Oscillator: Difference between revisions

Latest revision as of 16:43, 23 March 2026

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,^[1] as well the current smallest-known oscillator of that period,^[2] 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 (i.e. the overall pattern must have a nonzero strict volatility). 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 59 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. Since 2023, oscillators of all periods less than 43 have been known showing that Life is omniperiodic.

The lowest population for which an infinite number of non-trivial oscillators are known to exist is 29, as two 12-cell pentadecathlons can reflect a 5-cell glider back and forth indefinitely in the correct position. The smallest example of this is the p60 glider shuttle, with period-180, 300, and all other periods of the form 120n+60 possible with no extra cells required. 29 is conjectured to be the lowest population for which an infinite number of distinct non-trivial oscillators exist.^[3]

Period	First discovered	Discoverer	Year of discovery		Smallest known	Minimum # of cells
2	blinker	John Conway	1969		blinker	3
3	pulsar	John Conway	1970		caterer	12
4	pinwheel	Simon Norton	1970		mazing, mold	12
5	octagon 2	Sol Goodman, Arthur Taber	1971		pseudo-barberpole	15
6	$rats	David Buckingham	1972		unix	16
7	burloaferimeter	David Buckingham	1972		28P7.1, 28P7.2, 28P7.3, burloaferimeter	28
8	figure eight	Simon Norton	1970		figure eight	12
9	worker bee	David Buckingham	1972		29P9	29
10	42P10.3	David Buckingham	≤1976		24P10	24
11	38P11.1	David Buckingham	1977		rattlesnake, diamondback	33
12	dinner table	Robert Wainwright	1972		mold on fire-spitting	31
13	Buckingham's p13	David Buckingham	1976		Beluchenko's p13	34
14	tumbler	George Collins	1970		tumbler	16
15	pentadecathlon	John Conway	1970		pentadecathlon	12
16	two pre-L hasslers	Robert Wainwright	1983		Rob's p16	21
17	54P17.1	Dean Hickerson	1997		honey thieves	36
18	117P18^{[note 1]}	David Buckingham	≤1991		p18 bi-block hassler, p18 phase shifter	43
19	cribbage	Mitchell Riley	2023		cribbage	92
20	145P20^{[note 1]}	Noam Elkies	1995		mold on fumarole	30
21	124P21^{[note 1]}	Robert Wainwright	1995		32P21	32
22	168P22.1	Noam Elkies	1997		Jason's p22	36
23	David Hilbert	Luka Okanishi, praosylen	2019		54P23	54
24	186P24^{[note 1]}	Bill Gosper	1994		caterer on figure eight	24
25	134P25	Noam Elkies	1994		30P25	30
26	p26 pre-pulsar shuttle	David Buckingham	1983		p26 honey farm hassler	60
27	123P27.1	Noam Elkies	2002		56P27	56
28	newshuttle	David Buckingham	1973		mold on 34P14 shuttle	46
29	p29 pre-pulsar shuttle	David Buckingham	1980		p29 pre-pulsar shuttle	54
30	queen bee shuttle	Bill Gosper	1970		queen bee shuttle	20
31	Merzenich's p31	Matthias Merzenich	2010		Merzenich's p31	48
32	gourmet	David Buckingham	1978		p32 honey farm hassler	45
33	258P3 on Achim's p11	Noam Elkies, Achim Flammenkamp	1997		caterer on rattlesnake	46
34	74P34	Mitchell Riley	2022		74P34	74
35	p35 beehive hassler^{[note 1]}	Dean Hickerson	1995		p35 honey farm hassler	44
36	p36 toad hassler^{[note 1]}	Robert Wainwright	1984		22P36	22
37	Beluchenko's p37	Nicolay Beluchenko	2009		58P37	58
38	44P38	David Raucci	2022		42P38	42
39	134P39.1	Noam Elkies, David Buckingham	2000		caterer on Beluchenko's p13	46
40	p40 B-heptomino shuttle^{[note 1]}	David Buckingham	1991		Beluchenko's p40	26
41	208P41	Nora Brown	2023		p41 pi-heptomino hassler	170
42	p42 glider shuttle^{[note 1]}	Noam Elkies	1994		unix on 34P14 shuttle	50
43	p43 Snark loop	Mike Playle	2013		p43 pi-heptomino hassler^[4]	70
44	p44 pi-heptomino hassler	David Buckingham	1992		mold on rattlesnake	45
45	pentadecathlon on snacker	Mark Niemiec, John Conway	≤1992		p45 pi-heptomino hassler	29
46	twin bees shuttle	Bill Gosper	1971		twin bees shuttle	28
47	p47 pre-pulsar shuttle	David Buckingham	1982		p47 pre-pulsar shuttle	84
48	p48 toad hassler	Bill Gosper	1994		unix on Charity's p16	44
49	p49 bouncer loop	Noam Elkies	1999		44P49	44
50	p50 glider shuttle	Dean Hickerson	1992		24P10 on 30P25	58
51	Beluchenko's p51	Nicolay Beluchenko	2009		capped p51 gun	84
52	Four eaters hassling lumps of muck	David Buckingham	1977		four eaters hassling lumps of muck	35
53	p53 Snark loop	Mike Playle	2013		94P53	94
54	p54 shuttle	David Buckingham	1973		43P54	43
55	p55 pre-pulsar hassler	David Buckingham	1986		pseudo-barberpole on rattlesnake	49
56	p56 B-heptomino shuttle^{[note 1]}	David Buckingham	≤1991		p56 B-heptomino shuttle	45
57	p57 Herschel loop 1	Dietrich Leithner	1997		112P57	112
58	p58 toadsucker	Bill Gosper	1994		p58 pi-heptomino hassler, 54p58	54
59	p59 Herschel loop 1	David Buckingham	1997		p59 pi-heptomino hassler	86
60	p60 glider shuttle	?	≤1971		mold on pentadecathlon	24
61	p61 Herschel loop 1	David Buckingham	1996		p61 pi-heptomino hassler	134
62	Herschel loop	David Buckingham	1996		66P62	66
63	Herschel loop	David Buckingham	1996		32P21 phase-shifting p5	64
64	Herschel loop	David Buckingham	1996		Merzenich's p64	34
65	Herschel loop	David Buckingham	1996		fumarole on Beluchenko's p13	52
66	p66 glider shuttle	Robert Wainwright	1984	caterer on Jason's p22	48
67	Herschel loop	David Buckingham	1996	p67 Snark loop	228
68	Herschel loop	David Buckingham	1996	p68 century hassler	38
69	Herschel loop	David Buckingham	1996	55P23 on Grin reagent weld loading dock	103
70	Herschel loop	David Buckingham	1996	fumarole on 34P14 shuttle	52
71	Herschel loop	David Buckingham	1996	p71 dependent reflector loop	92
72	two blockers hassling R-pentomino	Robert Wainwright	1990	figure eight on 22P36	36
73	Herschel loop	David Buckingham	1996	p73 lumps of muck hassler	68
74	Herschel loop	David Buckingham	1996	Raucci's p74	84
75	6 bits	Robert Wainwright	1984	pentadecathlon on 30P25	42
76	Herschel loop	David Buckingham	1996	p76 pi-heptomino shuttle	52
77	Herschel loop	David Buckingham	1996	34P7 on rattlesnake	67
78	Herschel loop	David Buckingham	1996	p6 thumb on Beluchenko's p13	61
79	Herschel loop	David Buckingham	1996	p79 pi-heptomino hassler	80
80	middleweight volcano on Achim's other p16	Dean Hickerson, Achim Flammenkamp	1994	fumarole on Rob's p16	39
81	Herschel loop	David Buckingham	1996	p81 180° glider loop	146
82	Herschel loop	David Buckingham	1996	p82 lumps of muck hassler	48
83	Herschel loop	David Buckingham	1996	62P83	62
84	pi orbital	Noam Elkies	1995	p84 honey farm hassler	42
85	Herschel loop	David Buckingham	1996	p85 R-pentomino hassler	68
86	Herschel loop	David Buckingham	1996	76P86	76
87	p3 sparker on p29 pentadecathlon hassler	Bill Gosper	1994	84P87	84
88	p44n glider loop	David Buckingham	1992	figure eight on rattlesnake	45
89	Herschel loop	David Buckingham	1996	transparent long boat glider loop	164
90	p30n glider loop	?	≤1973	unix on p45 pi-heptomino hassler	45
91	Herschel loop	David Buckingham	1996	34P7 on Beluchenko's p13	68
92	p46n glider loop	Bill Gosper	1971	mold on twin bees shuttle	44
93	Herschel loop	David Buckingham	1996	caterer on Merzenich's p31	60
94	capped P94S	Dean Hickerson	1990	54P94	54
95	Herschel loop	David Buckingham	1996	toaster variant on Cribbage	137
96	p96 Hans Leo hassler	Noam Elkies	1995	period-48 glider gun with boat-bit	59
97	Herschel loop	David Buckingham	1996	transparent long boat glider loop	164
98	Herschel loop	David Buckingham	1996	Gallus, p98 glider shuttle	105
99	Herschel loop	David Buckingham	1996	rattlesnake on 42P9	75
100	centinal	Bill Gosper	≤1987	mold on 30P25	42
101	Herschel loop	David Buckingham	1996	116P101	116
102	p102+18n traffic jam	Dean Hickerson	1994	Raucci's p102	67
103	Herschel loop	David Buckingham	1996	siffrin's p103	68
104	p100+4n traffic jam	Bill Gosper	1994	figure eight on Beluchenko's p13	46
105	pentadecathlon on 44P7.2	?	≤1992	34P7 on pentadecathlon	46
106	Herschel loop	David Buckingham	1996	66P106	66
107	Herschel loop	David Buckingham	1996	86P107	86
108	p54 shuttle on figure eight	?	≤1992	22P36 phase-shifting p5	54
109	Herschel loop	David Buckingham	1996	p109 rectifier loop	156
110	p110 traffic jam	Bill Gosper	1994	pseudo-barberpole on Jason's p22	51
111	Herschel loop	David Buckingham	1996	fire-spitting on p37 lumps of muck hassler	91
112	p100+4n traffic jam	Bill Gosper	1994	tumbler on Rich's p16	50
113	Herschel loop	David Buckingham	1996	86P113	86
114	p66+24n glider shuttle	Robert Wainwright	1984	caterer on 42P38	54
115	Herschel loop	David Buckingham	1996	92P115	92
116	p4 sparker on p29 pentadecathlon hassler	Bill Gosper	1994	mold on p58 pi-heptomino hassler	68
117	Herschel loop	David Buckingham	1996	Beluchenko's p13 on 42P9	76
118	Herschel loop	David Buckingham	1996	86P118	86
119	Herschel loop	David Buckingham	1996	72P119	72
120	p30n glider loop	?	≤1973	figure eight on pentadecathlon	24
122	Herschel loop	David Buckingham	1996	p122 R-pentomino hassler	102
123	Herschel loop	David Buckingham	1996	p123 R-pentomino hassler	116
124	p124 lumps of muck hassler	Dean Hickerson	1994	mold on Merzenich's p31	60
126	p102+6n traffic jam	Noam Elkies	≤1996	p126 R-pentomino hassler	52
127	Herschel loop	David Buckingham	1996	74P127	74
128	spark-assisted p128 Herschel loop	David Buckingham	1991	60P128	60
129	Herschel loop	David Buckingham	1996	p129 R-pentomino hassler	38
130	p50+40n glider shuttle	Dean Hickerson	1992	fumarole on 70P26	88
132	p44n glider loop	David Buckingham	1992	mold on Jason's p33	72
133	Herschel loop	David Buckingham	1996	p133 B-heptomino hassler	84
135	106P135	Bill Gosper	1989	pentadecathlon on 56P27	68
136	p136 spark-assisted Herschel loop	David Buckingham	1991	figure eight on p68 century hassler	50
138	p46n glider loop	Bill Gosper	1971	Gabriel's p138	36
140	p100+10n traffic jam	Bill Gosper	1994	p140 two-glider octomino hassler	58
141	Herschel loop	David Buckingham	1996	fire-spitting on p47 pre-pulsar shuttle	103
143	Herschel loop	David Buckingham	1996	p11 thumb on Beluchenko's p13	69
144	capped p144 gunstar	David Buckingham	1990	Achim's p144	42
146	Herschel loop	David Buckingham	1996	p146 pi-heptomino hassler	51
150	p30n glider loop	?	≤1973	unix on 30P25	46
152	p136+8n Herschel loop	David Buckingham	1991	figure eight on 42P38	54
156	p152+4n Herschel loop	David Buckingham	1991	unix on p52 LOM hassler	66
158	Herschel loop	David Buckingham	1996	p158 pi-heptomino hassler	96
160	p136+8n Herschel loop	David Buckingham	1991	p160 pi-heptomino hassler	56
165	p165 glider shuttle	Robert Wainwright	≤1989	rattlesnake on pentadecathlon	45
166	Herschel loop	David Buckingham	1996	p166 R-pentomino hassler	102
171	p150+3n Herschel loop	David Buckingham	1991	p171 pi-heptomino hassler	128
177	p150+3n Herschel loop	David Buckingham	1991	Karel's p177, Caterer on 92P59^[5]	104
187	Herschel loop	David Buckingham	1996	p187 century hassler	112
188	p94n glider loop	Dean Hickerson	1990	mold on 54P94	68
192	p136+8n Herschel loop	David Buckingham	1991	57P192	57
196	p152+4n Herschel loop	David Buckingham	1991	mold on 44P49	56
199	Herschel loop	David Buckingham	1996	84P199	84
200	p100n glider loop	Bill Gosper	≤1987	figure eight on 30P25	42
201	p150+3n Herschel loop	David Buckingham	1991	Capped period-201 glider gun	98
220	p152+4n Herschel loop	David Buckingham	1991	p220 honey farm shuttle	74
226	Herschel loop	David Buckingham	1996	Boat-bitted 86P113	84
232	figure eight on p29 pre-pulsar shuttle	?	?	figure eight on p29 pre-pulsar shuttle	66
246	p246 glider shuttle	Dean Hickerson	1992	unix on p82 lumps of muck hassler	64
256	spark-assisted p256 Herschel loop	David Buckingham	1991	86P256	86
312	p136+8n Herschel loop	David Buckingham	1991	60P312	60
368	p46n glider loop	Bill Gosper	1971	period-184 glider gun with boat-bits	48
384	p136+8n Herschel loop	David Buckingham	1991	49P384	49
492	p150+3n Herschel loop	David Buckingham	1991	period-246 glider gun with boat-bit	87
856	capped period-856 glider gun	David Buckingham	1991	p856 glider shuttle	92

