Oscillator

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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.

We make a distinction between "interesting" and "boring" oscillators: many true-period oscillators can be constructed or "engineered" from existing oscillator rotors interacting in some form (often from spark and/or thumb reactions), or via looping gliders or other spaceships in an existing circuit. While these are perfectly valid as oscillators, they are generally not regarded as particularly interesting due to their basic and systematic construction. We therefore have two sets of columns in the tables below to list both the absolute smallest oscillator of that period, alongside the smallest interesting oscillator for each.

Smallest known oscillators of each period

For non-trivial examples of the same population, we break minimum population ties by checking which has a lower average population, and, failing that, the lowest population's minimum bounding box.

Period Absolute Interesting
Smallest known Minimum # of cells Smallest known Minimum # of cells
2 blinker 3 blinker 3
3 caterer 12 caterer 12
4 mazing, mold 12 mold 12
5 pseudo-barberpole 15 pseudo-barberpole 15
6 unix 16 unix 16
7 28P7.1, 28P7.2, 28P7.3, burloaferimeter 28 burloaferimeter 28
8 figure eight 12 figure eight 12
9 29P9 29 29P9 29
10 24P10 24 24P10 24
11 rattlesnake 33 rattlesnake 33
12 dinner table 33 dinner table 33
13 Beluchenko's p13 34 Beluchenko's p13 34
14 tumbler 16 tumbler 16
15 pentadecathlon 12 pentadecathlon 12
16 Rob's p16 21 Rob's p16 21
17 honey thieves 36 honey thieves 36
18 p18 bi-block hassler 43 p18 bi-block hassler 43
19 None found
20 mold on fumarole 30 dockyard 48
21 caterer on 28P7.3 40 p21 honey farm hassler 60
22 Jason's p22 36 Jason's p22 36
23 David Hilbert 122 David Hilbert 122
24 caterer on figure eight 24 p24 shuttle 38
25 p25 pre-pulsar shuttle 83 p25 pre-pulsar shuttle 83
26 87P26 87 p26 pre-pulsar shuttle 144
27 56P27 56 56P27 56
28 mold on 34P14 shuttle 46 p28 pre-pulsar shuttle 53
29 p29 pre-pulsar shuttle 54 p29 pre-pulsar shuttle 54
30 queen bee shuttle 20 queen bee shuttle 20
31 Merzenich's p31 48 Merzenich's p31 48
32 gourmet 66 gourmet 66
33 caterer on rattlesnake 46 Jason's p33 60
34 No non-trivial examples found
35 p35 honey farm hassler 44 p35 honey farm hassler 44
36 22P36 22 22P36 22
37 Beluchenko's p37 124 Beluchenko's p37 124
38 None found
39 caterer on Beluchenko's p13 46 ?
40 Beluchenko's p40 26 Beluchenko's p40 26
41 None found
42 unix on 34P14 shuttle 50 p42 pulsar hassler 148
43 p43 Snark loop 228 ?
