Oscillator

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 (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.

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.

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	David Buckingham	≤1991		p18 bi-block hassler, p18 phase shifter	43
19	cribbage	Mitchell Riley	2023		cribbage	92
20	145P20	Noam Elkies	1995		mold on fumarole	30
21	124P21	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	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	Dean Hickerson	1995		p35 honey farm hassler	44
36	p36 toad hassler	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	David Buckingham	1991		Beluchenko's p40	26
41	208P41	Nico Brown	2023		p41 pi-heptomino hassler	170
42	p42 glider shuttle	Noam Elkies	1994		unix on 34P14 shuttle	50
43	p43 Snark loop	Mike Playle	2013		p43 pi-heptomino hassler	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	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	Grin reagent weld loading dock on 55P23	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	p5 billiard table on Cribbage	141
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	transparent long boat glider loop	180
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	93P115	93
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	p118 rectifier loop	154
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	118
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	62P128	62
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			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	Herschel loop			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	Herschel loop	David Buckingham	1996	p171 pi-heptomino hassler	128
177	p150+3n Herschel loop	David Buckingham	1991	Karel's p177, Caterer on 92P59	104
187	Herschel loop			p187 century hassler	112
188	p94n glider loop	Dean Hickerson	1990	mold on 54P94	68
192	Herschel loop			59P192	59
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	Herschel loop			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	Herschel loop			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

Flipper

A flipper is any oscillator that forms its mirror image halfway through its period. For example, see p60 toad flipper.

See also

• List of common oscillators
• Flipping oscillators (category)
• Oscillators (category)
• Omniperiodic
• Table of oscillators by period
• Prime-period oscillators
• Oscillator periods status table
• Almost oscillator
• Oscillizer - analyze and get vital statistics for an oscillator

External links

• Oscillator at Wikipedia
• Oscillator at the Life Lexicon
• Flipper at the Life Lexicon

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