Notes

↑ ^1.0 ^1.1 ^1.2 ^1.3 ^1.4 ^1.5 ^1.6 ^1.7 ^1.8 Non-trivial oscillators of this period could have been constructed from two oscillators of lower period (usually sparkers), both of which were known by an earlier date. However, no such LCM oscillators were attested prior to the discovery of this oscillator.

References

↑ Dean Hickerson's oscillator stamp collection. Retrieved on April 11, 2009.
↑ Jeremy Tan (July 3, 2021). Re: Smallest Known Oscillators to p106 (and Beyond) (discussion thread) at the ConwayLife.com forums
↑ Connor Steppie (March 13, 2024). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
↑ Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
↑ Period1GliderGun (July 12, 2023). Re: Smallest Known Oscillators to p106 (and Beyond) (discussion thread) at the ConwayLife.com forums

External links

Forum threads

Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
Smallest Known Oscillators to p106 (and Beyond) (discussion thread) at the ConwayLife.com forums
First Known Oscillators for Each Period (discussion thread) at the ConwayLife.com forums

[lcm-4] 1.0 ^1.1 ^1.2 ^1.3 ^1.4 ^1.5 ^1.6 ^1.7 ^1.8 Non-trivial oscillators of this period could have been constructed from two oscillators of lower period (usually sparkers), both of which were known by an earlier date. However, no such LCM oscillators were attested prior to the discovery of this oscillator.

[1] Dean Hickerson's oscillator stamp collection. Retrieved on April 11, 2009.