44 mold on rattlesnake 45 p44 pi-heptomino hassler 102
45 pentadecathlon on thumb 1 48 p45 pi-heptomino hassler 86
46 twin bees shuttle 28 twin bees shuttle 28
47 p47 pre-pulsar shuttle 84 p47 pre-pulsar shuttle 84
48 unix on Rich's p16 52 69P48 69
49 p49 bumper loop 206 p49 skewed pulsar hassler 784
50 p50 traffic jam 92 p50 traffic jam 92
51 90P51 90 Beluchenko's p51 112
52 four eaters hassling lumps of muck 35 four eaters hassling lumps of muck 35
53 p53 Snark loop 228 ?
54 p54 shuttle 48 p54 shuttle 48
55 pseudo-barberpole on rattlesnake 49 p55 pre-pulsar hassler 136
56 p56 B-heptomino shuttle 45 p56 B-heptomino shuttle 45
57 p57 bumper loop 152 ?
58 p58 pre-pulsar shuttle 104 p58 pre-pulsar shuttle 104
59 p59 Snark loop 228 ?
60 mold on pentadecathlon 24 two queen bee shuttles hassling blinker 33
61 p61 Snark loop 228 ?
62 110P62 110 110P62 110
63 snacker on 38P7.2 78 p63 skewed pulsar hassler 244
64 Merzenich's p64 34 Merzenich's p64 34
65 fumarole on Beluchenko's p13 52 p65 pre-pulsar shuttle 454
66 caterer on 36P22 48 p66 R-pentomino hassler 552
67 p67 Snark loop 228 ?
68 72P68 72 ?
69 p69 bumper loop 152 ?
70 fumarole on 34P14 shuttle 52 78P70 78
71 p71 Snark loop 228 ?
72 figure eight on 22P36 36 two blockers hassling R-pentomino 47
73 p73 Snark loop 228 ?
74 Raucci's p74 84 Raucci's p74 84
75 6 bits 49 ?
76 p76 pi-heptomino hassler 82 p76 pi-heptomino hassler 82
77 77P77 77 ?
78 p6 thumb on Beluchenko's p13 61 ?
79 p79 Snark loop 228 ?
80 fumarole on Rob's p16 39 two Beluchenko's p40s hassling blinker 59
81 p81 bumper loop 152 ?
82 p82 Snark loop 208 ?
83 p83 Snark loop 228 ?
84 52P84 52 52P84 52
85 74P85 74 ?
86 p86 Snark loop 208 ?
87 84P87 84 84P87 84
88 figure eight on rattlesnake 45 49P88 49
89 p89 Snark loop 228 ?
90 thumb 1 on queen bee shuttle 56 diuresis 66
91 44P7 on Beluchenko's p13 78 ?
92 50P92.1, twin bees shuttle on 22P4.3 50 50P92.1 50
93 caterer on Merzenich's p31 60 ?
94 capped AK-94 110 capped AK-94 110
95 p95 Snark loop 228 ?
96 p96 honey farm hassler 63 p96 honey farm hassler 63
97 p97 Snark loop 228 ?
98 Gallus 105 p98 R49 loop 146
99 48P9 on rattlesnake 82 ?
100 centinal 70 centinal 70
101 p101 Snark loop 228 ?
102 p102 bumper loop 126 two Beluchenko's p51s hassling beehive 249
103 p103 Snark loop 228 ?
104 figure eight on Beluchenko's p13 46 capped B-52 bomber 95
105 pentadecathlon on 37P7.1 49 ?
106 p106 rectifier loop 169 ?
107 p107 rectifier loop 136 ?
108 22P4.3 on 56P27 78 ?
109 p109 rectifier loop 156 ?
110 pseudo-barberpole on Jason's p22 51 ?
111 p111 rectifier loop 136 ?
112 tumbler on Rich's p16 50 ?
113 nihonium 106 nihonium 106
