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]] and a [[stator]]. | ||
Line 8: | Line 4: | ||
[[cellular automaton|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 [[glider]] or [[spaceship]]. Strictly speaking "glider" means the little figure so prevalent in [[Conway's Game of Life]], but the more general usage has now become popular. | [[cellular automaton|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 [[glider]] or [[spaceship]]. Strictly speaking "glider" means the little figure so prevalent in [[Conway's Game of Life]], but the more general usage has now become popular. | ||
==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 [[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. | 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, [[:Category:patterns found in 2013|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" | |||
|- | |- | ||
! Period | ! Period | ||
Line 17: | Line 12: | ||
! Discoverer | ! Discoverer | ||
! Year of discovery | ! Year of discovery | ||
! style="background-color:white;border-top-color:white;" | | |||
! Smallest known | |||
! Minimum # of cells | |||
|- | |- | ||
! [[:Category:Oscillators with period 2|2]] | ! [[:Category:Oscillators with period 2|2]] | ||
Line 22: | Line 20: | ||
| [[:Category:Patterns found by John Conway|John Conway]] | | [[:Category:Patterns found by John Conway|John Conway]] | ||
| [[:Category:Patterns found in 1970|1970]] | | [[:Category:Patterns found in 1970|1970]] | ||
| | |||
| [[blinker]] | |||
| [[:Category:Patterns with 3 cells|3]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 3|3]] | ! [[:Category:Oscillators with period 3|3]] | ||
Line 27: | Line 28: | ||
| John Conway | | John Conway | ||
| 1970 | | 1970 | ||
| | |||
| [[caterer]] | |||
| [[:Category:Patterns with 12 cells|12]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 4|4]] | ! [[:Category:Oscillators with period 4|4]] | ||
Line 32: | Line 36: | ||
| [[:Category:Patterns found by Simon Norton|Simon Norton]] | | [[:Category:Patterns found by Simon Norton|Simon Norton]] | ||
| 1970 | | 1970 | ||
| | |||
| [[mazing]], [[mold]] | |||
| [[:Category:Patterns with 12 cells|12]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 5|5]] | ! [[:Category:Oscillators with period 5|5]] | ||
Line 37: | Line 44: | ||
| [[:Category:Patterns found by Sol Goodman|Sol Goodman]], [[:Category:Patterns found by Arthur Taber|Arthur Taber]] | | [[:Category:Patterns found by Sol Goodman|Sol Goodman]], [[:Category:Patterns found by Arthur Taber|Arthur Taber]] | ||
| [[:Category:Patterns found in 1971|1971]] | | [[:Category:Patterns found in 1971|1971]] | ||
| | |||
| [[pseudo-barberpole]] | |||
| [[:Category:Patterns with 15 cells|15]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 6|6]] | ! [[:Category:Oscillators with period 6|6]] | ||
Line 42: | Line 52: | ||
| [[:Category:Patterns found by David Buckingham|David Buckingham]] | | [[:Category:Patterns found by David Buckingham|David Buckingham]] | ||
| [[:Category:Patterns found in 1972|1972]] | | [[:Category:Patterns found in 1972|1972]] | ||
| | |||
| [[unix]] | |||
| [[:Category:Patterns with 16 cells|16]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 7|7]] | ! [[:Category:Oscillators with period 7|7]] | ||
Line 47: | Line 60: | ||
| David Buckingham | | David Buckingham | ||
| 1972 | | 1972 | ||
| | |||
| [[28P7.1]], [[28P7.2]], [[burloaferimeter]] | |||
| [[:Category:Patterns with 28 cells|28]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 8|8]] | ! [[:Category:Oscillators with period 8|8]] | ||
Line 52: | Line 68: | ||
| Simon Norton | | Simon Norton | ||
| 1970 | | 1970 | ||
| | |||
| [[figure eight]] | |||
