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]] known as the [[Snark]] that allows oscillators of all periods 43 or greater to be constructed. | ||
<center>*An oscillator of this period can also be constructed from two [[sparker]]s both of which were known by an earlier date. However, this type of oscillator is generally considered "boring", and thus not listed here despite technically being [[non-trivial]].</center> | |||
{| class="wikitable" style="margin-left:auto;margin-right:auto;" | {| class="wikitable" style="margin-left:auto;margin-right:auto;" | ||
Line 16: | Line 19: | ||
! Minimum # of cells | ! Minimum # of cells | ||
|- | |- | ||
! | ! {{period|2|brief}} | ||
| [[blinker]] | | [[blinker]] | ||
| [[ | | [[John Conway]] | ||
| | | {{year|1970}} | ||
| | | | ||
| [[blinker]] | | [[blinker]] | ||
| | | {{cells|3}} | ||
|- | |- | ||
! | ! {{period|3|brief}} | ||
| [[pulsar]] | | [[pulsar]] | ||
| John Conway | | John Conway | ||
Line 30: | Line 33: | ||
| | | | ||
| [[caterer]] | | [[caterer]] | ||
| | | {{cells|12}} | ||
|- | |- | ||
! | ! {{period|4|brief}} | ||
| [[pinwheel]] | | [[pinwheel]] | ||
| [[ | | [[Simon Norton]] | ||
| 1970 | | 1970 | ||
| | | | ||
| [[mazing]], [[mold]] | | [[mazing]], [[mold]] | ||
| | | {{cells|12}} | ||
|- | |- | ||
! | ! {{period|5|brief}} | ||
| [[octagon 2]] | | [[octagon 2]] | ||
| [[ | | [[Sol Goodman]], [[Arthur Taber]] | ||
| | | {{year|1971}} | ||
| | | | ||
| [[pseudo-barberpole]] | | [[pseudo-barberpole]] | ||
| | | {{cells|15}} | ||
|- | |- | ||
! | ! {{period|6|brief}} | ||
| [[$rats]] | | [[$rats]] | ||
| [[ | | [[David Buckingham]] | ||
| | | {{year|1972}} | ||
| | | | ||
| [[unix]] | | [[unix]] | ||
| | | {{cells|16}} | ||
|- | |- | ||
! | ! {{period|7|brief}} | ||
| [[burloaferimeter]] | | [[burloaferimeter]] | ||
| David Buckingham | | David Buckingham | ||
Line 62: | Line 65: | ||
| | | | ||
| [[28P7.1]], [[28P7.2]], [[28P7.3]], [[burloaferimeter]] | | [[28P7.1]], [[28P7.2]], [[28P7.3]], [[burloaferimeter]] | ||
| | | {{cells|28}} | ||
|- | |- | ||
! | ! {{period|8|brief}} | ||
| [[figure eight]] | | [[figure eight]] | ||
| Simon Norton | | Simon Norton | ||
Line 70: | Line 73: | ||
| | | | ||
| [[figure eight]] | | [[figure eight]] | ||
| | | {{cells|12}} | ||
|- | |- | ||
! | ! {{period|9|brief}} | ||
| [[worker bee]] | | [[worker bee]] | ||
| David Buckingham | | David Buckingham | ||
Line 78: | Line 81: | ||
| | | | ||
| [[29P9]] | | [[29P9]] | ||
| | | {{cells|29}} | ||
|- | |- | ||
! | ! {{period|10|brief}} | ||
| [[42P10. | | [[42P10.3]] | ||
| David Buckingham | | David Buckingham | ||
| ≤ | | ≤{{year|1976}} | ||
| | | | ||
| [[24P10]] | | [[24P10]] | ||
| | | {{cells|24}} | ||
|- | |- | ||
! | ! {{period|11|brief}} | ||
| [[38P11.1]] | | [[38P11.1]] | ||
| David Buckingham | | David Buckingham | ||
| | | {{year|1977}} | ||
| | | | ||
| [[rattlesnake]] | | [[rattlesnake]] | ||
| | | {{cells|33}} | ||
|- | |- | ||
! | ! {{period|12|brief}} | ||
| [[dinner table]] | | [[dinner table]] | ||
| [[Robert Wainwright]] | | [[Robert Wainwright]] | ||
| | | {{year|1972}} | ||
| | | | ||
| [[dinner table]] | | [[dinner table]] | ||
| | | {{cells|33}} | ||
|- | |- | ||
