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. 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.
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
|
33
|
12
|
dinner table
|
Robert Wainwright
|
1972
|
dinner table
|
33
|
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
|
None found
|
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
|
p23 honey farm hassler
|
76
|
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
|
70P26
|
70
|
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
|
44P38
|
44
|
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
|
None found
|
42
|
p42 glider shuttle[note 1]
|
Noam Elkies
|
1994
|
unix on 34P14 shuttle
|
50
|
43
|
p43 Snark loop
|
Mike Playle
|
2013
|
Capped period-43 glider gun
|
80
|
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 glider shuttle
|
Noam Elkies
|
1999
|
p49 R-pentomino hassler
|
158
|
50
|
p50 glider shuttle
|
Dean Hickerson
|
1992
|
24P10 on 30P25
|
58
|
51
|
Beluchenko's p51
|
Nicolay Beluchenko
|
2009
|
90P51
|
90
|
52
|
Four eaters hassling lumps of muck
|
David Buckingham
|
1977
|
four eaters hassling lumps of muck
|
35
|
53
|
p53 Snark loop
|
Mike Playle
|
2013
|
p53 Snark loop
|
228
|
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
|
p57 180° glider loop
|
146
|
58
|
p58 toadsucker
|
Bill Gosper
|
1994
|
p58 pi-heptomino hassler
|
54
|
59
|
p59 Herschel loop 1
|
David Buckingham
|
1997
|
108P59
|
108
|
60
|
p60 glider shuttle
|
?
|
≤1971
|
mold on pentadecathlon
|
24
|
61
|
p61 Herschel loop 1
|
David Buckingham
|
1996
|
p61 Snark loop
|
228
|
62
|
Herschel loop
|
David Buckingham
|
1996
|
66P62
|
66
|
63
|
Herschel loop
|
David Buckingham
|
1996
|
34P7 on p9 thumb
|
74
|
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
|
72P68
|
72
|
69
|
Herschel loop
|
David Buckingham
|
1996
|
p69 180° glider loop
|
146
|
70
|
Herschel loop
|
David Buckingham
|
1996
|
fumarole on 34P14 shuttle
|
52
|
71
|
Herschel loop
|
David Buckingham
|
1996
|
p71 honey farm hassler
|
112
|
72
|
two blockers hassling R-pentomino
|
Robert Wainwright
|
1990
|
figure eight on 22P36
|
36
|
73
|
Herschel loop
|
David Buckingham
|
1996
|
p73 Snark loop
|
228
|
74
|
Herschel loop
|
David Buckingham
|
1996
|
Raucci's p74
|
84
|
75
|
6 bits
|
Robert Wainwright
|
1984
|
pentadecathlon on 30P25
|
46
|
76
|
Herschel loop
|
David Buckingham
|
1996
|
mold on 44P38
|
56
|
77
|
Herschel loop
|
David Buckingham
|
1996
|
34P7 on rattlesnake
|
71
|
78
|
Herschel loop
|
David Buckingham
|
1996
|
p6 thumb on Beluchenko's p13
|
61
|
79
|
Herschel loop
|
David Buckingham
|
1996
|
p79 Snark loop
|
228
|
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 pi-heptomino hassler
|
114
|
83
|
Herschel loop
|
David Buckingham
|
1996
|
62P83
|
62
|
84
|
caterer on p28 pre-pulsar shuttle variant
|
?
|
≤1994
|
p84 honey farm hassler
|
42
|
85
|
Herschel loop
|
David Buckingham
|
1996
|
p85 R-pentomino hassler
|
68
|
86
|
Herschel loop
|
David Buckingham
|
1996
|
Boat-bitted period-43 glider gun
|
78
|
87
|
caterer 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
|
p89 Snark loop
|
228
|
90
|
p30n glider loop
|
?
|
≤1973
|
unix on p45 pi-heptomino hassler
|
45
|
91
|
Herschel loop
|
David Buckingham
|
1996
|
34P7 on Beluchenko's p13
|
72
|
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
|
p94 R-pentomino hassler
|
68
|
95
|
Herschel loop
|
David Buckingham
|
1996
|
p95 180° glider loop
|
166
|
96
|
p96 Hans Leo hassler
|
Noam Elkies
|
1995
|
period-48 glider gun with boat-bit
|
59
|
97
|
Herschel loop
|
David Buckingham
|
1996
|
p97 Snark loop
|
228
|
98
|
Herschel loop
|
David Buckingham
|
1996
|
Gallus
|
105
|
99
|
Herschel loop
|
David Buckingham
|
1996
|
48P9 on rattlesnake
|
82
|
100
|
centinal
|
Bill Gosper
|
≤1987
|
mold on 30P25
|
42
|
101
|
Herschel loop
|
David Buckingham
|
1996
|
p101 Snark loop
|
228
|
102
|
p102+6n traffic jam
|
Noam Elkies
|
≤1996
|
Raucci's p102
|
67
|
103
|
Herschel loop
|
David Buckingham
|
1996
|
p103 Snark loop
|
228
|
104
|
p100+4n traffic jam
|
Bill Gosper
|
1994
|
figure eight on Beluchenko's p13
|
46
|
105
|
pentadecathlon on 44P7.2
|
?