| [[:Category:Patterns with 12 cells|12]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 9|9]] | ! [[:Category:Oscillators with period 9|9]] | ||
Line 57: | Line 76: | ||
| David Buckingham | | David Buckingham | ||
| 1972 | | 1972 | ||
| | |||
| [[29P9]] | |||
| [[:Category:Patterns with 29 cells|29]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 10|10]] | ! [[:Category:Oscillators with period 10|10]] | ||
Line 62: | Line 84: | ||
| David Buckingham | | David Buckingham | ||
| ≤[[:Category:Patterns found in 1976|1976]] | | ≤[[:Category:Patterns found in 1976|1976]] | ||
| | |||
| [[24P10]] | |||
| [[:Category:Patterns with 24 cells|24]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 11|11]] | ! [[:Category:Oscillators with period 11|11]] | ||
Line 67: | Line 92: | ||
| David Buckingham | | David Buckingham | ||
| [[:Category:Patterns found in 1977|1977]] | | [[:Category:Patterns found in 1977|1977]] | ||
| | |||
| [[rattlesnake]] | |||
| [[:Category:Patterns with 33 cells|33]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 12|12]] | ! [[:Category:Oscillators with period 12|12]] | ||
Line 72: | Line 100: | ||
| [[Robert Wainwright]] | | [[Robert Wainwright]] | ||
| [[:Category:Patterns found in 1972|1972]] | | [[:Category:Patterns found in 1972|1972]] | ||
| | |||
| [[dinner table]] | |||
| [[:Category:Patterns with 33 cells|33]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 13|13]] | ! [[:Category:Oscillators with period 13|13]] | ||
Line 77: | Line 108: | ||
| David Buckingham | | David Buckingham | ||
| 1976 | | 1976 | ||
| | |||
| [[34P13]] | |||
| [[:Category:Patterns with 34 cells|34]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 14|14]] | ! [[:Category:Oscillators with period 14|14]] | ||
Line 82: | Line 116: | ||
| George Collins, Jr. | | George Collins, Jr. | ||
| 1970 | | 1970 | ||
| | |||
| [[tumbler]] | |||
| [[:Category:Patterns with 16 cells|16]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 15|15]] | ! [[:Category:Oscillators with period 15|15]] | ||
Line 87: | Line 124: | ||
| John Conway | | John Conway | ||
| 1970 | | 1970 | ||
| | |||
| [[pentadecathlon]] | |||
| [[:Category:Patterns with 12 cells|12]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 16|16]] | ! [[:Category:Oscillators with period 16|16]] | ||
Line 92: | Line 132: | ||
| Robert Wainwright | | Robert Wainwright | ||
| [[:Category:Patterns found in 1983|1983]] | | [[:Category:Patterns found in 1983|1983]] | ||
| | |||
| [[Achim's p16]] | |||
| [[:Category:Patterns with 32 cells|32]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 17|17]] | ! [[:Category:Oscillators with period 17|17]] | ||
Line 97: | Line 140: | ||
| [[:Category:Patterns found by Dean Hickerson|Dean Hickerson]] | | [[:Category:Patterns found by Dean Hickerson|Dean Hickerson]] | ||
| [[:Category:Patterns found in 1997|1997]] | | [[:Category:Patterns found in 1997|1997]] | ||
| | |||
| [[Honey thieves]] | |||
| [[:Category:Patterns with 36 cells|36]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 18|18]] | ! [[:Category:Oscillators with period 18|18]] | ||
Line 102: | Line 148: | ||
| David Buckingham | | David Buckingham | ||
| ≤[[:Category:Patterns found in 1991|1991]] | | ≤[[:Category:Patterns found in 1991|1991]] | ||
| | |||
| [[43P18]] | |||
| [[:Category:Patterns with 43 cells|43]] | |||
|- | |- | ||
! class="red_td" | 19 | ! class="red_td" | 19 | ||
| class="red_td" colspan=" | | class="red_td" colspan="6" | ''None found'' | ||
|- | |- | ||
! [[:Category:Oscillators with period 20|20]] | ! [[:Category:Oscillators with period 20|20]] | ||
Line 110: | Line 159: | ||
| [[Noam Elkies]] | | [[Noam Elkies]] | ||
| [[:Category:Patterns found in 1995|1995]] | | [[:Category:Patterns found in 1995|1995]] | ||
| | |||