! | ! {{period|13|brief}} | ||
| [[ | | [[Buckingham's p13]] | ||
| David Buckingham | | David Buckingham | ||
| 1976 | | 1976 | ||
| | | | ||
| [[ | | [[Beluchenko's p13]] | ||
| | | {{cells|34}} | ||
|- | |- | ||
! | ! {{period|14|brief}} | ||
| [[tumbler]] | | [[tumbler]] | ||
| George Collins | | [[George Collins]] | ||
| 1970 | | 1970 | ||
| | | | ||
| [[tumbler]] | | [[tumbler]] | ||
| | | {{cells|16}} | ||
|- | |- | ||
! | ! {{period|15|brief}} | ||
| [[pentadecathlon]] | | [[pentadecathlon]] | ||
| John Conway | | John Conway | ||
Line 126: | Line 129: | ||
| | | | ||
| [[pentadecathlon]] | | [[pentadecathlon]] | ||
| | | {{cells|12}} | ||
|- | |- | ||
! | ! {{period|16|brief}} | ||
| [[two pre-L hasslers]] | | [[two pre-L hasslers]] | ||
| Robert Wainwright | | Robert Wainwright | ||
| | | {{year|1983}} | ||
| | | | ||
| [[Achim's p16]] | | [[Achim's p16]] | ||
| | | {{cells|32}} | ||
|- | |- | ||
! | ! {{period|17|brief}} | ||
| [[54P17.1]] | | [[54P17.1]] | ||
| [[ | | [[Dean Hickerson]] | ||
| | | {{year|1997}} | ||
| | | | ||
| [[honey thieves]] | | [[honey thieves]] | ||
| | | {{cells|36}} | ||
|- | |- | ||
! | ! {{period|18|brief}} | ||
| [[117P18]] | | [[117P18]]* | ||
| David Buckingham | | David Buckingham | ||
| ≤ | | ≤{{year|1991}} | ||
| | | | ||
| [[p18 bi-block hassler]] | | [[p18 bi-block hassler]] | ||
| | | {{cells|43}} | ||
|- | |- | ||
! class="red_td" | 19 | ! class="red_td" | 19 | ||
| class="red_td" colspan="6" | ''None found'' | | class="red_td" colspan="6" | ''None found'' | ||
|- | |- | ||
! | ! {{period|20|brief}} | ||
| [[145P20]] | | [[145P20]]* | ||
| [[Noam Elkies]] | | [[Noam Elkies]] | ||
| | | {{year|1995}} | ||
| | | | ||
| [[mold on fumarole]] | | [[mold on fumarole]] | ||
| | | {{cells|30}} | ||
|- | |- | ||
! | ! {{period|21|brief}} | ||
| [[124P21]] | | [[124P21]]* | ||
| Robert Wainwright | | Robert Wainwright | ||
| 1995 | | 1995 | ||
| | | | ||
| [[caterer on 28P7.3]] | | [[caterer on 28P7.3]] | ||
| | | {{cells|40}} | ||
|- | |- | ||
! | ! {{period|22|brief}} | ||
| [[168P22.1]] | | [[168P22.1]] | ||
| Noam Elkies | | Noam Elkies | ||
| 1997 | | 1997 | ||
| | | | ||
| [[ | | [[Jason's p22]] | ||
| | | {{cells|36}} | ||
|- | |- | ||
! | ! {{period|23|brief}} | ||
| | | [[David Hilbert]] | ||
| [[Luka Okanishi]], [[Aidan F. Pierce]] | |||
| {{year|2019}} | |||
| | |||
| [[David Hilbert]] | |||
| {{cells|122}} | |||
|- | |- | ||
! | ! {{period|24|brief}} | ||
| [[186P24]] | | [[186P24]]* | ||
| [[Bill Gosper]] | | [[Bill Gosper]] | ||
| | | {{year|1994}} | ||
| | | | ||
| [[caterer on figure eight]] | | [[caterer on figure eight]] | ||
| | | {{cells|24}} | ||
|- | |- | ||
! | ! {{period|25|brief}} | ||
| [[134P25]] | | [[134P25]] | ||
| Noam Elkies | | Noam Elkies | ||
Line 196: | Line 204: | ||
| | | | ||
| [[98P25|p25 honey farm hassler]] | | [[98P25|p25 honey farm hassler]] | ||
| | | {{cells|88}} | ||
|- | |- | ||
! | ! {{period|26|brief}} | ||
| [[pre-pulsar shuttle | | [[p26 pre-pulsar shuttle]] | ||
| David Buckingham | | David Buckingham | ||
| 1983 | | 1983 | ||
| | | | ||
| [[87P26]] | | [[87P26]] | ||
| | | {{cells|87}} | ||
|- | |- | ||
! | ! {{period|27|brief}} | ||