114 Ocellus 92 ?
115 p115 rectifier loop 136 ?
116 102P116 102 ?
117 117P117 117 capped period-117 glider gun 162
118 p118 rectifier loop 154 ?
119 p119 rectifier loop 136 ?
120 figure eight on pentadecathlon 24 capped Simkin glider gun 45
121 ? ? ? ?
122 ? ? p122 L122p2 loop 184
123 ? ? ? ?
124 mold on Merzenich's p31 60 p124 lumps of muck hassler 144
125 ? ? ? ?
126 snacker on 34P14 shuttle 74 ? ?
127 ? ? ? ?
128 ? ? ? ?
129 p129 bumper loop 152 ?
130 55P10 on Beluchenko's p13 89 p130 shuttle 124
131 ? ? ? ?
132 mold on Jason's p33 72 p132 pi-heptomino hassler 132
133 ? ? ? ?
134 ? ? ? ?
135 pentadecathlon on 56P27 68 ?
136 ? ? ? ?
137 ? ? ? ?
138 Gabriel's p138 36 Gabriel's p138 36
139 ? ? ? ?
140 34P14 shuttle on dockyard 82 ? ?
141 p47 pre-pulsar shuttle phase-shifting 28P7.1 114 p47 pre-pulsar shuttle phase-shifting 28P7.1 114
142 ? ? ? ?
143 ? ? ? ?
144 Achim's p144 42 Achim's p144 42
150 p150 buckaroo shuttle 51 ? ?
152 figure eight on p76 pi-heptomino hassler 94 ? ?
156 Jason's p156 92 Jason's p156 92
165 rattlesnake on pentadecathlon 45 ? ?
168 figure eight on p21 honey farm hassler 72 pi orbital 197
177 Karel's p177 104 Karel's p177 104
184 figure eight on twin bees shuttle 40 capped period-184 glider gun 50
186 unix on Merzenich's p31 64 ? ?
188 AK-94 with boat-bits 108 AK-94 with boat-bits 108
196 p196 pi-heptomino hassler 66 p196 pi-heptomino hassler 66
200 figure eight on centinal 82 ?
217 p217 rectifier loop 116 Raucci's p217 236
226 nihonium* 107 nihonium* 107
230 fumarole on twin bees shuttle 46 ?
240 pentadecathlon on Rob's p16 33 Simkin glider gun with boat-bits 43
246 period-246 glider gun relative 68 period-246 glider gun relative 68
256 capped period-256 glider gun 104 capped period-256 glider gun 104
276 two Gabriel's p138s hassling block 76 two Gabriel's p138s hassling block 76
300 pentadecathlon on centinal 88 ? ?
312 60P312 60 60P312 60
320 fumarole on Merzenich's p64 52 ? ?
360 thumb 1 on Beluchenko's p40 62 capped period-360 glider gun 108
368 period-184 glider gun with boat-bits 50 period-184 glider gun with boat-bits 50
486 ? ? p486 R-pentomino hassler 142
492 period-246 glider gun with boat-bit 87 period-246 glider gun with boat-bit 87
496 Rob's p16 on Merzenich's p31 69 ? ?
504 R126 loop 111 R126 loop 111
512 period-256 glider gun with boat-bits 100 period-256 glider gun with boat-bits 100
576 ? ? p576 R-pentomino hassler 184
808 p808 bouncer/bumper loop 120 ?
856 p856 bouncer/bumper loop 120 ?
2700 p2700 glider shuttle 29 Crystallization and decay oscillator 144
15240 p15240 glider shuttle 67 ?
40894 p40894 rectifier loop 123 ?

