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 and a stator.

Cellular automaton theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a glider or spaceship. Strictly speaking "glider" means the little figure so prevalent in Conway's Game of Life, but the more general usage has now become popular.

Important oscillators by period

A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one cell that oscillates at the full period. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed. For any period 61 or greater an oscillator can be constructed using the Herschel track method. In April, 2013 Mike Playle found a small 90-degree stable reflector that allows oscillators of all periods 43 or greater to be constructed.

Period	First discovered	Discoverer	Year of discovery		Smallest known	Minimum # of cells
2	blinker	John Conway	1970		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, 28P7.4, burloaferimeter	28
8	figure eight	Simon Norton	1970		figure eight	12
9	worker bee	David Buckingham	1972		29P9	29
10	42P10.1	David Buckingham	≤1976		24P10	24
11	38P11.1	David Buckingham	1977		rattlesnake	33
12	dinner table	Robert Wainwright	1972		dinner table	33
13	65P13.1	David Buckingham	1976		34P13	34
14	tumbler	George Collins, Jr.	1970		tumbler	16
15	pentadecathlon	John Conway	1970		pentadecathlon	12
16	two pre-L hasslers	Robert Wainwright	1983		Achim's p16	32
17	54P17.1	Dean Hickerson	1997		Honey thieves	36
18	117P18	David Buckingham	≤1991		43P18	43
19	None found
20	145P20	Noam Elkies	1995		mold on fumarole	30
21	124P21	Robert Wainwright	1995		caterer on 28P7.4	40
22	168P22.1	Noam Elkies	1997		36P22	36
23	None found
24	186P24	Bill Gosper	1994		caterer on figure eight	24
25	134P25	Noam Elkies	1994		p25 honey farm hassler	88
26	pre-pulsar shuttle 26	David Buckingham	1983		87P26	87
27	123P27.1	Noam Elkies	2002		56P27	56
28	Newshuttle	David Buckingham	1973		pre-pulsar shuttle 28, mold on 41P7.2, T-nosed p4 on 28P7.4	53
29	pre-pulsar shuttle 29	David Buckingham	1980		pre-pulsar shuttle 29	54
30	queen bee shuttle	Bill Gosper	1970		queen bee shuttle	20
31	48P31	Matthias Merzenich	2010		48P31	48
32	gourmet	David Buckingham	1978		gourmet	66
33	258P3 on Achim's p11	Noam Elkies, Achim Flammenkamp	1997		caterer on rattlesnake	46
34	No non-trivial examples found
35	P35 beehive hassler	Dean Hickerson	1995		p35 honey farm hassler	44
36	P36 toad hassler	Robert Wainwright	1984		22P36	22
37	124P37	Nicolay Beluchenko	2009		124P37	124
38	None found
39	134P39.1	David Buckingham, Noam Elkies	2000		caterer on 34P13	46
40	P40 B-heptomino shuttle	David Buckingham	≤1991		26P40	26
41	None found
42	P42 glider shuttle	Noam Elkies	1994		p6 thumb on 28P7.4	55
43	P43 glider loop	Mike Playle	2013		P43 glider loop	228
44	P44 pi-heptomino hassler	David Buckingham	1992		mold on rattlesnake	45
45	pentadecathlon on snacker	?	≤1995		pentadecathlon on thumb 1	48
46	twin bees shuttle	Bill Gosper	1971		twin bees shuttle	28
47	pre-pulsar shuttle 47	David Buckingham	1982		pre-pulsar shuttle 47	84
48	P48 toad hassler	Bill Gosper	1994		unix on Rich's p16	52
49	p49 glider shuttle	Noam Elkies	1999		p49 glider loop	228
50	P50 glider shuttle	Dean Hickerson	1992		P50 traffic jam	92
51	112P51	Nicolay Beluchenko	2009		92P51	92
52	35P52	David Buckingham	1977		35P52	35
53	P53 glider loop	Mike Playle	2013		P53 glider loop	228
54	P54 shuttle	David Buckingham	1974		P54 shuttle	48
55	pre-pulsar hassler 55	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		P57 glider loop	228
58	P58 toadsucker	Bill Gosper	1994		pre-pulsar shuttle 58	104
59	P59 Herschel loop 1	David Buckingham	1997		P59 glider loop	228
60	P60 glider shuttle	David Buckingham	≤ 1971		mold on pentadecathlon	24
61	P61 Herschel loop 1	David Buckingham	1996		P61 glider loop	228
62	?	?	?		110P62	110
63	?	?	?		snacker on 38P7.2	78
64	?	?	?		Merzenich's p64	34
65	?	?	?		fumarole on 34P13	52
66	?	?	?		caterer on 36P22	48
67	?	?	?		?	?
68	?	?	?		?	?
69	?	?	?		?	?
70	?	?	?		78P70	78
71	?	?	?		?	?
72	47P72	Robert Wainwright	1990		figure eight on 22P36	36
73	?	?	?		?	?
74	?	?	?		?	?
75	?	?	?		6 bits	49
76	?	?	?		?	?
77	?	?	?		77P77	77
78	?	?	?		p6 thumb on 34P13	61
79	?	?	?		?	?
80	?	?	?		fumarole on Rich's p16	52
81	?	?	?		?	?
82	?	?	?		?	?
83	?	?	?		?	?
84	?	?	?		52P84	52
85	?	?	?		?	?
86	?	?	?		?	?
87	?	?	?		84P87	84
88	P88 pi-heptomino hassler	Dean Hickerson	1994		figure eight on rattlesnake	45
89	?	?	?		?	?
90	?	?	?		fumarole on 43P18	61
91	?	?	?		?	?
92	?	?	?		twin bees shuttle on 22P4.3	50
93	?	?	?		caterer on 48P31	60
94	?	?	?		?	?
95	?	?	?		?	?
96	?	?	?		caterer on 68P32	80
97	?	?	?		?	?
98	?	?	?		?	?
99	?	?	?		?	?
100	Centinal	Bill Gosper	≤1987		centinal	70
104	?	?	?		figure eight on 34P13	46
105	?	?	?		pentadecathlon on 37P7.1	49
108	?	?	?		22P4.3 on 56P27	78
110	P110 traffic jam	Bill Gosper	1994		pseudo-barberpole on 36P22	51
120	?	?	?		figure eight on pentadecathlon	24
124	P124 lumps of muck hassler	Dean Hickerson	1994		mold on 48P31	60
132	P132 pi-heptomino hassler	David Buckingham	≤1994		?	?
135	106P135	Bill Gosper	1989		pentadecathlon on 56P27	68
138	?	?	?		Gabriel's p138	36
144	Achim's p144	Achim Flammenkamp	1994		Achim's p144	42
156	P156 Hans Leo hassler	Noam Elkies	1995		92P156	92
177	?	?	?		104P177	104
200	P200 traffic jam	Bill Gosper	1994		figure eight on centinal	82
312	period-tripled p104 gun	Dave Greene	2004		60P312	60

See also

• List of common oscillators
• List of oscillators
• Omniperiodic
• Oscillator periods status table

External links

• Oscillator at the Life Lexicon