[post132979-2] Jeremy Tan (July 3, 2021). Re: Smallest Known Oscillators to p106 (and Beyond) (discussion thread) at the ConwayLife.com forums

[post180140-3] Connor Steppie (March 13, 2024). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums

[5] Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums

[post163608-6] Period1GliderGun (July 12, 2023). Re: Smallest Known Oscillators to p106 (and Beyond) (discussion thread) at the ConwayLife.com forums

[1]

[2]

[3]

[note 1]

[4]

[5]

Oscillator: Difference between revisions

Latest revision as of 16:43, 23 March 2026

Important oscillators by period

Notes

References

See also

External links

Forum threads

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@@ Line 1: / Line 1: @@
 {{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).
-In general [[cellular automaton]] theory the term oscillator usually covers [[spaceship]]s as well, but this usage is not normal in [[Conway's Game of Life]].
+[[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 [[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.
+A list of the first-discovered oscillator of each period,<ref>{{CiteHickersonOscillators|accessdate=April 11, 2009}}</ref> as well the current smallest-known oscillator of that period,<ref name="post132979" /> 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 (i.e. the overall pattern must have a nonzero [[strict volatility]]). 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.
-<table border="0" cellpadding="0" cellspacing="0" width="100%"><tr><td align="center" width="50%">
+For any period 59 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. Since {{year|2023}}, oscillators of all periods less than 43 have been known showing that Life is [[omniperiodic]].
-{| class="wikitable"
-|-
+The lowest population for which an infinite number of non-trivial oscillators are known to exist is 29, as two 12-cell pentadecathlons can reflect a 5-cell glider back and forth indefinitely in the correct position. The smallest example of this is the [[p60 glider shuttle]], with period-180, 300, and all other periods of the form 120n+60 possible with no extra cells required. 29 is conjectured to be the lowest population for which an infinite number of distinct non-trivial oscillators exist.<ref name="post180140"/>
+{| class="sortable wikitable" style="margin-left:auto;margin-right:auto;"
 ! Period
 ! First discovered
 ! Discoverer
 ! Year of discovery
+! class=unsortable|
+! Smallest known
+! Minimum # of cells
 |-
-! [[:Category:Oscillators with period 2|2]]
+! {{period|2|brief}}
+| [[blinker]]
+|[[John Conway]]
+| {{year|1969}}
+| rowspan="500" style="border: none;" |
 | [[blinker]]
-| [[:Category:Patterns found by John Conway|John Conway]]
+| {{cells|3}}
-| [[:Category:Patterns found in 1970|1970]]
 |-
-! [[:Category:Oscillators with period 3|3]]
+! {{period|3|brief}}
 | [[pulsar]]
-| John Conway
+|John Conway
 | 1970
+| [[caterer]]
+| {{cells|12}}
 |-
-! [[:Category:Oscillators with period 4|4]]
+! {{period|4|brief}}
 | [[pinwheel]]
-| [[:Category:Patterns found by Simon Norton|Simon Norton]]
+|[[Simon Norton]]
 | 1970
+| [[mazing]], [[mold]]
+| {{cells|12}}
 |-
-! [[:Category:Oscillators with period 5|5]]
+! {{period|5|brief}}
 | [[octagon 2]]
-| [[:Category:Patterns found by Sol Goodman|Sol Goodman]], [[:Category:Patterns found by Arthur Taber|Arthur Taber]]
+|[[Sol Goodman]], [[Arthur Taber]]
-| [[:Category:Patterns found in 1971|1971]]
+| {{year|1971}}
+| [[pseudo-barberpole]]
+| {{cells|15}}
 |-
-! [[:Category:Oscillators with period 6|6]]
+! {{period|6|brief}}
-| [[$rats]], [[sombreros]]
+| [[$rats]]
-| [[:Category:Patterns found by David Buckingham|David Buckingham]]
+|[[David Buckingham]]
-| [[:Category:Patterns found in 1972|1972]]
+| {{year|1972}}
+| [[unix]]
+| {{cells|16}}
 |-
-! [[:Category:Oscillators with period 7|7]]
+! {{period|7|brief}}
 | [[burloaferimeter]]
-| David Buckingham
+|David Buckingham
 | 1972
+| [[28P7.1]], [[28P7.2]], [[28P7.3]], [[burloaferimeter]]
+| {{cells|28}}
 |-
-! [[:Category:Oscillators with period 8|8]]
+! {{period|8|brief}}
 | [[figure eight]]
-| Simon Norton
+|Simon Norton
 | 1970
+| [[figure eight]]
+| {{cells|12}}
 |-
-! [[:Category:Oscillators with period 9|9]]
+! {{period|9|brief}}
 | [[worker bee]]
-| David Buckingham
+|David Buckingham
 | 1972
+| [[29P9]]
+| {{cells|29}}
 |-
-! [[:Category:Oscillators with period 10|10]]
+! {{period|10|brief}}
-| [[42P10.1]]
+| [[42P10.3]]
-| David Buckingham
+|David Buckingham
-| &le;[[:Category:Patterns found in 1976|1976]]
+| data-sort-value="1976"|&le;{{year|1976}}
+| [[24P10]]
+| {{cells|24}}
 |-
-! [[:Category:Oscillators with period 11|11]]
+! {{period|11|brief}}
 | [[38P11.1]]
-| David Buckingham
+|David Buckingham
-| [[:Category:Patterns found in 1977|1977]]
+| {{year|1977}}
+| [[rattlesnake]], [[diamondback]]
+| {{cells|33}}
 |-
-! [[:Category:Oscillators with period 12|12]]
+! {{period|12|brief}}
 | [[dinner table]]
-| [[Robert Wainwright]]
+|[[Robert Wainwright]]
-| [[:Category:Patterns found in 1972|1972]]
+| {{year|1972}}
+| [[mold on fire-spitting]]
+| {{cells|31}}
 |-
-! [[:Category:Oscillators with period 13|13]]
+! {{period|13|brief}}
-| [[65P13.1]]
+| [[Buckingham's p13]]
-| David Buckingham
+|David Buckingham
 | 1976
+| [[Beluchenko's p13]]
+| {{cells|34}}
 |-
-! [[:Category:Oscillators with period 14|14]]
+! {{period|14|brief}}
 | [[tumbler]]
-| George Collins, Jr.
+|[[George Collins]]
 | 1970
+| [[tumbler]]
+| {{cells|16}}
 |-
-! [[:Category:Oscillators with period 15|15]]
+! {{period|15|brief}}
 | [[pentadecathlon]]
-| John Conway
+|John Conway
 | 1970
+| [[pentadecathlon]]
+| {{cells|12}}
 |-
-! [[:Category:Oscillators with period 16|16]]
+! {{period|16|brief}}
 | [[two pre-L hasslers]]
-| Robert Wainwright
+|Robert Wainwright
-| [[:Category:Patterns found in 1983|1983]]
+| {{year|1983}}
+| [[Rob's p16]]
+| {{cells|21}}
 |-
-! [[:Category:Oscillators with period 17|17]]
+! {{period|17|brief}}
 | [[54P17.1]]
-| [[:Category:Patterns found by Dean Hickerson|Dean Hickerson]]
