Oscillator: Difference between revisions

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{{Glossary}}
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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]].
 
[[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==
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.
 
<table border="0" cellpadding="0" cellspacing="0" width="100%"><tr><td align="center" width="50%">
{| class="wikitable"
|-
! Period
! First discovered
! Discoverer
! Year of discovery
|-
! [[:Category:Oscillators with period 2|2]]
| [[blinker]]
| [[:Category:Patterns found by John Conway|John Conway]]
| [[:Category:Patterns found in 1970|1970]]
|-
! [[:Category:Oscillators with period 3|3]]
| [[pulsar]]
| John Conway
| 1970
|-
! [[:Category:Oscillators with period 4|4]]
| [[pinwheel]]
| [[:Category:Patterns found by Simon Norton|Simon Norton]]
| 1970
|-
! [[:Category:Oscillators with period 5|5]]
| [[octagon 2]]
| [[:Category:Patterns found by Sol Goodman|Sol Goodman]], [[:Category:Patterns found by Arthur Taber|Arthur Taber]]
| [[:Category:Patterns found in 1971|1971]]
|-
! [[:Category:Oscillators with period 6|6]]
| [[$rats]]
| [[:Category:Patterns found by David Buckingham|David Buckingham]]
| [[:Category:Patterns found in 1972|1972]]
|-
! [[:Category:Oscillators with period 7|7]]
| [[burloaferimeter]]
| David Buckingham
| 1972
|-
! [[:Category:Oscillators with period 8|8]]
| [[figure eight]]
| Simon Norton
| 1970
|-
! [[:Category:Oscillators with period 9|9]]
| [[worker bee]]
| David Buckingham
| 1972
|-
! [[:Category:Oscillators with period 10|10]]
| [[42P10.1]]
| David Buckingham
| &le;[[:Category:Patterns found in 1976|1976]]
|-
! [[:Category:Oscillators with period 11|11]]
| [[38P11.1]]
| David Buckingham
| [[:Category:Patterns found in 1977|1977]]
|-
! [[:Category:Oscillators with period 12|12]]
| [[dinner table]]
| [[Robert Wainwright]]
| [[:Category:Patterns found in 1972|1972]]
|-
! [[:Category:Oscillators with period 13|13]]
| [[65P13.1]]
| David Buckingham
| 1976
|-
! [[:Category:Oscillators with period 14|14]]
| [[tumbler]]
| George Collins, Jr.
| 1970
|-
! [[:Category:Oscillators with period 15|15]]
| [[pentadecathlon]]
| John Conway
| 1970
|-
! [[:Category:Oscillators with period 16|16]]
| [[two pre-L hasslers]]
| Robert Wainwright
| [[:Category:Patterns found in 1983|1983]]
|-
! [[:Category:Oscillators with period 17|17]]
| [[54P17.1]]
| [[:Category:Patterns found by Dean Hickerson|Dean Hickerson]]
| [[:Category:Patterns found in 1997|1997]]
|-
! [[:Category:Oscillators with period 18|18]]
| [[117P18]]
| David Buckingham
| &le;[[:Category:Patterns found in 1991|1991]]
|-
! class="red_td" | 19
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 20|20]]
| [[145P20]]
| [[Noam Elkies]]
| [[:Category:Patterns found in 1995|1995]]
|-
! [[:Category:Oscillators with period 21|21]]
| [[124P21]]
| Robert Wainwright
| 1995
|-
! [[:Category:Oscillators with period 22|22]]
| [[168P22.1]]
| Noam Elkies
| 1997
|-
! class="red_td" | 23
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 24|24]]
| [[186P24]]
| [[Bill Gosper]]
| [[:Category:Patterns found in 1994|1994]]
|-
! [[:Category:Oscillators with period 25|25]]
| [[134P25]]
| Noam Elkies
| 1994
|-
! [[:Category:Oscillators with period 26|26]]
| [[pre-pulsar shuttle 26]]
| David Buckingham
| 1983
|-
! [[:Category:Oscillators with period 27|27]]
| [[123P27.1]]
| Noam Elkies
| [[:Category:Patterns found in 2002|2002]]
|-
! [[:Category:Oscillators with period 28|28]]
| [[Newshuttle]]
| David Buckingham
| [[:Category:patterns found in 1973|1973]]
|-