| [[mold on fumarole]] | |||
| [[:Category:Patterns with 30 cells|30]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 21|21]] | ! [[:Category:Oscillators with period 21|21]] | ||
Line 115: | Line 167: | ||
| Robert Wainwright | | Robert Wainwright | ||
| 1995 | | 1995 | ||
| | |||
| [[caterer on 42P7.1]] | |||
| [[:Category:Patterns with 54 cells|54]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 22|22]] | ! [[:Category:Oscillators with period 22|22]] | ||
Line 120: | Line 175: | ||
| Noam Elkies | | Noam Elkies | ||
| 1997 | | 1997 | ||
| | |||
| [[36P22]] | |||
| [[:Category:Patterns with 36 cells|36]] | |||
|- | |- | ||
! class="red_td" | 23 | ! class="red_td" | 23 | ||
| class="red_td" colspan=" | | class="red_td" colspan="6" | ''None found'' | ||
|- | |- | ||
! [[:Category:Oscillators with period 24|24]] | ! [[:Category:Oscillators with period 24|24]] | ||
Line 128: | Line 186: | ||
| [[Bill Gosper]] | | [[Bill Gosper]] | ||
| [[:Category:Patterns found in 1994|1994]] | | [[:Category:Patterns found in 1994|1994]] | ||
| | |||
| [[caterer on figure eight]] | |||
| [[:Category:Patterns with 24 cells|24]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 25|25]] | ! [[:Category:Oscillators with period 25|25]] | ||
Line 133: | Line 194: | ||
| Noam Elkies | | Noam Elkies | ||
| 1994 | | 1994 | ||
| | |||
| [[p25 honey farm hassler]] | |||
| [[:Category:Patterns with 88 cells|88]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 26|26]] | ! [[:Category:Oscillators with period 26|26]] | ||
Line 138: | Line 202: | ||
| David Buckingham | | David Buckingham | ||
| 1983 | | 1983 | ||
| | |||
| [[87P26]] | |||
| [[:Category:Patterns with 87 cells|87]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 27|27]] | ! [[:Category:Oscillators with period 27|27]] | ||
Line 143: | Line 210: | ||
| Noam Elkies | | Noam Elkies | ||
| [[:Category:Patterns found in 2002|2002]] | | [[:Category:Patterns found in 2002|2002]] | ||
| | |||
| [[56P27]] | |||
| [[:Category:Patterns with 56 cells|56]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 28|28]] | ! [[:Category:Oscillators with period 28|28]] | ||
Line 148: | Line 218: | ||
| David Buckingham | | David Buckingham | ||
| [[:Category:patterns found in 1973|1973]] | | [[:Category:patterns found in 1973|1973]] | ||
| | |||
| [[pre-pulsar shuttle 28]], [[mold on 41P7.2]] | |||
| [[:Category:Patterns with 53 cells|53]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 29|29]] | ! [[:Category:Oscillators with period 29|29]] | ||
Line 153: | Line 226: | ||
| David Buckingham | | David Buckingham | ||
| [[:Category:patterns found in 1980|1980]] | | [[:Category:patterns found in 1980|1980]] | ||
| | |||
| [[pre-pulsar shuttle 29]] | |||
| [[:Category:Patterns with 54 cells|54]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 30|30]] | ! [[:Category:Oscillators with period 30|30]] | ||
Line 158: | Line 234: | ||
| Bill Gosper | | Bill Gosper | ||
| 1970 | | 1970 | ||
| | |||
| [[queen bee shuttle]] | |||
| [[:Category:Patterns with 20 cells|20]] | |||
|- | |- | ||
! [[:Category:oscillators with period 31|31]] | ! [[:Category:oscillators with period 31|31]] | ||
Line 163: | Line 242: | ||
| [[Matthias Merzenich]] | | [[Matthias Merzenich]] | ||
| [[:Category:patterns found in 2010|2010]] | | [[:Category:patterns found in 2010|2010]] | ||
| | |||
| [[48P31]] | |||
| [[:Category:patterns with 48 cells|48]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 32|32]] | ! [[:Category:Oscillators with period 32|32]] | ||
Line 168: | Line 250: | ||
| David Buckingham | | David Buckingham | ||
| [[:Category:Patterns found in 1978|1978]] | | [[:Category:Patterns found in 1978|1978]] | ||
| | |||
| [[gourmet]] | |||