|
≤1992
|
pentadecathlon on 37P7.1
|
49
|
106
|
Herschel loop
|
David Buckingham
|
1996
|
p106 rectifier loop
|
169
|
107
|
Herschel loop
|
David Buckingham
|
1996
|
p107 rectifier loop
|
136
|
108
|
p54 shuttle on figure eight
|
?
|
≤1992
|
22P4.3 on 56P27
|
78
|
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
|
? on 58P37
|
97
|
112
|
p100+4n traffic jam
|
Bill Gosper
|
1994
|
tumbler on Rich's p16
|
50
|
113
|
Herschel loop
|
David Buckingham
|
1996
|
nihonium
|
106
|
114
|
p66+24n glider shuttle
|
Robert Wainwright
|
1984
|
caterer on 44P38
|
57
|
115
|
Herschel loop
|
David Buckingham
|
1996
|
p115 rectifier loop
|
136
|
116
|
p100+4n traffic jam
|
Bill Gosper
|
1994
|
102P116
|
102
|
117
|
Herschel loop
|
David Buckingham
|
1996
|
112P117
|
112
|
118
|
Herschel loop
|
David Buckingham
|
1996
|
p118 rectifier loop
|
154
|
119
|
Herschel loop
|
David Buckingham
|
1996
|
p119 rectifier loop
|
136
|
120
|
p30n glider loop
|
?
|
≤1973
|
figure eight on pentadecathlon
|
24
|
124
|
p124 lumps of muck hassler
|
Dean Hickerson
|
1994
|
mold on Merzenich's p31
|
60
|
126
|
p102+6n traffic jam
|
Noam Elkies
|
≤1996
|
snacker on 34P14 shuttle
|
74
|
127
|
Herschel loop
|
David Buckingham
|
1996
|
74P127
|
74
|
128
|
spark-assisted p128 Herschel loop
|
David Buckingham
|
1991
|
p128 glider shuttle
|
92
|
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
|
135
|
106P135
|
Bill Gosper
|
1989
|
pentadecathlon on 56P27
|
68
|
136
|
p136 spark-assisted Herschel loop
|
David Buckingham
|
1991
|
p136 glider shuttle
|
92
|
138
|
p46n glider loop
|
Bill Gosper
|
1971
|
Gabriel's p138
|
36
|
140
|
p100+10n traffic jam
|
Bill Gosper
|
1994
|
34P14 shuttle on dockyard
|
82
|
141
|
Herschel loop
|
David Buckingham
|
1996
|
p47 pre-pulsar shuttle phase-shifting 28P7.1
|
114
|
143
|
Herschel loop
|
David Buckingham
|
1996
|
rattlesnake on 66P13
|
99
|
144
|
capped p144 gunstar
|
David Buckingham
|
1990
|
Achim's p144
|
42
|
146
|
Herschel loop
|
David Buckingham
|
1996
|
p146 pi-heptomino hassler
|
52
|
150
|
p30n glider loop
|
?
|
≤1973
|
unix on 30P25
|
46
|
152
|
p136+8n Herschel loop
|
David Buckingham
|
1991
|
figure eight on 44P38
|
60
|
156
|
p152+4n Herschel loop
|
David Buckingham
|
1991
|
p156 unix loop
|
86
|
165
|
p165 glider shuttle
|
Robert Wainwright
|
≤1989
|
rattlesnake on pentadecathlon
|
45
|
166
|
Herschel loop
|
David Buckingham
|
1996
|
p166 R-pentomino hassler
|
102
|
177
|
p150+3n Herschel loop
|
David Buckingham
|
1991
|
Karel's p177
|
104
|
188
|
p94n glider loop
|
Dean Hickerson
|
1990
|
mold on p94 R-pentomino hassler
|
80
|
196
|
p152+4n Herschel loop
|
David Buckingham
|
1991
|
p196 pi-heptomino hassler
|
66
|
199
|
Herschel loop
|
David Buckingham
|
1996
|
84P199
|
84
|
200
|
p100n glider loop
|
Bill Gosper
|
≤1987
|
figure eight on 30P25
|
42
|
220
|
p100+4n traffic jam
|
Bill Gosper
|
1994
|
p220 honey farm shuttle
|
74
|
226
|
Herschel loop
|
David Buckingham
|
1996
|
nihonium*
|
107
|
232
|
figure eight on p29 pre-pulsar shuttle
|
?
|
?
|
figure eight on p29 pre-pulsar shuttle
|
66
|
246
|
p246 glider shuttle
|
Dean Hickerson
|
1992
|
period-246 glider gun variant
|
68
|
256
|
spark-assisted p256 Herschel loop
|
David Buckingham
|
1991
|
p256 glider shuttle
|
92
|
312
|
p136+8n Herschel loop
|
David Buckingham
|
1991
|
60P312
|
60
|
368
|
p46n glider loop
|
Bill Gosper
|
1971
|
period-184 glider gun with boat-bits
|
50
|
492
|
p150+3n Herschel loop
|
David Buckingham
|
1991
|
period-246 glider gun with boat-bit
|
87
|
856
|
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.
Notes
References
See also
External links
Forum threads