! [[:Category:Oscillators with period 29|29]]
| [[pre-pulsar shuttle 29]]
| David Buckingham
| [[:Category:patterns found in 1980|1980]]
|-
! [[:Category:Oscillators with period 30|30]]
| [[queen bee shuttle]]
| Bill Gosper
| 1970
|-
! [[:Category:oscillators with period 31|31]]
| [[48P31]]
| [[Matthias Merzenich]]
| [[:Category:patterns found in 2010|2010]]
|-
! [[:Category:Oscillators with period 32|32]]
| [[gourmet]]
| David Buckingham
| [[:Category:Patterns found in 1978|1978]]
|-
! [[:Category:Oscillators with period 33|33]]
| [[258P3 on Achim's p11]]
| Noam Elkies, [[:Category:Patterns found by Achim Flammenkamp|Achim Flammenkamp]]
| 1997
|-
! class="red_td" | 34
| class="red_td" colspan="3" | ''No non-trivial examples found''
|-
! [[:Category:Oscillators with period 35|35]]
| [[P35 beehive hassler]]
| Dean Hickerson
| 1995
|-
! [[:Category:oscillators with period 36|36]]
| [[P36 toad hassler]]
| Robert Wainwright
| 1984
|-
! [[:Category:Oscillators with period 37|37]]
| [[124P37]]
| [[:Category:Patterns found by Nicolay Beluchenko|Nicolay Beluchenko]]
| [[:Category:Patterns found in 2009|2009]]
|-
! class="red_td" | 38
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 39|39]]
| [[134P39.1]]
| David Buckingham, Noam Elkies
| [[:Category:Patterns found in 2000|2000]]
|-
! [[:Category:oscillators with period 40|40]]
| [[P40 B-heptomino shuttle]]
| David Buckingham
| &le;1991
|-
! class="red_td" | 41
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:oscillators with period 42|42]]
| [[P42 glider shuttle]]
| Noam Elkies
| 1994
|-
! [[:Category:oscillators with period 43|43]]
| [[P43 glider shuttle]]
| [[Mike Playle]]
| [[:Category:patterns found in 2013|2013]]
|-
! [[:Category:oscillators with period 44|44]]
| [[P44 pi-heptomino hassler]]
| David Buckingham
| 1992
|-
! [[:Category:Oscillators with period 45|45]]
| [[pentadecathlon on snacker]]
| ?
| &le;1995
|-
! [[:Category:Oscillators with period 46|46]]
| [[twin bees shuttle]]
| Bill Gosper
| 1971
|-
! [[:Category:oscillators with period 47|47]]
| [[pre-pulsar shuttle 47]]
| David Buckingham
| [[:Category:patterns found in 1982|1982]]
|-
! [[:Category:oscillators with period 48|48]]
| [[P48 toad hassler]]
| Bill Gosper
| 1994
|-
! [[:Category:Oscillators with period 49|49]]
| [[p49 glider shuttle]]
| Noam Elkies
| [[:Category:Patterns found in 1999|1999]]
|-
! [[:Category:oscillators with period 50|50]]
| [[P50 glider shuttle]]
| Dean Hickerson
| 1992
|-
! [[:Category:Oscillators with period 51|51]]
| [[112P51]]
| Nicolay Beluchenko
| 2009
|-
! [[:Category:Oscillators with period 52|52]]
| [[35P52]]
| David Buckingham
| 1977
|-
! [[:Category:oscillators with period 53|53]]
| [[P53 glider shuttle]]
| [[Mike Playle]]
| [[:Category:patterns found in 2013|2013]]
|-
! [[:Category:Oscillators with period 54|54]]
| [[P54 shuttle]]
| David Buckingham
| 1974
|-
! [[:Category:Oscillators with period 55|55]]
| [[pre-pulsar hassler 55]]
| David Buckingham
| [[:Category:patterns found in 1986|1986]]
|-
! [[:Category:oscillators with period 56|56]]
| [[P56 B-heptomino shuttle]]
| David Buckingham
| &le;1991
|-
! [[:Category:Oscillators with period 57|57]]
| [[P57 Herschel loop 1]]
| [[:Category:patterns found by Dietrich Leithner|Dietrich Leithner]]
| 1997
|-
! [[:Category:oscillators with period 58|58]]
| [[P58 toadsucker]]
| Bill Gosper
| 1994
|-
! [[:Category:oscillators with period 59|59]]
| [[P59 Herschel loop 1]]
| David Buckingham
| 1997
|-
! [[:Category:oscillators with period 60|60]]
| [[P60 glider shuttle]]
| David Buckingham
| &le; 1971
|-
! [[:Category:oscillators with period 61|61]]
| [[P61 Herschel loop 1]]