| [[:Category:Patterns with 66 cells|66]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 33|33]] | ! [[:Category:Oscillators with period 33|33]] | ||
Line 173: | Line 258: | ||
| Noam Elkies, [[:Category:Patterns found by Achim Flammenkamp|Achim Flammenkamp]] | | Noam Elkies, [[:Category:Patterns found by Achim Flammenkamp|Achim Flammenkamp]] | ||
| 1997 | | 1997 | ||
| | |||
| [[caterer on rattlesnake]] | |||
| [[:Category:Patterns with 46 cells|46]] | |||
|- | |- | ||
! class="red_td" | 34 | ! class="red_td" | 34 | ||
| class="red_td" colspan=" | | class="red_td" colspan="6" | ''No non-trivial examples found'' | ||
|- | |- | ||
! [[:Category:Oscillators with period 35|35]] | ! [[:Category:Oscillators with period 35|35]] | ||
Line 181: | Line 269: | ||
| Dean Hickerson | | Dean Hickerson | ||
| 1995 | | 1995 | ||
| | |||
| [[p35 honey farm hassler]] | |||
| [[:Category:patterns with 44 cells|44]] | |||
|- | |- | ||
! [[:Category:oscillators with period 36|36]] | ! [[:Category:oscillators with period 36|36]] | ||
Line 186: | Line 277: | ||
| Robert Wainwright | | Robert Wainwright | ||
| 1984 | | 1984 | ||
| | |||
| [[22P36]] | |||
| [[:Category:patterns with 22 cells|22]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 37|37]] | ! [[:Category:Oscillators with period 37|37]] | ||
Line 191: | Line 285: | ||
| [[: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]] | ||
| | |||
| [[124P37]] | |||
| [[:Category:Patterns with 124 cells|124]] | |||
|- | |- | ||
! class="red_td" | 38 | ! class="red_td" | 38 | ||
| class="red_td" colspan=" | | class="red_td" colspan="6" | ''None found'' | ||
|- | |- | ||
! [[:Category:Oscillators with period 39|39]] | ! [[:Category:Oscillators with period 39|39]] | ||
Line 199: | Line 296: | ||
| David Buckingham, Noam Elkies | | David Buckingham, Noam Elkies | ||
| [[:Category:Patterns found in 2000|2000]] | | [[:Category:Patterns found in 2000|2000]] | ||
| | |||
| [[caterer on 34P13]] | |||
| [[:Category:Patterns with 46 cells|46]] | |||
|- | |- | ||
! [[:Category:oscillators with period 40|40]] | ! [[:Category:oscillators with period 40|40]] | ||
Line 204: | Line 304: | ||
| David Buckingham | | David Buckingham | ||
| ≤1991 | | ≤1991 | ||
| | |||
| [[26P40]] | |||
| [[:Category:patterns with 26 cells|26]] | |||
|- | |- | ||
! class="red_td" | 41 | ! class="red_td" | 41 | ||
| class="red_td" colspan=" | | class="red_td" colspan="6" | ''None found'' | ||
|- | |- | ||
! [[:Category:oscillators with period 42|42]] | ! [[:Category:oscillators with period 42|42]] | ||
Line 212: | Line 315: | ||
| Noam Elkies | | Noam Elkies | ||
| 1994 | | 1994 | ||
| | |||
| [[unix on 41P7.2]] | |||
| [[:Category:Patterns with 57 cells|57]] | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 43|43]] | ||
| | | [[P43 glider loop]] | ||
| [[Mike Playle]] | |||
| [[:Category:patterns found in 2013|2013]] | |||
| | |||
| [[P43 glider loop]] | |||
| [[:Category:patterns with 228 cells|228]] | |||
|- | |- | ||
! [[:Category:oscillators with period 44|44]] | ! [[:Category:oscillators with period 44|44]] | ||
Line 220: | Line 331: | ||
| David Buckingham | | David Buckingham | ||
| 1992 | | 1992 | ||
| | |||
| [[mold on rattlesnake]] | |||
| [[:Category:patterns with 45 cells|45]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 45|45]] | ! [[:Category:Oscillators with period 45|45]] | ||
Line 225: | Line 339: | ||
| ? | | ? | ||
| ≤1995 | | ≤1995 | ||
| | |||
| [[pentadecathlon on thumb 1]] | |||
| [[:Category:patterns with 48 cells|48]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 46|46]] | ! [[:Category:Oscillators with period 46|46]] | ||
Line 230: | Line 347: | ||
| Bill Gosper | | Bill Gosper | ||
| 1971 | | 1971 | ||
| | |||
| [[twin bees shuttle]] | |||