+|[[Dean Hickerson]]
-| [[:Category:Patterns found in 1997|1997]]
+| {{year|1997}}
+| [[honey thieves]]
+| {{cells|36}}
 |-
-! [[:Category:Oscillators with period 18|18]]
+! {{period|18|brief}}
-| [[117P18]]
+| [[117P18]]{{refn|group=note|name=lcm|[[Non-trivial]] oscillators of this period could have been constructed from two oscillators of lower period (usually [[sparker]]s), both of which were known by an earlier date. However, no such [[LCM oscillator]]s were attested prior to the discovery of this oscillator.}}
-| David Buckingham
+|David Buckingham
-| &le;[[:Category:Patterns found in 1991|1991]]
+| data-sort-value="1991"|&le;{{year|1991}}
+| [[p18 bi-block hassler]], [https://catagolue.hatsya.com/object?apgcode=xp18_wc93xs112ogggzbdhe96kk801zw1213&rule=b3s23 p18 phase shifter]
+| {{cells|43}}
 |-
-! class="red_td" | 19
+! {{period|19|brief}}
-| class="red_td" colspan="3" | ''None found''
+| [[cribbage]]
+| [[Mitchell Riley]]
+| {{year|2023}}
+| [[cribbage]]
+| {{cells|92}}
 |-
-! [[:Category:Oscillators with period 20|20]]
+! {{period|20|brief}}
-| [[145P20]]
+| [[145P20]]{{refn|group=note|name=lcm}}
-| [[Noam Elkies]]
+|[[Noam Elkies]]
-| [[:Category:Patterns found in 1995|1995]]
+| {{year|1995}}
+| [[mold on fumarole]]
+| {{cells|30}}
 |-
-! [[:Category:Oscillators with period 21|21]]
+! {{period|21|brief}}
-| [[124P21]]
+| [[124P21]]{{refn|group=note|name=lcm}}
-| Robert Wainwright
+|Robert Wainwright
 | 1995
+| [[32P21]]
+| {{cells|32}}
 |-
-! [[:Category:Oscillators with period 22|22]]
+! {{period|22|brief}}
 | [[168P22.1]]
-| Noam Elkies
+|Noam Elkies
 | 1997
+| [[Jason's p22]]
+| {{cells|36}}
 |-
-! class="red_td" | 23
+! {{period|23|brief}}
-| class="red_td" colspan="3" | ''None found''
+| [[David Hilbert]]
+|[[Luka Okanishi]], [[praosylen]]
+| {{year|2019}}
+| [[54P23]]
+| {{cells|54}}
 |-
-! [[:Category:Oscillators with period 24|24]]
+! {{period|24|brief}}
-| [[144P24]], [[186P24]]
+| [[186P24]]{{refn|group=note|name=lcm}}
-| Noam Elkies, Bill Gosper
+|[[Bill Gosper]]
-| [[:Category:Patterns found in 1994|1994]]
+| {{year|1994}}
+| [[caterer on figure eight]]
+| {{cells|24}}
 |-
-! [[:Category:Oscillators with period 25|25]]
+! {{period|25|brief}}
 | [[134P25]]
-| Noam Elkies
+|Noam Elkies
 | 1994
+| [[30P25]]
+| {{cells|30}}
+|-
+! {{period|26|brief}}
+| [[p26 pre-pulsar shuttle]]
+|David Buckingham
+| 1983
+| [[p26 honey farm hassler]]
+| {{cells|60}}
 |-
-! [[:Category:Oscillators with period 27|27]]
+! {{period|27|brief}}
 | [[123P27.1]]
-| Noam Elkies
+|Noam Elkies
-| [[:Category:Patterns found in 2002|2002]]
+| {{year|2002}}
+| [[56P27]]
+| {{cells|56}}
+|-
+! {{period|28|brief}}
+| [[newshuttle]]
+|David Buckingham
+| {{year|1973}}
+| [[mold on 34P14 shuttle]]
+| {{cells|46}}
 |-
-! [[:Category:Oscillators with period 28|28]]
+! {{period|29|brief}}
-| [[Newshuttle]]
+| [[p29 pre-pulsar shuttle]]
-| David Buckingham
+|David Buckingham
-| [[:Category:patterns found in 1973|1973]]<ref>{{CiteHickersonOscillators}}</ref>
+| {{year|1980}}
+| [[p29 pre-pulsar shuttle]]
+| {{cells|54}}
 |-
-! [[:Category:Oscillators with period 30|30]]
+! {{period|30|brief}}
 | [[queen bee shuttle]]
-| Bill Gosper
+|Bill Gosper
 | 1970
+| [[queen bee shuttle]]
+| {{cells|20}}
 |-
-! class="red_td" | 31
+! {{period|31|brief}}
-| class="red_td" colspan="3" | ''None found''
+| [[Merzenich's p31]]
+|[[Matthias Merzenich]]
+| {{year|2010}}
+| [[Merzenich's p31]]
+| {{cells|48}}
 |-
-! [[:Category:Oscillators with period 32|32]]
+! {{period|32|brief}}
 | [[gourmet]]
-| David Buckingham
+|David Buckingham
-| [[:Category:Patterns found in 1978|1978]]
+| {{year|1978}}
+| [[p32 honey farm hassler]]
+| {{cells|45}}
 |-
-! [[:Category:Oscillators with period 33|33]]
+! {{period|33|brief}}
-| (?)
+| [[258P3 on Achim's p11]]
-| Noam Elkies, [[:Category:Patterns found by Achim Flammenkamp|Achim Flammenkamp]]
+|Noam Elkies, [[Achim Flammenkamp]]
 | 1997
+| [[caterer on rattlesnake]]
+| {{cells|46}}
 |-
-! class="red_td" | 34
+! {{period|34|brief}}
-| class="red_td" colspan="3" | ''No non-trivial examples found''
+| [[74P34]]
+|[[Mitchell Riley]]
+| 2022
+| [[74P34]]
+| {{cells|74}}
 |-
-! [[:Category:Oscillators with period 37|37]]
+! {{period|35|brief}}
-| [[124P37]]
+| [[p35 beehive hassler]]{{refn|group=note|name=lcm}}
-| [[:Category:Patterns found by Nicolay Beluchenko|Nicolay Beluchenko]]
+|Dean Hickerson
-| [[:Category:Patterns found in 2009|2009]]
+| 1995
+| [[p35 honey farm hassler]]
+| {{cells|44}}
 |-
-! class="red_td" | 38
+! {{period|36|brief}}
-| class="red_td" colspan="3" | ''None found''
+| [[p36 toad hassler]]{{refn|group=note|name=lcm}}
+|Robert Wainwright
+| 1984
+| [[22P36]]
+| {{cells|22}}
 |-
-! [[:Category:Oscillators with period 39|39]]
+! {{period|37|brief}}
+| [[Beluchenko's p37]]
+|[[Nicolay Beluchenko]]
+| {{year|2009}}
+| [[58P37]]
+| {{cells|58}}
+|-
+! {{period|38|brief}}
+| [[44P38]]
+|[[David Raucci]]
+| {{year|2022}}
+| [[42P38]]
+| {{cells|42}}
+|-
+! {{period|39|brief}}
 | [[134P39.1]]
-| David Buckingham, Noam Elkies
+|Noam Elkies, David Buckingham
-| [[:Category:Patterns found in 2000|2000]]
+| {{year|2000}}
+| [[caterer on Beluchenko's p13]]
+| {{cells|46}}
+|-
+! {{period|40|brief}}
+| [[p40 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
+|David Buckingham
+| 1991
+| [[Beluchenko's p40]]
+| {{cells|26}}
+|-
+! {{period|41|brief}}
+| [[208P41]]
+|Nora Brown
+| 2023
+| [[p41 pi-heptomino hassler]]
+| {{cells|170}}
+|-
+! {{period|42|brief}}
+| [[p42 glider shuttle]]{{refn|group=note|name=lcm}}
+|Noam Elkies
+| 1994
+| [[unix on 34P14 shuttle]]
+| {{cells|50}}
 |-
-! class="red_td" | 41
+! {{period|43|brief}}
-| class="red_td" colspan="3" | ''None found''
+| [[p43 Snark loop]]
+|[[Mike Playle]]
+| {{year|2013}}
+| [[p43 pi-heptomino hassler]]<ref>{{LinkForumThread|format=ref|p=153483|title=Re: Oscillator Discussion Thread}}</ref>
+| {{cells|70}}
 |-
-! class="red_td" | 43
+! {{period|44|brief}}
-| class="red_td" colspan="3" | ''None found''
+| [[p44 pi-heptomino hassler]]
