 toadsucker]] |

| Bill Gosper | | Bill Gosper | ||

| 1994 | | 1994 | ||

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|- | |- | ||

! [[:Category:oscillators with period 59|59]] | ! [[:Category:oscillators with period 59|59]] | ||

− | | [[ | + | | [[p59 Herschel loop 1]] |

| David Buckingham | | David Buckingham | ||

| 1997 | | 1997 | ||

| | | | ||

− | | [[ | + | | [[p59 glider loop]] |

| [[:Category:patterns with 228 cells|228]] | | [[:Category:patterns with 228 cells|228]] | ||

|- | |- | ||

! [[:Category:oscillators with period 60|60]] | ! [[:Category:oscillators with period 60|60]] | ||

− | | [[ | + | | [[p60 glider shuttle]] |

| David Buckingham | | David Buckingham | ||

| ≤ 1971 | | ≤ 1971 | ||

Line 464: | Line 465: | ||

|- | |- | ||

! [[:Category:oscillators with period 61|61]] | ! [[:Category:oscillators with period 61|61]] | ||

− | | [[ | + | | [[p61 Herschel loop 1]] |

| David Buckingham | | David Buckingham | ||

| [[:Category:patterns found in 1996|1996]] | | [[:Category:patterns found in 1996|1996]] | ||

| | | | ||

− | | [[ | + | | [[p61 glider loop]] |

| [[:Category:patterns with 228 cells|228]] | | [[:Category:patterns with 228 cells|228]] | ||

|- | |- | ||

Line 500: | Line 501: | ||

| ? | | ? | ||

| | | | ||

− | | [[fumarole on | + | | [[fumarole on Beluchenko's p13]] |

| [[:Category:patterns with 52 cells|52]] | | [[:Category:patterns with 52 cells|52]] | ||

|- | |- | ||

Line 540: | Line 541: | ||

| ? | | ? | ||

| | | | ||

− | | [[ | + | | [[fumarole on 34P14 shuttle]] |

| [[:Category:patterns with 52 cells|52]] | | [[:Category:patterns with 52 cells|52]] | ||

|- | |- | ||

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|- | |- | ||

! [[:Category:Oscillators with period 72|72]] | ! [[:Category:Oscillators with period 72|72]] | ||

− | | [[ | + | | [[two blockers hassling R-pentomino]] |

| Robert Wainwright | | Robert Wainwright | ||

| 1990 | | 1990 | ||

Line 604: | Line 605: | ||

| ? | | ? | ||

| | | | ||

− | | [[p6 thumb on | + | | [[p6 thumb on Beluchenko's p13]] |

| [[:Category:Patterns with 61 cells|61]] | | [[:Category:Patterns with 61 cells|61]] | ||

|- | |- | ||

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|- | |- | ||

! [[:Category:oscillators with period 88|88]] | ! [[:Category:oscillators with period 88|88]] | ||

− | | [[P44 pi-heptomino hassler#Image gallery| | + | | [[P44 pi-heptomino hassler#Image gallery|p88 pi-heptomino hassler]] |

| Dean Hickerson | | Dean Hickerson | ||

| 1994 | | 1994 | ||

Line 724: | Line 725: | ||

| ? | | ? | ||

| | | | ||

− | | [[caterer on | + | | [[caterer on Merzenich's p31]] |

| [[:Category:patterns with 60 cells|60]] | | [[:Category:patterns with 60 cells|60]] | ||

|- | |- | ||

Line 732: | Line 733: | ||

| ? | | ? | ||

| | | | ||

− | | | + | | {{LinkCatagolue|xp94_x696o8b9czy065x33xc871xggzooyd643zwgg04ahhha4y5c871z4701yfoozw8e13xggzy34701xmmggo5jzya146w343|patternname=capped|style=raw}} [[AK-94]] |

− | | | + | | [[:Category:patterns with 110 cells|110]] |

|- | |- | ||

! [[:Category:oscillators with period 95|95]] | ! [[:Category:oscillators with period 95|95]] | ||

Line 776: | Line 777: | ||

|- | |- | ||

! [[:Category:Oscillators with period 100|100]] | ! [[:Category:Oscillators with period 100|100]] | ||

− | | [[ | + | | [[centinal]] |

| Bill Gosper | | Bill Gosper | ||

| ≤[[:Category:patterns found in 1987|1987]] | | ≤[[:Category:patterns found in 1987|1987]] | ||

Line 788: | Line 789: | ||

| ? | | ? | ||

| | | | ||

− | | [[figure eight on | + | | [[figure eight on Beluchenko's p13]] |

| [[:Category:Patterns with 46 cells|46]] | | [[:Category:Patterns with 46 cells|46]] | ||

|- | |- | ||

Line 808: | Line 809: | ||

|- | |- | ||

! [[:Category:Oscillators with period 110|110]] | ! [[:Category:Oscillators with period 110|110]] | ||

− | | [[ | + | | [[p110 traffic jam]] |

| Bill Gosper | | Bill Gosper | ||

| 1994 | | 1994 | ||

Line 824: | Line 825: | ||

|- | |- | ||

! [[:Category:Oscillators with period 124|124]] | ! [[:Category:Oscillators with period 124|124]] | ||

− | | [[ | + | | [[p124 lumps of muck hassler]] |

| Dean Hickerson | | Dean Hickerson | ||

| 1994 | | 1994 | ||

| | | | ||

− | | [[mold on | + | | [[mold on Merzenich's p31]] |

| [[:Category:patterns with 60 cells|60]] | | [[:Category:patterns with 60 cells|60]] | ||

|- | |- | ||

! [[:Category:Oscillators with period 132|132]] | ! [[:Category:Oscillators with period 132|132]] | ||

− | | [[ | + | | [[p132 pi-heptomino hassler]] |

| David Buckingham | | David Buckingham | ||

| ≤1994 | | ≤1994 | ||

Line 864: | Line 865: | ||

|- | |- | ||

! [[:Category:Oscillators with period 156|156]] | ! [[:Category:Oscillators with period 156|156]] | ||

− | | [[ | + | | [[p156 Hans Leo hassler]] |

| Noam Elkies | | Noam Elkies | ||

| 1995 | | 1995 | ||

| | | | ||

− | | [[ | + | | [[Jason's p156]] |

| [[:Category:Patterns with 92 cells|92]] | | [[:Category:Patterns with 92 cells|92]] | ||

|- | |- | ||

Line 876: | Line 877: | ||

| ? | | ? | ||

| | | | ||

− | | [[ | + | | [[Karel's p177]] |

| [[:Category:patterns with 104 cells|104]] | | [[:Category:patterns with 104 cells|104]] | ||

|- | |- | ||

! [[:Category:Oscillators with period 200|200]] | ! [[:Category:Oscillators with period 200|200]] | ||

− | | [[ | + | | [[p200 traffic jam]] |

| Bill Gosper | | Bill Gosper | ||

| 1994 | | 1994 |

## Revision as of 19:46, 5 October 2019

An **oscillator** is a pattern that is a predecessor of itself. That is, it is a pattern that repeats itself after a fixed number of generations (known as its period). The term is usually restricted to finite patterns that are not still lifes, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a rotor (the individual cells that actually oscillate) and a stator (the cells which remain alive throughout its whole period).

Cellular automaton theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a spaceship.

## Important oscillators by period

A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one cell that oscillates at the full period. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed. For any period 61 or greater an oscillator can be constructed using the Herschel track method. In April, 2013 Mike Playle found a small 90-degree stable reflector that allows oscillators of all periods 43 or greater to be constructed.

## See also

## External links

- Oscillator at Wikipedia

- Oscillator at the Life Lexicon