First known oscillators of each period

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 Absolute Interesting
First discovered Discoverer Year of discovery First discovered Discoverer Year of discovery
2 blinker John Conway 1970 blinker John Conway 1970
3 pulsar John Conway 1970 pulsar John Conway 1970
4 pinwheel Simon Norton 1970 pinwheel Simon Norton 1970
5 octagon 2 Sol Goodman, Arthur Taber 1971 octagon 2 Sol Goodman, Arthur Taber 1971
6 $rats David Buckingham 1972 $rats David Buckingham 1972
7 burloaferimeter David Buckingham 1972 burloaferimeter David Buckingham 1972
8 figure eight Simon Norton 1970 figure eight Simon Norton 1970
9 worker bee David Buckingham 1972 worker bee David Buckingham 1972
10 42P10.3 David Buckingham 1976 42P10.3 David Buckingham 1976
11 38P11.1 David Buckingham 1977 38P11.1 David Buckingham 1977
12 dinner table Robert Wainwright 1972 dinner table Robert Wainwright 1972
13 Buckingham's p13 David Buckingham 1976 Buckingham's p13 David Buckingham 1976
14 tumbler George Collins 1970 tumbler George Collins 1970
15 pentadecathlon John Conway 1970 pentadecathlon John Conway 1970
16 two pre-L hasslers Robert Wainwright 1983 two pre-L hasslers Robert Wainwright 1983
17 54P17.1 Dean Hickerson 1997 54P17.1 Dean Hickerson 1997
18 117P18[note 1] David Buckingham 1991 117P18 David Buckingham 1991
19 None found
20 145P20[note 1] Noam Elkies 1995 145P20 Noam Elkies 1995
21 124P21[note 1] Robert Wainwright 1995 124P21 Robert Wainwright 1995
22 168P22.1 Noam Elkies 1997 168P22.1 Noam Elkies 1997
23 David Hilbert Luka Okanishi, Aidan F. Pierce 2019 David Hilbert Luka Okanishi, Aidan F. Pierce 2019
24 186P24[note 1] Bill Gosper 1994 186P24 Bill Gosper 1994
25 134P25 Noam Elkies 1994 134P25 Noam Elkies 1994
26 p26 pre-pulsar shuttle David Buckingham 1983 p26 pre-pulsar shuttle David Buckingham 1983
27 123P27.1 Noam Elkies 2002 123P27.1 Noam Elkies 2002
28 newshuttle David Buckingham 1973 newshuttle David Buckingham 1973
29 p29 pre-pulsar shuttle David Buckingham 1980 p29 pre-pulsar shuttle David Buckingham 1980
30 queen bee shuttle Bill Gosper 1970 queen bee shuttle Bill Gosper 1970
31 Merzenich's p31 Matthias Merzenich 2010 Merzenich's p31 Matthias Merzenich 2010
32 gourmet David Buckingham 1978 gourmet David Buckingham 1978
33 258P3 on Achim's p11 Noam Elkies, Achim Flammenkamp 1997 Jason's p33 Jason Summers 2000
34 No non-trivial examples found
35 p35 beehive hassler[note 1] Dean Hickerson 1995 p35 beehive hassler Dean Hickerson 1995
36 p36 toad hassler[note 1] Robert Wainwright 1984 p36 toad hassler Robert Wainwright 1984
37 Beluchenko's p37 Nicolay Beluchenko 2009 Beluchenko's p37 Nicolay Beluchenko 2009
38 None found
39 134P39.1 David Buckingham, Noam Elkies 2000 ? ? ?
40 p40 B-heptomino shuttle[note 1] David Buckingham 1991 p40 B-heptomino shuttle David Buckingham 1991
41 None found
42 p42 glider shuttle[note 1] Noam Elkies 1994 ? ? ?
43 p43 Snark loop Mike Playle 2013 ? ? ?
44 p44 pi-heptomino hassler David Buckingham 1992 p44 pi-heptomino hassler David Buckingham 1992
45 pentadecathlon on snacker ? 1995 Capped period-45 glider gun Matthias Merzenich 2010
46 twin bees shuttle Bill Gosper 1971 twin bees shuttle Bill Gosper 1971
47 p47 pre-pulsar shuttle David Buckingham 1982 p47 pre-pulsar shuttle David Buckingham 1982
48 p48 toad hassler Bill Gosper 1994 p48 toad hassler Bill Gosper 1994
49 p49 glider shuttle Noam Elkies 1999 p49 glider shuttle Noam Elkies 1999
50 p50 glider shuttle Dean Hickerson 1992 p50 traffic jam Noam Elkies 1994
51 Beluchenko's p51 Nicolay Beluchenko 2009 Beluchenko's p51 Nicolay Beluchenko 2009
52 Four eaters hassling lumps of muck David Buckingham 1977 Four eaters hassling lumps of muck David Buckingham 1977
53 p53 Snark loop Mike Playle 2013 ? ? ?
54 p54 shuttle David Buckingham 1973 p54 shuttle David Buckingham 1973