+|David Buckingham
+| 1992
+| [[mold on rattlesnake]]
+| {{cells|45}}
 |-
-! [[:Category:Oscillators with period 46|46]]
+! {{period|45|brief}}
+| [[pentadecathlon on snacker]]
+| [[Mark Niemiec]], John Conway
+| data-sort-value="1992"|&le;1992
+| [[p45 pi-heptomino hassler]]
+| {{cells|29}}
+|-
+! {{period|46|brief}}
 | [[twin bees shuttle]]
-| Bill Gosper
+|Bill Gosper
 | 1971
+| [[twin bees shuttle]]
+| {{cells|28}}
+|-
+! {{period|47|brief}}
+| [[p47 pre-pulsar shuttle]]
+|David Buckingham
+| {{year|1982}}
+| [[p47 pre-pulsar shuttle]]
+| {{cells|84}}
+|-
+! {{period|48|brief}}
+| [[p48 toad hassler]]
+|Bill Gosper
+| 1994
+| [[unix on Charity's p16]]
+| {{cells|44}}
+|-
+! {{period|49|brief}}
+| [[p49 bouncer loop]]
+|Noam Elkies
+| {{year|1999}}
+| [[44P49]]
+| {{cells|44}}
 |-
-! [[:Category:Oscillators with period 49|49]]
+! {{period|50|brief}}
-| [[440P49.1]]
+| [[p50 glider shuttle]]
-| Noam Elkies
+|Dean Hickerson
-| [[:Category:Patterns found in 1999|1999]]
+| 1992
+| [[24P10 on 30P25]]
+| {{cells|58}}
 |-
-! [[:Category:Oscillators with period 51|51]]
+! {{period|51|brief}}
-| [[112P51]]
+| [[Beluchenko's p51]]
-| Nicolay Beluchenko
+|Nicolay Beluchenko
 | 2009
+| [[Period-51 glider gun|capped p51 gun]]
+| {{cells|84}}
+|-
+! {{period|52|brief}}
+| [[Four eaters hassling lumps of muck]]
+|David Buckingham
+| 1977
+| [[four eaters hassling lumps of muck]]
+| {{cells|35}}
+|-
+! {{period|53|brief}}
+| [[p53 Snark loop]]
+|Mike Playle
+| {{year|2013}}
+| [[94P53]]
+| {{cells|94}}
+|-
+! {{period|54|brief}}
+| [[p54 shuttle]]
+|David Buckingham
+| {{year|1973}}
+| [[43P54]]
+| {{cells|43}}
+|-
+! {{period|55|brief}}
+| [[p55 pre-pulsar hassler]]
+|David Buckingham
+| {{year|1986}}
+| [[pseudo-barberpole on rattlesnake]]
+| {{cells|49}}
+|-
+! {{period|56|brief}}
+| [[p56 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
+|David Buckingham
+|data-sort-value="1991"| &le;1991
+| [[p56 B-heptomino shuttle]]
+| {{cells|45}}
+|-
+! {{period|57|brief}}
+| [[p57 Herschel loop 1]]
+|[[Dietrich Leithner]]
+| 1997
+| [[112P57]]
+| {{cells|112}}
+|-
+! {{period|58|brief}}
+| [[p58 toadsucker]]
+|Bill Gosper
+| 1994
+| [[p58 pi-heptomino hassler]], {{LinkCatagolue|xp58_y932aczy5ooy3osogzyi76y0cczz33y06eggggy3ggzy5131y311zy9354c|patternname=54p58|style=raw}}
+| {{cells|54}}
+|-
+! {{period|59|brief}}
+| [[p59 Herschel loop 1]]
+|David Buckingham
+| 1997
+| [[p59 pi-heptomino hassler]]
+| {{cells|86}}
+|-
+! {{period|60|brief}}
+| [[p60 glider shuttle]]
+| ?
+|data-sort-value="1971"| &le;1971
+| [[mold on pentadecathlon]]
+| {{cells|24}}
+|-
+! {{period|61|brief}}
+| [[p61 Herschel loop 1]]
+|David Buckingham
+| {{year|1996}}
+| [[p61 pi-heptomino hassler]]
+| {{cells|134}}
+|-
+! {{period|62|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[66P62]]
+| {{cells|66}}
+|-
+! {{period|63|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[64P63|32P21 phase-shifting p5]]
+| {{cells|64}}
 |-
-! class="red_td" | 53
+! {{period|64|brief}}
-| class="red_td" colspan="3" | ''None found''
+| Herschel loop
+| David Buckingham
+| 1996
+| [[Merzenich's p64]]
+| {{cells|34}}
 |-
-! [[:Category:Oscillators with period 54|54]]
+! {{period|65|brief}}
-| [[P54 shuttle]]
+| Herschel loop
 | David Buckingham
-| 1974
+| 1996
+| [[fumarole on Beluchenko's p13]]
+| {{cells|52}}
 |-
-! [[:Category:Oscillators with period 72|72]]
+! {{period|66|brief}}
-| [[47P72]]
+| [[p42 glider shuttle|p66 glider shuttle]]
 | Robert Wainwright
+| 1984
+| [[caterer on Jason's p22]]
+| {{cells|48}}
+|-
+! {{period|67|brief}}
+| [[p67 Herschel loop|Herschel loop]]
+| David Buckingham
+| 1996
+| [[p67 Snark loop]]
+| {{cells|228}}
+|-
+! {{period|68|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[p68 century hassler]]
+| {{cells|38}}
+|-
+! {{period|69|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[54P23#LCM oscillators|55P23 on Grin reagent weld loading dock]]
+| {{cells|103}}
+|-
+! {{period|70|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[fumarole on 34P14 shuttle]]
+| {{cells|52}}
+|-
+! {{period|71|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[p71 dependent reflector loop]]
+| {{cells|92}}
+|-
+! {{period|72|brief}}
+| [[two blockers hassling R-pentomino]]
+|Robert Wainwright
 | 1990
+| [[figure eight on 22P36]]
+| {{cells|36}}
+|-
+! {{period|73|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[p73 lumps of muck hassler]]
+| {{cells|68}}
+|-
+! {{period|74|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[Raucci's p74]]
+| {{cells|84}}
+|-
+! {{period|75|brief}}
+| [[6 bits]]
+| Robert Wainwright
+| 1984
+| [[pentadecathlon on 30P25]]
+| {{cells|42}}
 |-
-! [[:Category:Oscillators with period 110|110]]
+! {{period|76|brief}}
-| [[P110 traffic jam]]
+| Herschel loop
+| David Buckingham
+| 1996
+| [[p76 pi-heptomino shuttle]]
+| {{cells|52}}
+|-
+! {{period|77|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[34P7 on rattlesnake]]
+| {{cells|67}}
+|-
+! {{period|78|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[p6 thumb on Beluchenko's p13]]
+| {{cells|61}}
+|-
+! {{period|79|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[p79 pi-heptomino hassler]]
+| {{cells|80}}
+|-
+! {{period|80|brief}}
+| [[middleweight volcano]] on [[Achim's other p16]]
+| Dean Hickerson, Achim Flammenkamp
+| 1994
+| [[fumarole on Rob's p16]]
+| {{cells|39}}
+|-
+! {{period|81|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| {{LinkCatagolue|xp81_yzyzwca23zyzyy33y2eu80gswsg0gzyzyw2a6y4178ewew121zyzyz0o4ozyzyugs26x1zyzyzxco4zyzyca64zzzyzyisg8zyu42ezzzyz08okzya86czyhoge2zyc696z0gxsws4oy5okgz1212ewe205vsy2ggzyaggkc011zya1|patternname=p81 180° glider loop|style=raw}}
+| {{cells|146}}
+|-
+! {{period|82|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[p82 lumps of muck hassler]]
+| {{cells|48}}
+|-
+! {{period|83|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[62P83]]
+| {{cells|62}}
+|-
+! {{period|84|brief}}
+| [[pi orbital]]
+| Noam Elkies
+| 1995
+| [[p84 honey farm hassler]]
+| {{cells|42}}
+|-