| [[:Category:patterns with 28 cells|28]] | |||
|- | |- | ||
! [[:Category:oscillators with period 47|47]] | ! [[:Category:oscillators with period 47|47]] | ||
Line 235: | Line 355: | ||
| David Buckingham | | David Buckingham | ||
| [[:Category:patterns found in 1982|1982]] | | [[:Category:patterns found in 1982|1982]] | ||
| | |||
| [[pre-pulsar shuttle 47]] | |||
| [[:Category:patterns with 84 cells|84]] | |||
|- | |- | ||
! [[:Category:oscillators with period 48|48]] | ! [[:Category:oscillators with period 48|48]] | ||
Line 240: | Line 363: | ||
| Bill Gosper | | Bill Gosper | ||
| 1994 | | 1994 | ||
| | |||
| [[65P48]] | |||
| [[:Category:patterns with 65 cells|65]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 49|49]] | ! [[:Category:Oscillators with period 49|49]] | ||
Line 245: | Line 371: | ||
| Noam Elkies | | Noam Elkies | ||
| [[:Category:Patterns found in 1999|1999]] | | [[:Category:Patterns found in 1999|1999]] | ||
| | |||
| [[p49 glider loop]] | |||
| [[:Category:Patterns with 228 cells|228]] | |||
|- | |- | ||
! [[:Category:oscillators with period 50|50]] | ! [[:Category:oscillators with period 50|50]] | ||
Line 250: | Line 379: | ||
| Dean Hickerson | | Dean Hickerson | ||
| 1992 | | 1992 | ||
| | |||
| [[P50 traffic jam]] | |||
| [[:Category:patterns with 92 cells|92]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 51|51]] | ! [[:Category:Oscillators with period 51|51]] | ||
Line 255: | Line 387: | ||
| Nicolay Beluchenko | | Nicolay Beluchenko | ||
| 2009 | | 2009 | ||
| | |||
| [[92P51]] | |||
| [[:Category:Patterns with 92 cells|92]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 52|52]] | ! [[:Category:Oscillators with period 52|52]] | ||
Line 260: | Line 395: | ||
| David Buckingham | | David Buckingham | ||
| 1977 | | 1977 | ||
| | |||
| [[35P52]] | |||
| [[:Category:Patterns with 35 cells|35]] | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 53|53]] | ||
| | | [[P53 glider loop]] | ||
| [[Mike Playle]] | |||
| [[:Category:patterns found in 2013|2013]] | |||
| | |||
| [[P53 glider loop]] | |||
| [[:Category:patterns with 228 cells|228]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 54|54]] | ! [[:Category:Oscillators with period 54|54]] | ||
Line 268: | Line 411: | ||
| David Buckingham | | David Buckingham | ||
| 1974 | | 1974 | ||
| | |||
| [[P54 shuttle]] | |||
| [[:Category:Patterns with 48 cells|48]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 55|55]] | ! [[:Category:Oscillators with period 55|55]] | ||
Line 273: | Line 419: | ||
| David Buckingham | | David Buckingham | ||
| [[:Category:patterns found in 1986|1986]] | | [[:Category:patterns found in 1986|1986]] | ||
| | |||
| [[pseudo-barberpole on rattlesnake]] | |||
| [[:Category:patterns with 49 cells|49]] | |||
|- | |- | ||
! [[:Category:oscillators with period 56|56]] | ! [[:Category:oscillators with period 56|56]] | ||
Line 278: | Line 427: | ||
| David Buckingham | | David Buckingham | ||
| ≤1991 | | ≤1991 | ||
| | |||
| [[P56 B-heptomino shuttle]] | |||
| [[:Category:patterns with 45 cells|45]] | |||
|- | |- | ||
! [[:Category:Oscillators with period 57|57]] | ! [[:Category:Oscillators with period 57|57]] | ||
Line 283: | Line 435: | ||
| [[:Category:patterns found by Dietrich Leithner|Dietrich Leithner]] | | [[:Category:patterns found by Dietrich Leithner|Dietrich Leithner]] | ||
| 1997 | | 1997 | ||
| | |||
| [[P57 glider loop]] | |||
| [[:Category:patterns with 228 cells|228]] | |||
|- | |- | ||
! [[:Category:oscillators with period 58|58]] | ! [[:Category:oscillators with period 58|58]] | ||
Line 288: | Line 443: | ||
| Bill Gosper | | Bill Gosper | ||
| 1994 | | 1994 | ||
| | |||
| [[pre-pulsar shuttle 58]] | |||
| [[:Category:patterns with 104 cells|104]] | |||
