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,[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 (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 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.

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 dinner table, caterer on 21P4.1 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 55P23 55
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 p43 pi-heptomino hassler[3] 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 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 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 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 p68 pi-heptomino hassler 71
69 Herschel loop David Buckingham 1996 caterer on 92P23 106
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 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 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 pi-heptomino hassler 82
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 76P86 76
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 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 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 54P94 54
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 transparent long boat glider loop 164
98 Herschel loop David Buckingham 1996 Gallus, p98 glider shuttle 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 transparent long boat glider loop 160
102 p102+6n traffic jam Noam Elkies ≤1996 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 115P106 115
107 Herschel loop David Buckingham 1996 p107 rectifier loop 136
108 p54 shuttle on figure eight ? ≤1992 mold on p54 R-pentomino hassler 55
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 86P113 86
114 p66+24n glider shuttle Robert Wainwright 1984 caterer on 44P38 57
115 Herschel loop David Buckingham 1996 93P115 93
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 80P128 80
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 34P20, 34P7 on 34P20 68
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 54P94 68
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 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 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

  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
  3. Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums

See also

External links

Forum threads