| [[123P27.1]] | | [[123P27.1]] | ||
| Noam Elkies | | Noam Elkies | ||
| | | {{year|2002}} | ||
| | | | ||
| [[56P27]] | | [[56P27]] | ||
| | | {{cells|56}} | ||
|- | |- | ||
! | ! {{period|28|brief}} | ||
| [[newshuttle]] | | [[newshuttle]] | ||
| David Buckingham | | David Buckingham | ||
| | | {{year|1973}} | ||
| | | | ||
| [[mold on 34P14 shuttle]] | | [[mold on 34P14 shuttle]] | ||
| | | {{cells|46}} | ||
|- | |- | ||
! | ! {{period|29|brief}} | ||
| [[pre-pulsar shuttle | | [[p29 pre-pulsar shuttle]] | ||
| David Buckingham | | David Buckingham | ||
| | | {{year|1980}} | ||
| | | | ||
| [[pre-pulsar shuttle | | [[p29 pre-pulsar shuttle]] | ||
| | | {{cells|54}} | ||
|- | |- | ||
! | ! {{period|30|brief}} | ||
| [[queen bee shuttle]] | | [[queen bee shuttle]] | ||
| Bill Gosper | | Bill Gosper | ||
Line 236: | Line 244: | ||
| | | | ||
| [[queen bee shuttle]] | | [[queen bee shuttle]] | ||
| | | {{cells|20}} | ||
|- | |- | ||
! | ! {{period|31|brief}} | ||
| [[ | | [[Merzenich's p31]] | ||
| [[Matthias Merzenich]] | | [[Matthias Merzenich]] | ||
| | | {{year|2010}} | ||
| | | | ||
| [[ | | [[Merzenich's p31]] | ||
| | | {{cells|48}} | ||
|- | |- | ||
! | ! {{period|32|brief}} | ||
| [[gourmet]] | | [[gourmet]] | ||
| David Buckingham | | David Buckingham | ||
| | | {{year|1978}} | ||
| | | | ||
| [[gourmet]] | | [[gourmet]] | ||
| | | {{cells|66}} | ||
|- | |- | ||
! | ! {{period|33|brief}} | ||
| [[258P3 on Achim's p11]] | | [[258P3 on Achim's p11]] | ||
| Noam Elkies, [[ | | Noam Elkies, [[Achim Flammenkamp]] | ||
| 1997 | | 1997 | ||
| | | | ||
| [[caterer on rattlesnake]] | | [[caterer on rattlesnake]] | ||
| | | {{cells|46}} | ||
|- | |- | ||
! | ! {{period|34|brief}} | ||
| class="red_td" colspan="6" | ''No non-trivial examples found'' | | class="red_td" colspan="6" | ''No non-trivial examples found'' | ||
|- | |- | ||
! | ! {{period|35|brief}} | ||
| [[p35 beehive hassler]] | | [[p35 beehive hassler]]* | ||
| Dean Hickerson | | Dean Hickerson | ||
| 1995 | | 1995 | ||
| | | | ||
| [[p35 honey farm hassler]] | | [[p35 honey farm hassler]] | ||
| | | {{cells|44}} | ||
|- | |- | ||
! | ! {{period|36|brief}} | ||
| [[p36 toad hassler]] | | [[p36 toad hassler]]* | ||
| Robert Wainwright | | Robert Wainwright | ||
| 1984 | | 1984 | ||
| | | | ||
| [[22P36]] | | [[22P36]] | ||
| | | {{cells|22}} | ||
|- | |- | ||
! | ! {{period|37|brief}} | ||
| [[ | | [[Beluchenko's p37]] | ||
| [[ | | [[Nicolay Beluchenko]] | ||
| | | {{year|2009}} | ||
| | | | ||
| [[ | | [[Beluchenko's p37]] | ||
| | | {{cells|124}} | ||
|- | |- | ||
! class="red_td" | 38 | ! class="red_td" | 38 | ||
| class="red_td" colspan="6" | ''None found'' | | class="red_td" colspan="6" | ''None found'' | ||
|- | |- | ||
! | ! {{period|39|brief}} | ||
| [[134P39.1]] | | [[134P39.1]] | ||
| David Buckingham, Noam Elkies | | David Buckingham, Noam Elkies | ||
| | | {{year|2000}} | ||
| | | | ||
| [[caterer on | | [[caterer on Beluchenko's p13]] | ||
| | | {{cells|46}} | ||
|- | |- | ||
! | ! {{period|40|brief}} | ||
| [[p40 B-heptomino shuttle]] | | [[p40 B-heptomino shuttle]]* | ||
| David Buckingham | | David Buckingham | ||
| ≤1991 | | ≤1991 | ||
| | | | ||