| David Buckingham
| [[:Category:patterns found in 1996|1996]]
|-
! [[:Category:Oscillators with period 72|72]]
| [[47P72]]
| Robert Wainwright
| 1990
|-
! [[:Category:oscillators with period 88|88]]
| [[P44 pi-heptomino hassler#Image gallery|P88 pi-heptomino hassler]]
| Dean Hickerson
| 1994
|-
! [[:Category:Oscillators with period 100|100]]
| [[Centinal]]
| Bill Gosper
| &le;[[:Category:patterns found in 1987|1987]]
|-
! [[:Category:Oscillators with period 110|110]]
| [[P110 traffic jam]]
| Bill Gosper
| 1994
|-
! [[:Category:Oscillators with period 124|124]]
| [[P124 lumps of muck hassler]]
| Dean Hickerson
| 1994
|-
! [[:Category:Oscillators with period 132|132]]
| [[P132 pi-heptomino hassler]]
| David Buckingham
| &le;1994
|-
! [[:Category:Oscillators with period 144|144]]
| [[Achim's p144]]
| Achim Flammenkamp
| 1994
|-
! [[:Category:Oscillators with period 156|156]]
| [[P156 Hans Leo hassler]]
| Noam Elkies
| 1995
|-
! [[:Category:Oscillators with period 200|200]]
| [[P200 traffic jam]]
| Bill Gosper
| 1994
|}</td><td align="center" width="50%">
{| class="wikitable"
|-
! Period
! Smallest known
! Minimum # of [[cell]]s
|-
! 2
| [[blinker]]
| [[:Category:Patterns with 3 cells|3]]
|-
! 3
| [[caterer]]
| [[:Category:Patterns with 12 cells|12]]
|-
! 4
| [[mazing]], [[mold]]
| [[:Category:Patterns with 12 cells|12]]
|-
! 5
| [[pseudo-barberpole]]
| [[:Category:Patterns with 15 cells|15]]
|-
! 6
| [[unix]]
| [[:Category:Patterns with 16 cells|16]]
|-
! 7
| [[28P7.1]], [[28P7.2]], [[burloaferimeter]]
| [[:Category:Patterns with 28 cells|28]]
|-
! 8
| [[figure eight]]
| [[:Category:Patterns with 12 cells|12]]
|-
! 9
| [[29P9]]
| [[:Category:Patterns with 29 cells|29]]
|-
! 10
| [[24P10]]
| [[:Category:Patterns with 24 cells|24]]
|-
! 11
| [[38P11.1]]
| [[:Category:Patterns with 38 cells|38]]
|-
! 12
| [[dinner table]]
| [[:Category:Patterns with 33 cells|33]]
|-
! 13
| [[34P13]]
| [[:Category:Patterns with 34 cells|34]]
|-
! 14
| [[tumbler]]
| [[:Category:Patterns with 16 cells|16]]
|-
! 15
| [[pentadecathlon]]
| [[:Category:Patterns with 12 cells|12]]
|-
! 16
| [[Achim's p16]]
| [[:Category:Patterns with 32 cells|32]]
|-
! 17
| [[54P17.1]]
| [[:Category:Patterns with 54 cells|54]]
|-
! 18
| [[43P18]]
| [[:Category:Patterns with 43 cells|43]]
|-
! class="red_td" | 19
| class="red_td" colspan="2" | ''None found''
|-
! 20
| [[mold on fumarole]]
| [[:Category:Patterns with 30 cells|30]]
|-
! 21
| [[caterer on 44P7.2]]
| [[:Category:Patterns with 56 cells|56]]
|-
! 22
| [[36P22]]
| [[:Category:Patterns with 36 cells|36]]
|-
! class="red_td" | 23
| class="red_td" colspan="2" | ''None found''
|-
! 24
| [[caterer on figure eight]]
| [[:Category:Patterns with 24 cells|24]]
|-
! 25
| [[pre-pulsar shuttle 25]]
| [[:Category:Patterns with 96 cells|96]]
|-
! 26
| [[p26 glider loop]]
| [[:Category:Patterns with 156 cells|156]]
|-
! 27
| [[56P27]]
| [[:Category:Patterns with 56 cells|56]]
|-
! 28
| [[mold on 41P7.2]]
| [[:Category:Patterns with 53 cells|53]]
|-
! 29
| [[pre-pulsar shuttle 29]]
| [[:Category:Patterns with 54 cells|54]]
|-
! 30
| [[queen bee shuttle]]
| [[:Category:Patterns with 20 cells|20]]
|-
! 31
| [[48P31]]
| [[:Category:patterns with 48 cells|48]]
|-
! 32
| [[gourmet]]
| [[:Category:Patterns with 66 cells|66]]
|-
! 33
| [[60P33]]
| [[:Category:Patterns with 60 cells|60]]
|-
! class="red_td" | 34
| class="red_td" colspan="2" | ''No non-trivial examples found''
|-
! 35
| [[50P35]]
| [[:Category:patterns with 50 cells|50]]
|-
! 36
| [[22P36]]
| [[:Category:patterns with 22 cells|22]]
|-
! 37
| [[124P37]]
| [[:Category:Patterns with 124 cells|124]]