|- | |- | ||
! [[:Category:oscillators with period 59|59]] | ! [[:Category:oscillators with period 59|59]] | ||
Line 293: | Line 451: | ||
| David Buckingham | | David Buckingham | ||
| 1997 | | 1997 | ||
| | |||
| [[P59 glider loop]] | |||
| [[:Category:patterns with 228 cells|228]] | |||
|- | |- | ||
! [[:Category:oscillators with period 60|60]] | ! [[:Category:oscillators with period 60|60]] | ||
Line 298: | Line 459: | ||
| David Buckingham | | David Buckingham | ||
| ≤ 1971 | | ≤ 1971 | ||
| | |||
| [[mold on pentadecathlon]] | |||
| [[:Category:patterns with 24 cells|24]] | |||
|- | |- | ||
! [[:Category:oscillators with period 61|61]] | ! [[:Category:oscillators with period 61|61]] | ||
Line 303: | Line 467: | ||
| 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: | ! [[:Category:oscillators with period 62|62]] | ||
| [[ | | ? | ||
| | | ? | ||
| | | ? | ||
| | |||
| [[110P62]] | |||
| [[:Category:patterns with 110 cells|110]] | |||
|- | |- | ||
! [[:Category:oscillators with period | ! [[:Category:oscillators with period 63|63]] | ||
| [[ | | ? | ||
| | | ? | ||
| | | ? | ||
| | |||
| [[snacker on 38P7.2]] | |||
| [[:Category:patterns with 78 cells|78]] | |||
|- | |- | ||
! [[:Category: | ! [[:Category:oscillators with period 64|64]] | ||
| [[ | | ? | ||
| | | ? | ||
| ? | |||
| | |||
| [[Merzenich's p64]] | |||
| [[:Category:patterns with 34 cells|34]] | |||
|- | |- | ||
! [[:Category: | ! [[:Category:oscillators with period 65|65]] | ||
| [[ | | ? | ||
| | | ? | ||
| | | ? | ||
| | |||
| [[fumarole on 34P13]] | |||
| [[:Category:patterns with 52 cells|52]] | |||
|- | |- | ||
! [[:Category: | ! [[:Category:oscillators with period 66|66]] | ||
| [[ | | ? | ||
| | | ? | ||
| | | ? | ||
| | |||
| [[caterer on 36P22]] | |||
| [[:Category:patterns with 48 cells|48]] | |||
|- | |- | ||
! [[:Category: | ! [[:Category:oscillators with period 67|67]] | ||
| | | ? | ||
| | | ? | ||
| | | ? | ||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! [[:Category: | ! [[:Category:oscillators with period 68|68]] | ||
| | | ? | ||
| | | ? | ||
| | | ? | ||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! [[:Category: | ! [[:Category:oscillators with period 69|69]] | ||
| | | ? | ||
| | | ? | ||
| | | ? | ||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! [[:Category: | ! [[:Category:oscillators with period 70|70]] | ||
| | | ? | ||
| | | ? | ||
| | | ? | ||
| | | | ||
| [[78P70]] | |||
| [[:Category:patterns with 78 cells|78]] | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 71|71]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:Oscillators with period 72|72]] | ||
| [[47P72]] | |||
| Robert Wainwright | |||
| 1990 | |||
| | |||
| [[figure eight on 22P36]] | |||
| | |||
| [[ | |||
| | |||
| | |||
| | |||
| [[figure eight | |||
| [[:Category:Patterns with 36 cells|36]] | | [[:Category:Patterns with 36 cells|36]] | ||
|- | |- | ||
! | ! [[:Category:oscillators with period 73|73]] | ||
| | | ? | ||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 74|74]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 75|75]] | ||
| [[ | | ? | ||
| [[:Category:Patterns with | | ? | ||
| ? | |||
| | |||
| [[6 bits]] | |||
| [[:Category:Patterns with 49 cells|49]] | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 76|76]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 77|77]] | ||
| [[ | | ? | ||
| [[:Category: | | ? | ||
| ? | |||
| | |||
| [[77P77]] | |||
| [[:Category:patterns with 77 cells|77]] | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 78|78]] | ||
| [[ | | ? | ||
| [[:Category:Patterns with | | ? | ||
| ? | |||
| | |||
| [[126P78.1]] | |||