| [[ | | [[Beluchenko's p40]] | ||
| | | {{cells|26}} | ||
|- | |- | ||
! class="red_td" | 41 | ! class="red_td" | 41 | ||
| class="red_td" colspan="6" | ''None found'' | | class="red_td" colspan="6" | ''None found'' | ||
|- | |- | ||
! | ! {{period|42|brief}} | ||
| [[p42 glider shuttle]] | | [[p42 glider shuttle]]* | ||
| Noam Elkies | | Noam Elkies | ||
| 1994 | | 1994 | ||
| | | | ||
| [[unix on 34P14 shuttle]] | | [[unix on 34P14 shuttle]] | ||
| | | {{cells|50}} | ||
|- | |- | ||
! | ! {{period|43|brief}} | ||
| [[p43 glider loop]] | | [[p43 glider loop]] | ||
| [[Mike Playle]] | | [[Mike Playle]] | ||
| | | {{year|2013}} | ||
| | | | ||
| [[p43 glider loop]] | | [[p43 glider loop]] | ||
| | | {{cells|228}} | ||
|- | |- | ||
! | ! {{period|44|brief}} | ||
| [[p44 pi-heptomino hassler]] | | [[p44 pi-heptomino hassler]] | ||
| David Buckingham | | David Buckingham | ||
Line 333: | Line 341: | ||
| | | | ||
| [[mold on rattlesnake]] | | [[mold on rattlesnake]] | ||
| | | {{cells|45}} | ||
|- | |- | ||
! | ! {{period|45|brief}} | ||
| [[pentadecathlon on snacker]] | | [[pentadecathlon on snacker]] | ||
| ? | | ? | ||
Line 341: | Line 349: | ||
| | | | ||
| [[pentadecathlon on thumb 1]] | | [[pentadecathlon on thumb 1]] | ||
| | | {{cells|48}} | ||
|- | |- | ||
! | ! {{period|46|brief}} | ||
| [[twin bees shuttle]] | | [[twin bees shuttle]] | ||
| Bill Gosper | | Bill Gosper | ||
Line 349: | Line 357: | ||
| | | | ||
| [[twin bees shuttle]] | | [[twin bees shuttle]] | ||
| | | {{cells|28}} | ||
|- | |- | ||
! | ! {{period|47|brief}} | ||
| [[pre-pulsar shuttle | | [[p47 pre-pulsar shuttle]] | ||
| David Buckingham | | David Buckingham | ||
| | | {{year|1982}} | ||
| | | | ||
| [[pre-pulsar shuttle | | [[p47 pre-pulsar shuttle]] | ||
| | | {{cells|84}} | ||
|- | |- | ||
! | ! {{period|48|brief}} | ||
| [[p48 toad hassler]] | | [[p48 toad hassler]] | ||
| Bill Gosper | | Bill Gosper | ||
Line 365: | Line 373: | ||
| | | | ||
| [[unix on Rich's p16]] | | [[unix on Rich's p16]] | ||
| | | {{cells|52}} | ||
|- | |- | ||
! | ! {{period|49|brief}} | ||
| [[p49 glider shuttle]] | | [[p49 glider shuttle]] | ||
| Noam Elkies | | Noam Elkies | ||
| | | {{year|1999}} | ||
| | | | ||
| [[p49 bumper loop]] | | [[p49 bumper loop]] | ||
| | | {{cells|206}} | ||
|- | |- | ||
! | ! {{period|50|brief}} | ||
| [[p50 glider shuttle]] | | [[p50 glider shuttle]] | ||
| Dean Hickerson | | Dean Hickerson | ||
Line 381: | Line 389: | ||
| | | | ||
| [[p50 traffic jam]] | | [[p50 traffic jam]] | ||
| | | {{cells|92}} | ||
|- | |- | ||
! | ! {{period|51|brief}} | ||
| [[ | | [[Beluchenko's p51]] | ||
| Nicolay Beluchenko | | Nicolay Beluchenko | ||
| 2009 | | 2009 | ||
| | | | ||
| [[92P51]] | | [[92P51]] | ||
| | | {{cells|92}} | ||
|- | |- | ||
! | ! {{period|52|brief}} | ||
| [[ | | [[Four eaters hassling lumps of muck]] | ||
| David Buckingham | | David Buckingham | ||
| 1977 | | 1977 | ||
| | | | ||
| [[ | | [[Four eaters hassling lumps of muck]] | ||
| | | {{cells|35}} | ||
|- | |- | ||
! | ! {{period|53|brief}} | ||
| [[p53 glider loop]] | | [[p53 glider loop]] | ||
| | | Mike Playle | ||
| | | {{year|2013}} | ||
| | | | ||
| [[p53 glider loop]] | | [[p53 glider loop]] | ||