55 p55 pre-pulsar hassler David Buckingham 1986 p55 pre-pulsar hassler David Buckingham 1986
56 p56 B-heptomino shuttle[note 1] David Buckingham 1991 p56 B-heptomino shuttle David Buckingham 1991
57 p57 Herschel loop 1 Dietrich Leithner 1997 Capped period-57 glider gun David Raucci 2021
58 p58 toadsucker Bill Gosper 1994 p58 toadsucker Bill Gosper 1994
59 p59 Herschel loop 1 David Buckingham 1997 ? ? ?
60 p60 glider shuttle David Buckingham 1971 ? ? ?
61 p61 Herschel loop 1 David Buckingham 1996 ? ? ?
62 ? ? ? 110P62 Noam Elkies 2010
63 ? ? ? p63 skewed pulsar hassler David Raucci 2021
64 ? ? ? Merzenich's p64 Matthias Merzenich 2010
65 ? ? ? p65 pre-pulsar shuttle David Raucci 2021
66 ? ? ? p66 R-pentomino hassler David Raucci 2021
72 two blockers hassling R-pentomino Robert Wainwright 1990 two blockers hassling R-pentomino Robert Wainwright 1990
74 p74 Herschel loop David Buckingham 1996 p74 honey farm hassler David Raucci 2021
75 6 bits Robert Wainwright 1984 6 bits Robert Wainwright 1984
76 ? ? ? p76 pi-heptomino hassler David Raucci 2021
80 Achim's other p16 on middleweight volcano Dean Hickerson 1994 ? ? ?
84 ? ? ? 52P84 Jason Summers 2007
88 p88 glider loop David Buckingham 1992 Period-doubled p44 pi-heptomino hassler Dean Hickerson 1994
90 ? ? ? ? ? ?
92 Capped period-92 glider gun Dean Hickerson 1991 Capped period-92 glider gun Dean Hickerson 1991
94 capped AK-47 gun Dean Hickerson 1990 capped AK-47 gun Dean Hickerson 1990
96 p96 Hans Leo hassler Noam Elkies 1995 p96 Hans Leo hassler Noam Elkies 1995
100 centinal Bill Gosper 1987 centinal Bill Gosper 1987
104 ? ? ? B-52 bomber Noam Elkies 1996
105 44P7.2 on pentadecathlon ? ? ? ? ?
108 Period-108 toadsucker/toadflipper David Buckingham 1992 ? ? ?
110 p110 traffic jam Bill Gosper 1994 p110 traffic jam Bill Gosper 1994
117 ? ? ? Capped period-117 glider gun David Raucci 2021
120 ? ? ? ? ? ?
124 p124 lumps of muck hassler Dean Hickerson 1994 p124 lumps of muck hassler Dean Hickerson 1994
128 R64 variant using p8 oscillators David Buckingham 1991 ? ? ?
130 ? ? ? p130 shuttle David Eppstein 2001
132 p132 glider loop David Buckingham 1992 ? ? ?
135 106P135 Bill Gosper 1989 106P135 Bill Gosper 1989
138 ? ? ? ? ? ?
144 capped p144 gunstar David Buckingham 1990 ? ? ?
147 ? ? ? p147 honey farm hassler David Raucci 2021
150 ? ? ? ? ? ?
156 p156 traffic jam oscillator Bill Gosper 1994 p156 Hans Leo hassler Noam Elkies 1995
165 p165 glider shuttle Robert Wainwright 1989 ? ? ?
168 ? ? ? Pi orbital Noam Elkies 1995
177 ? ? ? Karel's p177 Karel Suhadja 2007
184 Stop and go Dean Hickerson 1992 ? ? ?
188 Period-doubled AK-94 Multiple 1994 ? ? ?
196 ? ? ? p196 pi-heptomino hassler David Raucci 2021
200 p200 glider loop Bill Gosper 1987 p200 traffic jam Bill Gosper 1994
217 ? ? ? Raucci's p217 David Raucci 2021
230 p230 glider shuttle Dean Hickerson 1992 ? ? ?
246 p246 glider shuttle Dean Hickerson 1992 ? ? ?
256 ? ? ? ? ? ?
276 ? ? ? ? ? ?
282 p282 glider shuttle Bill Gosper 1992 ? ? ?
300 centinal on pentadecathlon Mark Niemiec 1994 ? ? ?
312 ? ? ? 60P312 Dave Greene 2004
329 44P7.2 on p47 pre-pulsar shuttle ? ? ? ? ?
360 ? ? ? Period-360 glider gun David Buckingham 1992
368 ? ? ? ? ? ?
486 ? ? ? p486 R-pentomino hassler David Raucci 2021
504 ? ? ? R126 loop ? ?
576 ? ? ? p576 R-pentomino hassler David Raucci 2021
808 p808 glider gun David Buckingham <1992 ? ? ?
856 p856 glider gun David Buckingham <1992 ? ? ?
2700 ? ? ? crystallization and decay oscillator Dean Hickerson 1990
15240 ? ? ? p120-based PRNG Dean Hickerson 1992
40894 ? ? ? p46-based PRNG Dean Hickerson 1995

Notes

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 An oscillator of this period can also be constructed from two sparkers 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.

See also

External links

Forum threads


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