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Revision as of 02:06, 29 May 2022

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 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, 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 87P26 87
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 No non-trivial examples found
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 Beluchenko's p37 124
38 44P38 David Raucci 2022 44P38 44
39 134P39.1 David Buckingham, Noam Elkies 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 p43 Snark loop 228
44 p44 pi-heptomino hassler David Buckingham 1992 mold on rattlesnake 45
45 pentadecathlon on snacker Mark Niemiec, John Conway ≤1995 pentadecathlon on thumb 1 48
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 30P3 on Rob's p16 51
49 p49 glider shuttle Noam Elkies 1999 p49 bumper loop 206
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 p54 shuttle 48
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 pre-pulsar shuttle 104
59 p59 Herschel loop 1 David Buckingham 1997 p59 Snark loop 228
60 p60 glider shuttle David Buckingham ≤ 1971 mold on pentadecathlon 24
61 p61 Herschel loop 1 David Buckingham 1996 p61 Snark loop 228
62 ? ? ? 66P62 66
63 ? ? ? meatball on p9 thumb 74
64 ? ? ? Merzenich's p64 34
65 ? ? ? fumarole on Beluchenko's p13 52
66 ? ? ? caterer on Jason's p22 48
67 ? ? ? p67 Snark loop 228
68 ? ? ? 72P68 72
69 ? ? ? p69 180° glider loop 146
70 ? ? ? fumarole on 34P14 shuttle 52
71 ? ? ? p71 Snark loop 228
72 two blockers hassling R-pentomino Robert Wainwright 1990 figure eight on 22P36 36
73 ? ? ? p73 Snark loop 228
74 p74 Herschel loop David Buckingham 1996 Raucci's p74 84
75 6 bits Robert Wainwright 1984 pentadecathlon on 30P25 46
76 ? ? ? mold on 44P38 56
77 ? ? ? meatball on rattlesnake 71
78 ? ? ? p6 thumb on Beluchenko's p13 61
79 ? ? ? p79 Snark loop 228
80 ? ? ? fumarole on Rob's p16 39
81 ? ? ? p81 180° glider loop 146
82 ? ? ? p82 Snark loop 208
83 ? ? ? p83 Snark loop 228
84 ? ? ? p84 honey farm hassler 42
85 ? ? ? 74P85 74
86 ? ? ? p86 Snark loop 208
87 ? ? ? 84P87 84
88 p88 glider loop David Buckingham 1992 figure eight on rattlesnake 45
89 ? ? ? p89 Snark loop 228
90 ? ? ? thumb 1 on queen bee shuttle 56
91 ? ? ? meatball on Beluchenko's p13 72
92 ? ? ? twin bees shuttle on 21P4.1 49
93 ? ? ? caterer on Merzenich's p31 60
94 capped AK-47 gun Dean Hickerson 1990 capped AK-94 110
95 ? ? ? p95 180° glider loop 166
96 ? ? ? period-48 glider gun with boat-bit 59
97 ? ? ? p97 Snark loop 228
98 ? ? ? Gallus 105
99 ? ? ? 48P9 on rattlesnake 82
100 centinal Bill Gosper ≤1987 mold on 30P25 42
101 ? ? ? p101 Snark loop 228
102 ? ? ? Raucci's p102 67
103 ? ? ? p103 Snark loop 228
104 ? ? ? figure eight on Beluchenko's p13 46
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 p110 traffic jam Bill Gosper 1994 pseudo-barberpole on Jason's p22 51
111 ? ? ? p111 rectifier loop 136
112 ? ? ? tumbler on Rich's p16 50
113 ? ? ? nihonium 106
114 ? ? ? caterer on 44P38 57
115 ? ? ? p115 rectifier loop 136
116 ? ? ? 102P116 102
117 ? ? ? 112P117 112
118 ? ? ? p118 rectifier loop 154
119 ? ? ? p119 rectifier loop 136
120 ? ? ? figure eight on pentadecathlon 24
124 p124 lumps of muck hassler Dean Hickerson 1994 mold on Merzenich's p31 60
126 ? ? ? snacker on 34P14 shuttle 74
128 ? ? ? p128 wing shuttle, p128 Coe-blocker loop 108
129 ? ? ? p129 180° glider loop 146
130 ? ? ? 55P10 on Beluchenko's p13 89
132 p132 glider loop David Buckingham 1992 mold on Jason's p33 72
135 106P135 Bill Gosper 1989 pentadecathlon on 56P27 68
136 ? ? ? p136 Coe-blocker loop 108
138 ? ? ? Gabriel's p138 36
140 p140 traffic jam Bill Gosper 1994 34P14 shuttle on dockyard 82
141 ? ? ? p47 pre-pulsar shuttle phase-shifting 28P7.1 114
143 ? ? ? p143 Bandersnatch loop 144
144 capped p144 gunstar David Buckingham 1990 Achim's p144 42
150 ? ? ? unix on 30P25 46
152 ? ? ? figure eight on 44P38 60
156 p156 traffic jam oscillator Bill Gosper 1994 p156 unix loop 86
165 ? ? ? rattlesnake on pentadecathlon 45
168 ? ? ? figure eight on 32P21 44
177 ? ? ? Karel's p177 104
184 ? ? ? figure eight on twin bees shuttle 40
186 ? ? ? unix on Merzenich's p31 64
188 ? ? ? AK-94 with boat-bits 108
196 ? ? ? p196 pi-heptomino hassler 66
200 p200 glider loop Bill Gosper ≤1987 figure eight on 30P25 42
226 ? ? ? nihonium* 107
230 ? ? ? fumarole on twin bees shuttle 46
231 ? ? ? rattlesnake on 32P21 66
232 ? ? ? figure eight on p29 pre-pulsar shuttle 66
240 ? ? ? pentadecathlon on Rob's p16 33
246 ? ? ? period-246 glider gun variant 68
256 ? ? ? p256 Coe-blocker loop 103
276 ? ? ? caterer on 50P92.1 62
300 ? ? ? pentadecathlon on centinal 88
312 ? ? ? 60P312 60
320 ? ? ? fumarole on Merzenich's p64 52
360 ? ? ? thumb 1 on Beluchenko's p40 62
368 ? ? ? period-184 glider gun with boat-bits 50
460 ? ? ? pseudo-barberpole on 50P92.1 65
492 ? ? ? period-246 glider gun with boat-bit 87
496 ? ? ? Rob's p16 on Merzenich's p31 69
512 ? ? ? period-256 glider gun with boat-bits 100
856 period-856 glider gun David Buckingham 1991 p856 Coe-blocker loop 103

Flipper

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

Notes

  1. ↑ 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

  1. ↑ Dean Hickerson's oscillator stamp collection. Retrieved on April 11, 2009.
  2. ↑ Jeremy Tan (July 3, 2021). Re: Smallest Known Oscillators to p106 (and Beyond) (discussion thread) at the ConwayLife.com forums

See also

Forum threads


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