+! {{period|85|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[p85 R-pentomino hassler]]
+| {{cells|68}}
+|-
+! {{period|86|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[76P86]]
+| {{cells|76}}
+|-
+! {{period|87|brief}}
+| p3 sparker on [[p29 pentadecathlon hassler]]
 | Bill Gosper
 | 1994
+| [[84P87]]
+| {{cells|84}}
+|-
+! {{period|88|brief}}
+| p44n glider loop
+|David Buckingham
+| 1992
+| [[figure eight on rattlesnake]]
+| {{cells|45}}
+|-
+! {{period|89|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| {{LinkCatagolue|xp89_yzy833y58e1e88gzyzyj330311ybckzyzyd3224e6y725acy165lozyzwgs2552ypggzyzy2gcoy1o8a6xca8y911zzzzysgy1g0gzy4ooy9153x6511y113xggzggyx4aa43z1qa6y135a4y767244cz023yag88c0cczye117871y5cc|patternname=transparent long boat glider loop|style=raw}}
+| {{cells|164}}
+|-
+! {{period|90|brief}}
+| p30n glider loop
+| ?
+| data-sort-value="1973"|&le;1973
+| [[unix on p45 pi-heptomino hassler]]
+| {{cells|45}}
 |-
-! [[:Category:Oscillators with period 132|132]]
+! {{period|91|brief}}
-| [[132P132]]
+| Herschel loop
 | David Buckingham
-| &le;1994
+| 1996
+| [[34P7 on Beluchenko's p13]]
+| {{cells|68}}
 |-
-! [[:Category:Oscillators with period 144|144]]
+! {{period|92|brief}}
-| [[Achim's p144]]
+| p46n glider loop
-| Achim Flammenkamp
+| Bill Gosper
-| 1994
+| 1971
+| [[mold on twin bees shuttle]]
+| {{cells|44}}
+|-
+! {{period|93|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[caterer on Merzenich's p31]]
+| {{cells|60}}
+|-
+! {{period|94|brief}}
+| capped [[P94S]]
+| Dean Hickerson
+| 1990
+| [[54P94]]
+| {{cells|54}}
+|-
+! {{period|95|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[Cribbage#LCM oscillators|toaster variant on Cribbage]]
+| {{cells|137}}
 |-
-! [[:Category:Oscillators with period 156|156]]
+! {{period|96|brief}}
-| [[P156 Hans Leo hassler]]
+| [[p96 Hans Leo hassler]]
 | Noam Elkies
 | 1995
+| [[period-48 glider gun with boat-bit]]
+| {{cells|59}}
+|-
+! {{period|97|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| {{LinkCatagolue|xp97_ydg88e1u8y533z0kcyb11313kzol56y1ca52y6115137zy4ggyp2552sgzy411y94ocx6a8ozyzxe24zzzzyzy448ezyzyg32acx634y9ggzyzy4178kk8yp11zyzyksogkggy68ka6y1ckl3zyzyp5ogoggyb65zyzyeooy52fge221|patternname=transparent long boat glider loop|style=raw}}
+| {{cells|164}}
 |-
-! [[:Category:Oscillators with period 200|200]]
+! {{period|98|brief}}
-| [[P200 traffic jam]]
+| Herschel loop
+| David Buckingham
+| 1996
+| [[Gallus]], [https://catagolue.hatsya.com/object/xp98_660g0fmy64a4x62z0cqb0t53y8ca8x66w66zw6fx66ydccxuczxccwccyeokn0qb6zy6ccx4a4y6du010cc/b3s23 p98 glider shuttle]
+| {{cells|105}}
+|-
+! {{period|99|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[Rattlesnake#LCM oscillators|rattlesnake on 42P9]]
+| {{cells|75}}
+|-
+! {{period|100|brief}}
+| [[centinal]]
+|Bill Gosper
+|data-sort-value="1987"|&le;1987
+| [[mold on 30P25]]
+| {{cells|42}}
+|-
+! {{period|101|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[116P101]]
+| {{cells|116}}
+|-
+! {{period|102|brief}}
+| p102+18n [[traffic jam]]
+| Dean Hickerson
+| data-sort-value="1994"|1994
+| [[Raucci's p102]]
+| {{cells|67}}
+|-
+! {{period|103|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[siffrin's p103]]
+| {{cells|68}}
+|-
+! {{period|104|brief}}
+| p100+4n [[traffic jam]]
+| Bill Gosper
+| 1994
+| [[figure eight on Beluchenko's p13]]
+| {{cells|46}}
+|-
+! {{period|105|brief}}
+| [[pentadecathlon]] on [[44P7.2]]
+| ?
+|data-sort-value="1992"| &le;1992
+| [[34P7]] on [[pentadecathlon]]
+| {{cells|46}}
+|-
+! {{period|106|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[66P106]]
+| {{cells|66}}
+|-
+! {{period|107|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[86P107]]
+| {{cells|86}}
+|-
+! {{period|108|brief}}
+| [[p54 shuttle]] on [[figure eight]]
+| ?
+|data-sort-value="1992"| &le;1992
+| {{LinkCatagolue|xp108_8o6pajkk8z32q921y8ca23z321y1131y08c8zy0c453|patternname=22P36 phase-shifting p5|style=raw}}
+| {{cells|54}}
+|-
+! {{period|109|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[rectifier|p109 rectifier loop]]
+| {{cells|156}}
+|-
+! {{period|110|brief}}
+| [[p110 traffic jam]]
 | Bill Gosper
 | 1994
-|}</td><td align="center" width="50%">
+| [[pseudo-barberpole on Jason's p22]]
-{| class="wikitable"
+| {{cells|51}}
 |-
-! Period
+! {{period|111|brief}}
-! Smallest known
+| Herschel loop
-! Minimum # of [[cell]]s
+| David Buckingham
+| 1996
+| [[fire-spitting on p37 lumps of muck hassler]]
+| {{cells|91}}
+|-
+! {{period|112|brief}}
+| p100+4n [[traffic jam]]
+| Bill Gosper
+| 1994
+| [[tumbler on Rich's p16]]
+| {{cells|50}}
+|-
+! {{period|113|brief}}
+| Herschel loop
+| David Buckingham
+| 1996
+| [[86P113]]
+| {{cells|86}}
+|-
+! {{period|114|brief}}
+| [[p42 glider shuttle|p66+24n glider shuttle]]
+| Robert Wainwright
+| 1984
+| [[caterer on 42P38]]
+| {{cells|54}}
 |-
-! 2
+! {{period|115|brief}}
-| [[blinker]]
+| Herschel loop
-| [[:Category:Patterns with 3 cells|3]]
+| David Buckingham
+| 1996
+| {{LinkCatagolue|xp115_y032acy0ezw6ioy2gy0c871zca16a4x317zy2o8a6y0gbbgn1e808ozya11mq0v5kk8zye343|patternname=92P115|style=raw}}
+| {{cells|92}}
 |-
-! 3
+! {{period|116|brief}}
-| [[caterer]]
+| p4 sparker on [[p29 pentadecathlon hassler]]
-| [[:Category:Patterns with 12 cells|12]]
+| Bill Gosper
+| 1994
+| {{LinkCatagolue|xp116_y6o4an7zy711zy166y5ok4kozym31e8zx32acyc6a8oz2egozy535453y5cc|patternname=mold on p58 pi-heptomino hassler|style=raw}}
+| {{cells|68}}
 |-
-! 4
+! {{period|117|brief}}
-| [[mazing]], [[mold]]
+| Herschel loop
-| [[:Category:Patterns with 12 cells|12]]
+| David Buckingham
+| 1996
+| [[Beluchenko's p13#LCM oscillators|Beluchenko's p13 on 42P9]]
+| {{cells|76}}
 |-
-! 5
+! {{period|118|brief}}
-| [[pseudo-barberpole]]
+| Herschel loop
-| [[:Category:Patterns with 15 cells|15]]
+| David Buckingham
+| 1996
+| [[86P118]]
+| {{cells|86}}
 |-
-! 6
+! {{period|119|brief}}
-| [[unix]]
+| Herschel loop
-| [[:Category:Patterns with 16 cells|16]]
+| David Buckingham
+| 1996
+| [[72P119]]
+| {{cells|72}}
 |-
-! 7
+! {{period|120|brief}}
