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 59 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 mold on fire-spitting 31
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 cribbage Mitchell Riley 2023 cribbage 92
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 54P23 54
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 p26 honey farm hassler 60
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 42P38 42
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 208P41 Nico Brown 2023 p41 pi-heptomino hassler 170
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 bouncer loop Noam Elkies 1999 44P49 44
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 94P53 94
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 112P57 112
58 p58 toadsucker Bill Gosper 1994 p58 pi-heptomino hassler, 54p58 54
59 p59 Herschel loop 1 David Buckingham 1997 p59 pi-heptomino hassler 86
60 p60 glider shuttle ? ≤1971 mold on pentadecathlon 24
61 p61 Herschel loop 1 David Buckingham 1996 p61 pi-heptomino hassler 134
62 Herschel loop David Buckingham 1996 66P62 66
63 Herschel loop David Buckingham 1996 32P21 phase-shifting p5 64
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 century hassler 38
69 Herschel loop David Buckingham 1996 Grin reagent weld loading dock on 55P23 103
70 Herschel loop David Buckingham 1996 fumarole on 34P14 shuttle 52
71 Herschel loop David Buckingham 1996 p71 dependent reflector loop 92
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 p76 pi-heptomino shuttle 52
77 Herschel loop David Buckingham 1996 34P7 on rattlesnake 67
78 Herschel loop David Buckingham 1996 p6 thumb on Beluchenko's p13 61
79 Herschel loop David Buckingham 1996 p79 pi-heptomino hassler 80
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 lumps of muck hassler 48
83 Herschel loop David Buckingham 1996 62P83 62
84 pi orbital Noam Elkies 1995 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 p3 sparker 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 68
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 toaster variant on Cribbage 137
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 rattlesnake on 42P9 75
100 centinal Bill Gosper ≤1987 mold on 30P25 42
101 Herschel loop David Buckingham 1996 116P101 116
102 p102+18n traffic jam Dean Hickerson 1994 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 66P106 66
107 Herschel loop David Buckingham 1996 86P107 86
108 p54 shuttle on figure eight ? ≤1992 22P36 phase-shifting p5 54
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 fire-spitting on p37 lumps of muck hassler 91
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 42P38 54
115 Herschel loop David Buckingham 1996 92P115 92
116 p4 sparker on p29 pentadecathlon hassler Bill Gosper 1994 mold on p58 pi-heptomino hassler 68
117 Herschel loop David Buckingham 1996 Beluchenko's p13 on 42P9 76
118 Herschel loop David Buckingham 1996 86P118 86
119 Herschel loop David Buckingham 1996 72P119 72
120 p30n glider loop ? ≤1973 figure eight on pentadecathlon 24
122 Herschel loop David Buckingham 1996 p122 R-pentomino hassler 102
123 p123 R-pentomino hassler 116
124 p124 lumps of muck hassler Dean Hickerson 1994 mold on Merzenich's p31 60
126 p102+6n traffic jam Noam Elkies ≤1996 p126 R-pentomino hassler 52
127 Herschel loop David Buckingham 1996 74P127 74
128 spark-assisted p128 Herschel loop David Buckingham 1991 62P128 62
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
133 Herschel loop p133 B-heptomino hassler 84
135 106P135 Bill Gosper 1989 pentadecathlon on 56P27 68
136 p136 spark-assisted Herschel loop David Buckingham 1991 figure eight on p68 century hassler 50
138 p46n glider loop Bill Gosper 1971 Gabriel's p138 36
140 p100+10n traffic jam Bill Gosper 1994 p140 two-glider octomino hassler 58
141 Herschel loop David Buckingham 1996 fire-spitting on p47 pre-pulsar shuttle 103
143 Herschel loop David Buckingham 1996 p11 thumb on Beluchenko's p13 69
144 capped p144 gunstar David Buckingham 1990 Achim's p144 42
146 Herschel loop David Buckingham 1996 p146 pi-heptomino hassler 51
150 p30n glider loop ? ≤1973 unix on 30P25 46
152 p136+8n Herschel loop David Buckingham 1991 figure eight on 42P38 54
156 p152+4n Herschel loop David Buckingham 1991 unix on p52 LOM hassler 66
158 Herschel loop David Buckingham 1996 p158 pi-heptomino hassler 96
160 Herschel loop p160 pi-heptomino hassler 56
165 p165 glider shuttle Robert Wainwright ≤1989 rattlesnake on pentadecathlon 45
166 Herschel loop David Buckingham 1996 p166 R-pentomino hassler 102
171 Herschel loop David Buckingham 1996 p171 pi-heptomino hassler 128
177 p150+3n Herschel loop David Buckingham 1991 Karel's p177, Caterer on 92P59[4] 104
187 Herschel loop p187 century hassler 112
188 p94n glider loop Dean Hickerson 1990 mold on 54P94 68
192 Herschel loop 59P192 59
196 p152+4n Herschel loop David Buckingham 1991 mold on 44P49 56
199 Herschel loop David Buckingham 1996 84P199 84
200 p100n glider loop Bill Gosper ≤1987 figure eight on 30P25 42
201 Herschel loop Capped period-201 glider gun 98
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 unix on p82 lumps of muck hassler 64
256 spark-assisted p256 Herschel loop David Buckingham 1991 86P256 86
312 p136+8n Herschel loop David Buckingham 1991 60P312 60
368 p46n glider loop Bill Gosper 1971 period-184 glider gun with boat-bits 48
384 Herschel loop 49P384 49
492 p150+3n Herschel loop David Buckingham 1991 period-246 glider gun with boat-bit 87
856 capped period-856 glider gun David Buckingham 1991 p856 glider shuttle 92

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
  4. Period1GliderGun (July 12, 2023). Re: Smallest Known Oscillators to p106 (and Beyond) (discussion thread) at the ConwayLife.com forums

See also

External links

Forum threads