| | | {{cells|228}} | ||
|- | |- | ||
! | ! {{period|54|brief}} | ||
| [[p54 shuttle]] | | [[p54 shuttle]] | ||
| David Buckingham | | David Buckingham | ||
| | | {{year|1973}} | ||
| | | | ||
| [[p54 shuttle]] | | [[p54 shuttle]] | ||
| | | {{cells|48}} | ||
|- | |- | ||
! | ! {{period|55|brief}} | ||
| [[pre-pulsar hassler | | [[p55 pre-pulsar hassler]] | ||
| David Buckingham | | David Buckingham | ||
| | | {{year|1986}} | ||
| | | | ||
| [[pseudo-barberpole on rattlesnake]] | | [[pseudo-barberpole on rattlesnake]] | ||
| | | {{cells|49}} | ||
|- | |- | ||
! | ! {{period|56|brief}} | ||
| [[p56 B-heptomino shuttle]] | | [[p56 B-heptomino shuttle]]* | ||
| David Buckingham | | David Buckingham | ||
| ≤1991 | | ≤1991 | ||
| | | | ||
| [[p56 B-heptomino shuttle]] | | [[p56 B-heptomino shuttle]] | ||
| | | {{cells|45}} | ||
|- | |- | ||
! | ! {{period|57|brief}} | ||
| [[p57 Herschel loop 1]] | | [[p57 Herschel loop 1]] | ||
| [[ | | [[Dietrich Leithner]] | ||
| 1997 | | 1997 | ||
| | | | ||
| [[p57 bumper loop]] | | [[p57 bumper loop]] | ||
| | | {{cells|152}} | ||
|- | |- | ||
! | ! {{period|58|brief}} | ||
| [[p58 toadsucker]] | | [[p58 toadsucker]] | ||
| Bill Gosper | | Bill Gosper | ||
| 1994 | | 1994 | ||
| | | | ||
| [[pre-pulsar shuttle | | [[p58 pre-pulsar shuttle]] | ||
| | | {{cells|104}} | ||
|- | |- | ||
! | ! {{period|59|brief}} | ||
| [[p59 Herschel loop 1]] | | [[p59 Herschel loop 1]] | ||
| David Buckingham | | David Buckingham | ||
Line 453: | Line 461: | ||
| | | | ||
| [[p59 glider loop]] | | [[p59 glider loop]] | ||
| | | {{cells|228}} | ||
|- | |- | ||
! | ! {{period|60|brief}} | ||
| [[p60 glider shuttle]] | | [[p60 glider shuttle]] | ||
| David Buckingham | | David Buckingham | ||
Line 461: | Line 469: | ||
| | | | ||
| [[mold on pentadecathlon]] | | [[mold on pentadecathlon]] | ||
| | | {{cells|24}} | ||
|- | |- | ||
! | ! {{period|61|brief}} | ||
| [[p61 Herschel loop 1]] | | [[p61 Herschel loop 1]] | ||
| David Buckingham | | David Buckingham | ||
| | | {{year|1996}} | ||
| | | | ||
| [[p61 glider loop]] | | [[p61 glider loop]] | ||
| | | {{cells|228}} | ||
|- | |- | ||
! | ! {{period|62|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 477: | Line 485: | ||
| | | | ||
| [[110P62]] | | [[110P62]] | ||
| | | {{cells|110}} | ||
|- | |- | ||
! | ! {{period|63|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 485: | Line 493: | ||
| | | | ||
| [[snacker on 38P7.2]] | | [[snacker on 38P7.2]] | ||
| | | {{cells|78}} | ||
|- | |- | ||
! | ! {{period|64|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 493: | Line 501: | ||
| | | | ||
| [[Merzenich's p64]] | | [[Merzenich's p64]] | ||
| | | {{cells|34}} | ||
|- | |- | ||
! | ! {{period|65|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
| ? | | ? | ||
| | | | ||
| [[fumarole on | | [[fumarole on Beluchenko's p13]] | ||
| | | {{cells|52}} | ||
|- | |- | ||
! | ! {{period|66|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 509: | Line 517: | ||
| | | | ||
| [[caterer on 36P22]] | | [[caterer on 36P22]] | ||
| | | {{cells|48}} | ||
|- | |- | ||