-| [[28P7.1]], [[28P7.2]], [[burloaferimeter]]
+| p30n glider loop
-| [[:Category:Patterns with 28 cells|28]]
+| ?
+| data-sort-value="1973"|&le;1973
+| [[figure eight on pentadecathlon]]
+| {{cells|24}}
 |-
-! 8
+! {{period|122|brief}}
-| [[figure eight]]
+| Herschel loop
-| [[:Category:Patterns with 12 cells|12]]
+| David Buckingham
+| 1996
+| [[R-pentomino hasslers#p122|p122 R-pentomino hassler]]
+| {{cells|102}}
 |-
-! 9
+! {{period|123|brief}}
-| [[29P9.1]]
+| Herschel loop
-| [[:Category:Patterns with 29 cells|29]]
+| David Buckingham
+| 1996
+| [[R-pentomino hasslers#p123|p123 R-pentomino hassler]]
+| {{cells|116}}
 |-
-! 10
+! {{period|124|brief}}
-| [[37P10.1]], 37P10.2
+| [[p124 lumps of muck hassler]]
-| [[:Category:Patterns with 37 cells|37]]
+| Dean Hickerson
+| 1994
+| [[mold on Merzenich's p31]]
+| {{cells|60}}
 |-
-! 11
+! {{period|126|brief}}
-| [[38P11.1]]
+| p102+6n [[traffic jam]]
-| [[:Category:Patterns with 38 cells|38]]
+| Noam Elkies
+| data-sort-value="1996"|&le;1996
+| [[R-pentomino hasslers#p126|p126 R-pentomino hassler]]
+| {{cells|52}}
 |-
-! 12
+! {{period|127|brief}}
-| [[dinner table]]
+| Herschel loop
-| [[:Category:Patterns with 33 cells|33]]
+| David Buckingham
+| 1996
+| [[74P127]]
+| {{cells|74}}
 |-
-! 13
+! {{period|128|brief}}
-| [[34P13.1]]
+| [[Period-256 glider gun#Gallery|spark-assisted p128 Herschel loop]]
-| [[:Category:Patterns with 34 cells|34]]
+| David Buckingham
+| 1991
+| [[60P128]]
+| {{cells|60}}
 |-
-! 14
+! {{period|129|brief}}
-| [[tumbler]]
+| Herschel loop
-| [[:Category:Patterns with 16 cells|16]]
+| David Buckingham
+| 1996
+| [[p129 R-pentomino hassler]]
+| {{cells|38}}
 |-
-! 15
+! {{period|130|brief}}
-| [[pentadecathlon]]
+| [[p50 glider shuttle|p50+40n glider shuttle]]
-| [[:Category:Patterns with 12 cells|12]]
+| Dean Hickerson
+| 1992
+| {{LinkCatagolue|xp130_x32acz31e88g0653zy01pgz66w1023z66w8gkcy2o62453zy08py532156zc8711w6aczxc453|patternname=fumarole on 70P26|style=raw}}
+| {{cells|88}}
 |-
-! 16
+! {{period|132|brief}}
-| [[Achim's p16]]
+| p44n glider loop
-| [[:Category:Patterns with 32 cells|32]]
+| David Buckingham
+| 1992
+| [[mold on Jason's p33]]
+| {{cells|72}}
 |-
-! 17
+! {{period|133|brief}}
-| [[54P17.1]]
+| Herschel loop
-| [[:Category:Patterns with 54 cells|54]]
+| David Buckingham
+| 1996
+| [[B-heptomino hasslers#p133|p133 B-heptomino hassler]]
+| {{cells|84}}
 |-
-! 18
+! {{period|135|brief}}
-| [[43P18]]
+| [[106P135]]
-| [[:Category:Patterns with 43 cells|43]]
+| Bill Gosper
+| {{year|1989}}
+| [[pentadecathlon on 56P27]]
+| {{cells|68}}
 |-
-! class="red_td" | 19
+! {{period|136|brief}}
-| class="red_td" colspan="2" | ''None found''
+| p136 spark-assisted Herschel loop
+| David Buckingham
+| 1991
+| {{LinkCatagolue|xp136_y6rb8oz0oggyhssszx23y56c53y6777zgs26zyf354c|patternname=figure eight on p68 century hassler|style=raw}}
+| {{cells|50}}
 |-
-! 20
+! {{period|138|brief}}
-| [[mold on fumarole]]
+| p46n glider loop
-| [[:Category:Patterns with 30 cells|30]]
+| Bill Gosper
+| 1971
+| [[Gabriel's p138]]
+| {{cells|36}}
 |-
-! 21
+! {{period|140|brief}}
-| [[jam on 44P7.2]]
+| p100+10n traffic jam
-| [[:Category:Patterns with 57 cells|57]]
+| Bill Gosper
+| 1994
+| [[p140 two-glider octomino hassler]]
+| {{cells|58}}
 |-
-! 22
+! {{period|141|brief}}
-| [[36P22.1]]
+| Herschel loop
-| [[:Category:Patterns with 36 cells|36]]
+| David Buckingham
+| 1996
+| [[fire-spitting on p47 pre-pulsar shuttle]]
+| {{cells|103}}
 |-
-! class="red_td" | 23
+! {{period|143|brief}}
-| class="red_td" colspan="2" | ''None found''
+| Herschel loop
+| David Buckingham
+| 1996
+| {{LinkCatagolue|xp143_xgbb88gzy1cd3gv04aczc4530gy1gr3zy1d5a64210g8c4066zy7kr6og|patternname=p11 thumb on Beluchenko's p13|style=raw}}
+| {{cells|69}}
 |-
-! 24
+! {{period|144|brief}}
-| [[caterer on figure eight]]
+| capped p144 [[gunstar]]
-| [[:Category:Patterns with 24 cells|24]]
+| David Buckingham
+| 1990
+| [[Achim's p144]]
+| {{cells|42}}
 |-
-! 25
+! {{period|146|brief}}
-| [[104P25]]
+| Herschel loop
-| [[:Category:Patterns with 104 cells|104]]
+| David Buckingham
+| 1996
+| [[p146 pi-heptomino hassler]]
+| {{cells|51}}
 |-
-! 26
+! {{period|150|brief}}
-| [[pre-pulsar shuttle 26]]
+| p30n glider loop
-| [[:Category:Patterns with 208 cells|208]]
+| ?
+| data-sort-value="1973"|&le;1973
+| [[unix on 30P25]]
+| {{cells|46}}
 |-
-! 27
+! {{period|152|brief}}
-| [[94P27.1]]
+| p136+8n Herschel loop
-| [[:Category:Patterns with 94 cells|94]]
+| David Buckingham
+| 1991
+| [[42P38#LCM oscillators|figure eight on 42P38]]
+| {{cells|54}}
 |-
-! 28
+! {{period|156|brief}}
-| [[pre-pulsar shuttle 28]]
+| p152+4n Herschel loop
-| [[:Category:Patterns with 54 cells|54]]
+| David Buckingham
+| 1991
+| {{LinkCatagolue|xp156_og8o0e93y266zx32wom5hley266zy312221y466zya6a8o033dew66|patternname=unix on p52 LOM hassler|style=raw}}
+| {{cells|66}}
 |-
-! 29
+! {{period|158|brief}}
-| [[pre-pulsar shuttle 29]]
+| Herschel loop
-| [[:Category:Patterns with 54 cells|54]]
+| David Buckingham
+| 1996
+| [[Pi-heptomino hasslers#p158|p158 pi-heptomino hassler]]
+| {{cells|96}}
 |-
-! 30
+! {{period|160|brief}}
-| [[queen bee shuttle]]
+| p136+8n Herschel loop
-| [[:Category:Patterns with 20 cells|20]]
+| David Buckingham
+| 1991
+| [[Pi-heptomino hasslers#p160|p160 pi-heptomino hassler]]
+| {{cells|56}}
 |-
-! class="red_td" | 31
+! {{period|165|brief}}
-| class="red_td" colspan="2" | ''None found''
+| [[p165 glider shuttle]]
+| Robert Wainwright
+| data-sort-value="1989"|&le;1989
+| [[rattlesnake on pentadecathlon]]
+| {{cells|45}}
 |-
-! 32
+! {{period|166|brief}}
-| [[gourmet]]
+| Herschel loop
-| [[:Category:Patterns with 66 cells|66]]
+| David Buckingham
+| 1996
+| [[R-pentomino hasslers#p166|p166 R-pentomino hassler]]
+| {{cells|102}}
 |-
-! 33
+! {{period|171|brief}}
-| [[92P33.1]]
+| p150+3n Herschel loop
-| [[:Category:Patterns with 92 cells|92]]
+| David Buckingham
+| 1991
+| [[Pi-heptomino hasslers#p171|p171 pi-heptomino hassler]]
+| {{cells|128}}
 |-
-! class="red_td" | 34