| [[:Category:Patterns with 126 cells|126]] | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 79|79]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 80|80]] | ||
| [[ | | ? | ||
| [[:Category:Patterns with | | ? | ||
| ? | |||
| | |||
| [[122P80.1]] | |||
| [[:Category:Patterns with 122 cells|122]] | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 81|81]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 82|82]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 83|83]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 84|84]] | ||
| | | ? | ||
| ? | |||
| ? | |||
| | |||
| [[114P84]] | |||
| [[:Category:patterns with 84 cells|84]] | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 85|85]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 86|86]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 87|87]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| [[84P87]] | |||
| | |||
| | |||
| | |||
| | |||
| [[ | |||
| [[:Category:patterns with 84 cells|84]] | | [[:Category:patterns with 84 cells|84]] | ||
|- | |- | ||
! | ! [[:Category:oscillators with period 88|88]] | ||
| [[P44 pi-heptomino hassler#Image gallery|P88 pi-heptomino hassler]] | |||
| Dean Hickerson | |||
| 1994 | |||
| | |||
| [[figure eight on rattlesnake]] | |||
| [[ | |||
|- | |||
| | |||
| | |||
| | |||
| [[ | |||
| [[:Category:patterns with 45 cells|45]] | | [[:Category:patterns with 45 cells|45]] | ||
|- | |- | ||
! | ! [[:Category:oscillators with period 89|89]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 90|90]] | ||
| [[ | | ? | ||
| [[:Category:patterns with | | ? | ||
| ? | |||
| | |||
| [[fumarole on 43P18]] | |||
| [[:Category:patterns with 61 cells|61]] | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 91|91]] | ||
| ? | |||
| | | ? | ||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 92|92]] | ||
| [[ | | ? | ||
| [[:Category:patterns with | | ? | ||
| ? | |||
| | |||
| [[twin bees shuttles hassling blinker]] | |||
| [[:Category:patterns with 61 cells|61]] | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 93|93]] | ||
| [[ | | ? | ||
| | | ? | ||
| ? | |||
| | |||
| [[caterer on 48P31]] | |||
| [[:Category:patterns with 60 cells|60]] | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 94|94]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 95|95]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 96|96]] | ||
| [[caterer on | | ? | ||
| [[:Category:patterns with | | ? | ||
| ? | |||
| | |||
| [[caterer on 68P32]] | |||
| [[:Category:patterns with 80 cells|80]] | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 97|97]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 98|98]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:oscillators with period 99|99]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| ? | |||
| ? | |||
|- | |- | ||
! | ! [[:Category:Oscillators with period 100|100]] | ||
| [[Centinal]] | |||
| Bill Gosper | |||
| ≤[[:Category:patterns found in 1987|1987]] | |||
| | |||
| [[ | |||
| | |||
| [[:Category:patterns | |||
| | |||
| [[centinal]] | | [[centinal]] | ||
| [[:Category:Patterns with 70 cells|70]] | | [[:Category:Patterns with 70 cells|70]] | ||
|- | |- | ||
! 104 | ! [[:Category:oscillators with period 104|104]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| [[figure eight on 34P13]] | | [[figure eight on 34P13]] | ||
| [[:Category:Patterns with 46 cells|46]] | | [[:Category:Patterns with 46 cells|46]] | ||
|- | |- | ||
! 105 | ! [[:Category:oscillators with period 105|105]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| [[pentadecathlon on 37P7.1]] | | [[pentadecathlon on 37P7.1]] | ||
| [[:Category:patterns with 49 cells|49]] | | [[:Category:patterns with 49 cells|49]] | ||
|- | |- | ||