! | ! {{period|67|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 519: | Line 527: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|68|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 527: | Line 535: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|69|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 535: | Line 543: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|70|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 541: | Line 549: | ||
| | | | ||
| [[fumarole on 34P14 shuttle]] | | [[fumarole on 34P14 shuttle]] | ||
| | | {{cells|52}} | ||
|- | |- | ||
! | ! {{period|71|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 551: | Line 559: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|72|brief}} | ||
| [[two blockers hassling R-pentomino]] | | [[two blockers hassling R-pentomino]] | ||
| Robert Wainwright | | Robert Wainwright | ||
Line 557: | Line 565: | ||
| | | | ||
| [[figure eight on 22P36]] | | [[figure eight on 22P36]] | ||
| | | {{cells|36}} | ||
|- | |- | ||
! | ! {{period|73|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 567: | Line 575: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|74|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 575: | Line 583: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|75|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 581: | Line 589: | ||
| | | | ||
| [[6 bits]] | | [[6 bits]] | ||
| | | {{cells|49}} | ||
|- | |- | ||
! | ! {{period|76|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 591: | Line 599: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|77|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 597: | Line 605: | ||
| | | | ||
| [[77P77]] | | [[77P77]] | ||
| | | {{cells|77}} | ||
|- | |- | ||
! | ! {{period|78|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
| ? | | ? | ||
| | | | ||
| [[p6 thumb on | | [[p6 thumb on Beluchenko's p13]] | ||
| | | {{cells|61}} | ||
|- | |- | ||
! | ! {{period|79|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 615: | Line 623: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|80|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 621: | Line 629: | ||
| | | | ||
| [[fumarole on Rich's p16]] | | [[fumarole on Rich's p16]] | ||
| | | {{cells|52}} | ||
|- | |- | ||
! | ! {{period|81|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 631: | Line 639: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|82|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 639: | Line 647: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|83|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 647: | Line 655: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|84|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 653: | Line 661: | ||
| | | | ||
| [[52P84]] | | [[52P84]] | ||
| | | {{cells|52}} | ||
|- | |- | ||
! | ! {{period|85|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 663: | Line 671: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|86|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 671: | Line 679: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|87|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 677: | Line 685: | ||
| | | | ||
| [[84P87]] | | [[84P87]] | ||
| | | {{cells|84}} | ||
|- | |- | ||