+! {{period|177|brief}}
-| class="red_td" colspan="2" | ''No non-trivial examples found''
+| p150+3n Herschel loop
+| David Buckingham
+| 1991
+| [[Karel's p177]], [[Caterer]] on [[92P59]]<ref name="post163608"/>
+| {{cells|104}}
 |-
-! 35
+! {{period|187|brief}}
-| [[50P35]]
+| Herschel loop
-| [[:Category:patterns with 50 cells|50]]
+| David Buckingham
+| 1996
+| [[Century hasslers#p187|p187 century hassler]]
+| {{cells|112}}
 |-
-! 36
+! {{period|188|brief}}
-| [[22P36]]
+| p94n glider loop
-| [[:Category:patterns with 22 cells|22]]
+| Dean Hickerson
+| 1990
+| {{LinkCatagolue|xp188_y8o8y1ca23zyj66zxooy4eoiczzydo4coy4ccz695qsoxggy3101zy511w8oy18czy7311|patternname=mold on 54P94|style=raw}}
+| {{cells|68}}
 |-
-! 37
+! {{period|192|brief}}
-| [[124P37]]
+| p136+8n Herschel loop
-| [[:Category:Patterns with 124 cells|124]]
+| David Buckingham
+| 1991
+| [[57P192]]
+| {{cells|57}}
 |-
-! class="red_td" | 38
+! {{period|196|brief}}
-| class="red_td" colspan="2" | ''None found''
+| p152+4n Herschel loop
+| David Buckingham
+| 1991
+| [[44P49#LCM_oscillators|mold on 44P49]]
+| {{cells|56}}
 |-
-! 39
+! {{period|199|brief}}
-| [[jam on 34P13.1]]
+| Herschel loop
-| [[:Category:Patterns with 47 cells|47]]
+| David Buckingham
+| 1996
+| [[84P199]]
+| {{cells|84}}
 |-
-! 40
+! {{period|200|brief}}
-| [[26P40]]
+| p100n glider loop
-| [[:Category:patterns with 26 cells|26]]
+| Bill Gosper
+| data-sort-value="1987"|&le;1987
+| [[figure eight on 30P25]]
+| {{cells|42}}
 |-
-! class="red_td" | 41
+! {{period|201|brief}}
-| class="red_td" colspan="2" | ''None found''
+| p150+3n Herschel loop
+| David Buckingham
+| 1991
+| Capped [[period-201 glider gun]]
+| {{cells|98}}
 |-
-! class="red_td" | 43
+! {{period|220|brief}}
-| class="red_td" colspan="2" | ''None found''
+| p152+4n Herschel loop
+| David Buckingham
+| 1991
+| [[p220 honey farm shuttle]]
+| {{cells|74}}
 |-
-! 46
+! {{period|226|brief}}
-| [[twin bees shuttle]]
+| Herschel loop
-| [[:Category:patterns with 28 cells|28]]
+| David Buckingham
+| 1996
+| {{LinkCatagolue|xp226_yfbdz8oy633z0123zyfggy166zy9ss8x1409cwcczyb33zy9oowo80gx3bsszy9ggx2046zy911zyx31e8zygo8y133zyg23|patternname=Boat-bitted|style=raw}} [[86P113]]
+| {{cells|84}}
 |-
-! 49
+! {{period|232|brief}}
-| [[440P49.1]]
+| [[figure eight on p29 pre-pulsar shuttle]]
-| [[:Category:Patterns with 440 cells|440]]
+| ?
+| data-sort-value="9999"|?
+| [[figure eight on p29 pre-pulsar shuttle]]
+| {{cells|66}}
 |-
-! 51
+! {{period|246|brief}}
-| [[112P51]]
+| [[p42 glider shuttle#Gallery|p246 glider shuttle]]
-| [[:Category:Patterns with 112 cells|112]]
+| Dean Hickerson
+| 1992
+| [[unix]] on [[p82 lumps of muck hassler]]
+| {{cells|64}}
 |-
-! 52
+! {{period|256|brief}}
-| [[35P52]]
+| [[Period-256 glider gun#Gallery|spark-assisted p256 Herschel loop]]
-| [[:Category:Patterns with 35 cells|35]]
+| David Buckingham
+| 1991
+| [[86P256]]
+| {{cells|86}}
 |-
-! class="red_td" | 53
+! {{period|312|brief}}
-| class="red_td" colspan="2" | ''None found''
+| p136+8n Herschel loop
+| David Buckingham
+| 1991
+| [[60P312]]
+| {{cells|60}}
 |-
-! 54
+! {{period|368|brief}}
-| [[P54 shuttle]]
+| p46n glider loop
-| [[:Category:Patterns with 48 cells|48]]
+| Bill Gosper
+| 1971
+| [[period-184 glider gun with boat-bits]]
+| {{cells|48}}
 |-
-! 72
+! {{period|384|brief}}
-| [[47P72]]
+| p136+8n Herschel loop
-| [[:Category:Patterns with 47 cells|47]]
+| David Buckingham
+| 1991
+| [[49P384]]
+| {{cells|49}}
 |-
-! 100
+! {{period|492|brief}}
-| [[centinal]]
+| p150+3n Herschel loop
-| [[:Category:Patterns with 70 cells|70]]
+| David Buckingham
+| 1991
+| [[period-246 glider gun with boat-bit]]
+| {{cells|87}}
 |-
-! 144
+! {{period|856|brief}}
-| [[achim's p144]]
+| capped [[period-856 glider gun]]
-| [[:Category:Patterns with 42 cells|42]]
+| David Buckingham
+| 1991
+| p856 glider shuttle <!-- same as 128, 136, and 256, but Catagolue won't recognize it-->
+| {{cells|92}}
 |}
-</td></tr></table>
-==See also==
+==Notes==
-*[[List of common oscillators]]
+<references group=note />
-*[[:Category:Oscillators|List of oscillators]]
-*[[Omniperiodic]]
 ==References==
-<references/>
+<references>
+<ref name="post132979">{{LinkForumThread
+|format = ref
+|title  = Re: Smallest Known Oscillators to p106 (and Beyond)
+|p      = 132979
+|author = Jeremy Tan
+|date   = July 3, 2021
+}}</ref>
+<ref name="post163608">{{LinkForumThread
+|format = ref
+|title  = Re: Smallest Known Oscillators to p106 (and Beyond)
+|p      = 163608
+|author = Period1GliderGun
+|date   = July 12, 2023
+}}</ref>
+<ref name="post180140">{{LinkForumThread
+|format = ref
+|title  = Re: Unproven conjectures
+|p      = 180140
+|author = Connor Steppie
+|date   = March 13, 2024
+}}</ref>
+</references>
+==See also==
+* [[List of common oscillators]]
+* {{CategoryLink|Flipping oscillators}}
+* {{CategoryLink|Oscillators}}
+* [[Omniperiodic]]
+* [[Table of oscillators by period]]
+* [[Prime-period oscillator]]s
+* [[LifeWiki:Game_of_Life_Status_page#Oscillator_periods|Oscillator periods status table]]
+* [[Almost oscillator]]
+* [[Oscillizer]] - analyze and get vital statistics for an oscillator
 ==External links==
-*[http://web.archive.org/web/20070918210303/www.math.ucdavis.edu/~dean/RLE/stamps.html Oscillator Stamp Collection] by Dean Hickerson, via [http://www.archive.org Archive.org]
+* {{LinkWikipedia|Oscillator_(cellular_automaton)}}
-*[http://www.argentum.freeserve.co.uk/lex_o.htm#oscillator Oscillator] at the Life Lexicon
+* {{LinkLexicon|lex_o.htm#oscillator}}
+* {{LinkLexicon|lex_f.htm#flipper|name=Flipper}}
+===Forum threads===
+* {{LinkForumThread|f=2|t=1437|title=Oscillator Discussion Thread}}
+* {{LinkForumThread|f=2|t=5338|title=Smallest Known Oscillators to p106 (and Beyond)}}
+* {{LinkForumThread|f=7|t=5351|title=First Known Oscillators for Each Period}}
+__NOTOC__

Oscillator: Difference between revisions

Latest revision as of 16:43, 23 March 2026

Important oscillators by period

Notes

References

See also

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