! 108 | ! [[:Category:oscillators with period 108|108]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| [[T-nosed p4 on 56P27]] | | [[T-nosed p4 on 56P27]] | ||
| [[:Category:patterns with 87 cells|87]] | | [[:Category:patterns with 87 cells|87]] | ||
|- | |- | ||
! 110 | ! [[:Category:Oscillators with period 110|110]] | ||
| [[P110 traffic jam]] | |||
| Bill Gosper | |||
| 1994 | |||
| | |||
| [[pseudo-barberpole on 36P22]] | | [[pseudo-barberpole on 36P22]] | ||
| [[:Category:Patterns with 51 cells|51]] | | [[:Category:Patterns with 51 cells|51]] | ||
|- | |- | ||
! 120 | ! [[:Category:oscillators with period 120|120]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| [[figure eight on pentadecathlon]] | | [[figure eight on pentadecathlon]] | ||
| [[:Category:Patterns with 24 cells|24]] | | [[:Category:Patterns with 24 cells|24]] | ||
|- | |- | ||
! 138 | ! [[:Category:Oscillators with period 124|124]] | ||
| [[P124 lumps of muck hassler]] | |||
| Dean Hickerson | |||
| 1994 | |||
| | |||
| [[mold on 48P31]] | |||
| [[:Category:patterns with 60 cells|60]] | |||
|- | |||
! [[:Category:Oscillators with period 132|132]] | |||
| [[P132 pi-heptomino hassler]] | |||
| David Buckingham | |||
| ≤1994 | |||
| | |||
| ? | |||
| ? | |||
|- | |||
! [[:Category:oscillators with period 135|135]] | |||
| ? | |||
| ? | |||
| ? | |||
| | |||
| [[106P135]] | |||
| [[:Category:patterns with 106 cells|106]] | |||
|- | |||
! [[:Category:oscillators with period 138|138]] | |||
| ? | |||
| ? | |||
| ? | |||
| | |||
| [[Gabriel's p138]] | | [[Gabriel's p138]] | ||
| [[:Category:patterns with 36 cells|36]] | | [[:Category:patterns with 36 cells|36]] | ||
|- | |- | ||
! 144 | ! [[:Category:Oscillators with period 144|144]] | ||
| [[Achim's p144]] | |||
| Achim Flammenkamp | |||
| 1994 | |||
| | |||
| [[Achim's p144]] | | [[Achim's p144]] | ||
| [[:Category:Patterns with 42 cells|42]] | | [[:Category:Patterns with 42 cells|42]] | ||
|- | |- | ||
! 156 | ! [[:Category:Oscillators with period 156|156]] | ||
| [[P156 Hans Leo hassler]] | |||
| Noam Elkies | |||
| 1995 | |||
| | |||
| [[92P156]] | | [[92P156]] | ||
| [[:Category:Patterns with 92 cells|92]] | | [[:Category:Patterns with 92 cells|92]] | ||
|- | |- | ||
! 177 | ! [[:Category:oscillators with period 177|177]] | ||
| ? | |||
| ? | |||
| ? | |||
| | |||
| [[104P177]] | | [[104P177]] | ||
| [[:Category:patterns with 104 cells|104]] | | [[:Category:patterns with 104 cells|104]] | ||
|- | |- | ||
! 312 | ! [[:Category:Oscillators with period 200|200]] | ||
| [[P200 traffic jam]] | |||
| Bill Gosper | |||
| 1994 | |||
| | |||
| [[Kok's galaxy on centinal]] | |||
| [[:Category:patterns with 98 cells|98]] | |||
|- | |||
! [[:Category:oscillators with period 312|312]] | |||
| ? | |||
| ? | |||
| ? | |||
| | |||
| [[60P312]] | | [[60P312]] | ||
| [[:Category:Patterns with 60 cells|60]] | | [[:Category:Patterns with 60 cells|60]] | ||
|} | |} | ||
==See also== | ==See also== | ||
Line 678: | Line 900: | ||
*[[:Category:Oscillators|List of oscillators]] | *[[:Category:Oscillators|List of oscillators]] | ||
*[[Omniperiodic]] | *[[Omniperiodic]] | ||
*[[LifeWiki:Game_of_Life_Status_page#Oscillator_periods|Oscillator periods status table]] | |||
==External links== | ==External links== | ||
{{LinkLexicon|lex_o.htm#oscillator}} | {{LinkLexicon|lex_o.htm#oscillator}} | ||
{{LinkWeisstein|Oscillator.html}} | {{LinkWeisstein|Oscillator.html}} |
Revision as of 21:02, 25 June 2017
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 and a stator.
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 glider or spaceship. Strictly speaking "glider" means the little figure so prevalent in Conway's Game of Life, but the more general usage has now become popular.
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 the Life Lexicon