! | ! {{period|88|brief}} | ||
| [[P44 pi-heptomino hassler#Image gallery|p88 pi-heptomino hassler]] | | [[P44 pi-heptomino hassler#Image gallery|p88 pi-heptomino hassler]] | ||
| Dean Hickerson | | Dean Hickerson | ||
Line 685: | Line 693: | ||
| | | | ||
| [[figure eight on rattlesnake]] | | [[figure eight on rattlesnake]] | ||
| | | {{cells|45}} | ||
|- | |- | ||
! | ! {{period|89|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 695: | Line 703: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|90|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 701: | Line 709: | ||
| | | | ||
| [[fumarole on 43P18]] | | [[fumarole on 43P18]] | ||
| | | {{cells|61}} | ||
|- | |- | ||
! | ! {{period|91|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 711: | Line 719: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|92|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 717: | Line 725: | ||
| | | | ||
| [[twin bees shuttle on 22P4.3]] | | [[twin bees shuttle on 22P4.3]] | ||
| | | {{cells|50}} | ||
|- | |- | ||
! | ! {{period|93|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
| ? | | ? | ||
| | | | ||
| [[caterer on | | [[caterer on Merzenich's p31]] | ||
| | | {{cells|60}} | ||
|- | |- | ||
! | ! {{period|94|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
| ? | | ? | ||
| | | | ||
| | | {{LinkCatagolue|xp94_x696o8b9czy065x33xc871xggzooyd643zwgg04ahhha4y5c871z4701yfoozw8e13xggzy34701xmmggo5jzya146w343|patternname=capped|style=raw}} [[AK-94]] | ||
| | | {{cells|110}} | ||
|- | |- | ||
! | ! {{period|95|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 743: | Line 751: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|96|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 749: | Line 757: | ||
| | | | ||
| [[caterer on 68P32]] | | [[caterer on 68P32]] | ||
| | | {{cells|80}} | ||
|- | |- | ||
! | ! {{period|97|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 759: | Line 767: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|98|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 767: | Line 775: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|99|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 775: | Line 783: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|100|brief}} | ||
| [[centinal]] | | [[centinal]] | ||
| Bill Gosper | | Bill Gosper | ||
| ≤ | | ≤{{year|1987}} | ||
| | | | ||
| [[centinal]] | | [[centinal]] | ||
| | | {{cells|70}} | ||
|- | |- | ||
! | ! {{period|104|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
| ? | | ? | ||
| | | | ||
| [[figure eight on | | [[figure eight on Beluchenko's p13]] | ||
| | | {{cells|46}} | ||
|- | |- | ||
! | ! {{period|105|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 797: | Line 805: | ||
| | | | ||
| [[pentadecathlon on 37P7.1]] | | [[pentadecathlon on 37P7.1]] | ||
| | | {{cells|49}} | ||
|- | |- | ||
! | ! {{period|108|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 805: | Line 813: | ||
| | | | ||
| [[22P4.3 on 56P27]] | | [[22P4.3 on 56P27]] | ||
| | | {{cells|78}} | ||
|- | |- | ||
! | ! {{period|110|brief}} | ||
| [[p110 traffic jam]] | | [[p110 traffic jam]] | ||
| Bill Gosper | | Bill Gosper | ||
Line 813: | Line 821: | ||