|-
! class="red_td" | 38
| class="red_td" colspan="2" | ''None found''
|-
! 39
| [[caterer on 34P13]]
| [[:Category:Patterns with 46 cells|46]]
|-
! 40
| [[26P40]]
| [[:Category:patterns with 26 cells|26]]
|-
! class="red_td" | 41
| class="red_td" colspan="2" | ''None found''
|-
! 42
| [[unix on 41P7.2]]
| [[:Category:Patterns with 57 cells|57]]
|-
! 43
| [[P43 glider shuttle]]
| [[:Category:patterns with 228 cells|228]]
|-
! 44
| [[mold on 36P22]]
| [[:Category:patterns with 50 cells|50]]
|-
! 45
| [[pentadecathlon on thumb 1]]
| [[:Category:patterns with 48 cells|48]]
|-
! 46
| [[twin bees shuttle]]
| [[:Category:patterns with 28 cells|28]]
|-
! 47
| [[pre-pulsar shuttle 47]]
| [[:Category:patterns with 84 cells|84]]
|-
! 48
| [[69P48]]
| [[:Category:patterns with 69 cells|69]]
|-
! 49
| [[p49 glider shuttle]]
| [[:Category:Patterns with 228 cells|228]]
|-
! 50
| [[P50 traffic jam]]
| [[:Category:patterns with 92 cells|92]]
|-
! 51
| [[112P51]]
| [[:Category:Patterns with 112 cells|112]]
|-
! 52
| [[35P52]]
| [[:Category:Patterns with 35 cells|35]]
|-
! 53
| [[P53 glider shuttle]]
| [[:Category:patterns with 228 cells|228]]
|-
! 54
| [[P54 shuttle]]
| [[:Category:Patterns with 48 cells|48]]
|-
! 55
| [[fumarole on Achim's p11]]
| [[:Category:patterns with 90 cells|90]]
|-
! 56
| [[P56 B-heptomino shuttle]]
| [[:Category:patterns with 45 cells|45]]
|-
! 57
| [[P57 glider shuttle]]
| [[:Category:patterns with 228 cells|228]]
|-
! 58
| [[P58 glider shuttle]]
| [[:Category:patterns with 208 cells|208]]
|-
! 59
| [[P59 glider shuttle]]
| [[:Category:patterns with 228 cells|228]]
|-
! 60
| [[mold on pentadecathlon]]
| [[:Category:patterns with 24 cells|24]]
|-
! 61
| [[P61 glider shuttle]]
| [[:Category:patterns with 228 cells|228]]
|-
! 63
| [[snacker on 38P7.2]]
| [[:Category:patterns with 78 cells|78]]
|-
! 65
| [[fumarole on 34P13]]
| [[:Category:patterns with 52 cells|52]]
|-
! 66
| [[caterer on 36P22]]
| [[:Category:patterns with 48 cells|48]]
|-
! 70
| [[78P70]]
| [[:Category:patterns with 78 cells|78]]
|-
! 72
| [[47P72]]
| [[:Category:Patterns with 47 cells|47]]
|-
! 75
| [[6 bits]]
| [[:Category:Patterns with 49 cells|49]]
|-
! 88
| [[49P88]]
| [[:Category:patterns with 49 cells|49]]
|-
! 90
| [[fumarole on 43P18]]
| [[:Category:patterns with 61 cells|61]]
|-
! 96
| [[caterer on 68P32]]
| [[:Category:patterns with 80 cells|80]]
|-
! 99
| [[extended snacker on Achim's p11]]
| [[:Category:patterns with 124 cells|124]]
|-
! 100
| [[centinal]]
| [[:Category:Patterns with 70 cells|70]]
|-
! 104
| [[figure eight on 34P13]]
| [[:Category:Patterns with 46 cells|46]]
|-
! 105
| [[pentadecathlon on 37P7.1]]
| [[:Category:patterns with 49 cells|49]]
|-
! 108
| [[T-nosed p4 on 56P27]]
| [[:Category:patterns with 87 cells|87]]
|-
! 110
| [[pseudo-barberpole on 36P22]]
| [[:Category:Patterns with 51 cells|51]]
|-
! 120
| [[figure eight on pentadecathlon]]
| [[:Category:Patterns with 24 cells|24]]
|-
! 138
| [[Gabriel's p138]]
| [[:Category:patterns with 36 cells|36]]
|-
! 144
| [[Achim's p144]]
| [[:Category:Patterns with 42 cells|42]]
|-
! 156
| [[92P156]]
| [[:Category:Patterns with 92 cells|92]]
|-
! 177
| [[104P177]]
| [[:Category:patterns with 104 cells|104]]
|-
! 312
| [[60P312]]
| [[:Category:Patterns with 60 cells|60]]
|}
</td></tr></table>
 
==See also==
*[[List of common oscillators]]
*[[:Category:Oscillators|List of oscillators]]
*[[Omniperiodic]]
 
==External links==
{{LinkLexicon|lex_o.htm#oscillator}}
{{LinkWeisstein|Oscillator.html}}

Revision as of 16:19, 21 October 2013

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