# 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]] | ||

|- | |- | ||

Line 176: | Line 177: | ||

| 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 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 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]] | ||

|- | |- | ||

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| ≤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 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]] | ||

|- | |- | ||

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| [[p54 shuttle]] | | [[p54 shuttle]] | ||

| David Buckingham | | David Buckingham | ||

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

| | | | ||

| [[p54 shuttle]] | | [[p54 shuttle]] | ||

Line 500: | Line 501: | ||

| ? | | ? | ||

| | | | ||

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

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

|- | |- | ||

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]] | ||

|- | |- | ||

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 788: | Line 789: | ||

| ? | | ? | ||

| | | | ||

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

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

|- | |- | ||

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| 1994 | | 1994 | ||

| | | | ||

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

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

|- | |- | ||

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| ? | | ? | ||

| | | | ||

− | | [[ | + | | [[Karel's p177]] |

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

|- | |- |

## 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