| | | | ||
| [[pseudo-barberpole on 36P22]] | | [[pseudo-barberpole on 36P22]] | ||
| | | {{cells|51}} | ||
|- | |- | ||
! | ! {{period|120|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 821: | Line 829: | ||
| | | | ||
| [[figure eight on pentadecathlon]] | | [[figure eight on pentadecathlon]] | ||
| | | {{cells|24}} | ||
|- | |- | ||
! | ! {{period|124|brief}} | ||
| [[p124 lumps of muck hassler]] | | [[p124 lumps of muck hassler]] | ||
| Dean Hickerson | | Dean Hickerson | ||
| 1994 | | 1994 | ||
| | | | ||
| [[mold on | | [[mold on Merzenich's p31]] | ||
| | | {{cells|60}} | ||
|- | |- | ||
! | ! {{period|132|brief}} | ||
| [[p132 pi-heptomino hassler]] | | [[p132 pi-heptomino hassler]] | ||
| David Buckingham | | David Buckingham | ||
Line 839: | Line 847: | ||
| ? | | ? | ||
|- | |- | ||
! | ! {{period|135|brief}} | ||
| [[106P135]] | | [[106P135]] | ||
| Bill Gosper | | Bill Gosper | ||
| | | {{year|1989}} | ||
| | | | ||
| [[pentadecathlon on 56P27]] | | [[pentadecathlon on 56P27]] | ||
| | | {{cells|68}} | ||
|- | |- | ||
! | ! {{period|138|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
Line 853: | Line 861: | ||
| | | | ||
| [[Gabriel's p138]] | | [[Gabriel's p138]] | ||
| | | {{cells|36}} | ||
|- | |- | ||
! | ! {{period|144|brief}} | ||
| [[Achim's p144]] | | [[Achim's p144]] | ||
| Achim Flammenkamp | | Achim Flammenkamp | ||
Line 861: | Line 869: | ||
| | | | ||
| [[Achim's p144]] | | [[Achim's p144]] | ||
| | | {{cells|42}} | ||
|- | |- | ||
! | ! {{period|156|brief}} | ||
| [[p156 Hans Leo hassler]] | | [[p156 Hans Leo hassler]] | ||
| Noam Elkies | | Noam Elkies | ||
| 1995 | | 1995 | ||
| | | | ||
| [[ | | [[Jason's p156]] | ||
| | | {{cells|92}} | ||
|- | |- | ||
! | ! {{period|177|brief}} | ||
| ? | | ? | ||
| ? | | ? | ||
| ? | | ? | ||
| | | | ||
| [[ | | [[Karel's p177]] | ||
| | | {{cells|104}} | ||
|- | |- | ||
! | ! {{period|200|brief}} | ||
| [[p200 traffic jam]] | | [[p200 traffic jam]] | ||
| Bill Gosper | | Bill Gosper | ||
Line 885: | Line 893: | ||
| | | | ||
| [[figure eight on centinal]] | | [[figure eight on centinal]] | ||
| | | {{cells|82}} | ||
|- | |- | ||
! | ! {{period|312|brief}} | ||
| period-tripled [[p104 gun]] | | period-tripled [[p104 gun]] | ||
| Dave Greene | | [[Dave Greene]] | ||
| 2004 | | 2004 | ||
| | | | ||
| [[60P312]] | | [[60P312]] | ||
| | | {{cells|60}} | ||
|} | |} | ||
Line 900: | Line 908: | ||
*[[:Category:Oscillators|List of oscillators]] | *[[:Category:Oscillators|List of oscillators]] | ||
*[[Omniperiodic]] | *[[Omniperiodic]] | ||
*[[Table of oscillators by period]] | |||
*[[LifeWiki:Game_of_Life_Status_page#Oscillator_periods|Oscillator periods status table]] | *[[LifeWiki:Game_of_Life_Status_page#Oscillator_periods|Oscillator periods status table]] | ||
Revision as of 20:19, 27 January 2020
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 known as the Snark that allows oscillators of all periods 43 or greater to be constructed.
See also
- List of common oscillators
- List of oscillators
- Omniperiodic
- Table of oscillators by period
- Oscillator periods status table
External links
- Oscillator at Wikipedia
- Oscillator at the Life Lexicon