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 and a stator.

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 glider or spaceship. Strictly speaking "glider" means the little figure so prevalent in Conway's Game of Life, but the more general usage has now become popular.

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. In April, 2013 Mike Playle found a small 90-degree stable reflector that allows oscillators of all periods 43 or greater to be constructed.

Period First discovered Discoverer Year of discovery
2 blinker John Conway 1970
3 pulsar John Conway 1970
4 pinwheel Simon Norton 1970
5 octagon 2 Sol Goodman, Arthur Taber 1971
6 $rats David Buckingham 1972
7 burloaferimeter David Buckingham 1972
8 figure eight Simon Norton 1970
9 worker bee David Buckingham 1972
10 42P10.1 David Buckingham 1976
11 38P11.1 David Buckingham 1977
12 dinner table Robert Wainwright 1972
13 65P13.1 David Buckingham 1976
14 tumbler George Collins, Jr. 1970
15 pentadecathlon John Conway 1970
16 two pre-L hasslers Robert Wainwright 1983
17 54P17.1 Dean Hickerson 1997
18 117P18 David Buckingham 1991
19 None found
20 145P20 Noam Elkies 1995
21 124P21 Robert Wainwright 1995
22 168P22.1 Noam Elkies 1997
23 None found
24 186P24 Bill Gosper 1994
25 134P25 Noam Elkies 1994
26 pre-pulsar shuttle 26 David Buckingham 1983
27 123P27.1 Noam Elkies 2002
28 Newshuttle David Buckingham 1973
29 pre-pulsar shuttle 29 David Buckingham 1980
30 queen bee shuttle Bill Gosper 1970
31 48P31 Matthias Merzenich 2010
32 gourmet David Buckingham 1978
33 258P3 on Achim's p11 Noam Elkies, Achim Flammenkamp 1997
34 No non-trivial examples found
35 P35 beehive hassler Dean Hickerson 1995
36 P36 toad hassler Robert Wainwright 1984
37 124P37 Nicolay Beluchenko 2009
38 None found
39 134P39.1 David Buckingham, Noam Elkies 2000
40 P40 B-heptomino shuttle David Buckingham ≤1991
41 None found
42 P42 glider shuttle Noam Elkies 1994
43 P43 glider shuttle Mike Playle 2013
44 P44 pi-heptomino hassler David Buckingham 1992
45 pentadecathlon on snacker  ? ≤1995
46 twin bees shuttle Bill Gosper 1971
47 pre-pulsar shuttle 47 David Buckingham 1982
48 P48 toad hassler Bill Gosper 1994
49 p49 glider shuttle Noam Elkies 1999
50 P50 glider shuttle Dean Hickerson 1992
51 112P51 Nicolay Beluchenko 2009
52 35P52 David Buckingham 1977
53 P53 glider shuttle Mike Playle 2013
54 P54 shuttle David Buckingham 1974
55 pre-pulsar hassler 55 David Buckingham 1986
56 P56 B-heptomino shuttle David Buckingham ≤1991
57 P57 Herschel loop 1 Dietrich Leithner 1997
58 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
72 47P72 Robert Wainwright 1990
88 P88 pi-heptomino hassler Dean Hickerson 1994
100 Centinal Bill Gosper 1987
110 P110 traffic jam Bill Gosper 1994
124 P124 lumps of muck hassler Dean Hickerson 1994
132 P132 pi-heptomino hassler David Buckingham ≤1994
144 Achim's p144 Achim Flammenkamp 1994
156 P156 Hans Leo hassler Noam Elkies 1995
200 P200 traffic jam Bill Gosper 1994
Period Smallest known Minimum # of cells
2 blinker 3
3 caterer 12
4 mazing, mold 12
5 pseudo-barberpole 15
6 unix 16
7 28P7.1, 28P7.2, burloaferimeter 28
8 figure eight 12
9 29P9 29
10 24P10 24
11 38P11.1 38
12 dinner table 33
13 34P13 34
14 tumbler 16
15 pentadecathlon 12
16 Achim's p16 32
17 54P17.1 54
18 43P18 43
19 None found
20 mold on fumarole 30
21 caterer on 44P7.2 56
22 36P22 36
23 None found
24 caterer on figure eight 24
25 p25 honey farm hassler 93
26 p26 glider shuttle 148
27 56P27 56
28 mold on 41P7.2 53
29 pre-pulsar shuttle 29 54
30 queen bee shuttle 20
31 48P31 48
32 gourmet 66
33 60P33 60
34 No non-trivial examples found
35 50P35 50
36 22P36 22
37 124P37 124
38 None found
39 caterer on 34P13 46
40 26P40 26
41 None found
42 unix on 41P7.2 57
43 P43 glider shuttle 228
44 mold on 36P22 50
45 pentadecathlon on thumb 1 48
46 twin bees shuttle 28
47 pre-pulsar shuttle 47 84
48 69P48 69
49 p49 glider shuttle 228
50 P50 traffic jam 92
51 112P51 112
52 35P52 35
53 P53 glider shuttle 228
54 P54 shuttle 48
55 fumarole on Achim's p11 90
56 P56 B-heptomino shuttle 45
57 P57 glider shuttle 228
58 P58 glider shuttle 208
59 P59 glider shuttle 228
60 mold on pentadecathlon 24
61 P61 glider shuttle 228
63 snacker on 38P7.2 78
65 fumarole on 34P13 52
66 caterer on 36P22 48
70 78P70 78
72 47P72 47
75 6 bits 49
88 49P88 49
90 fumarole on 43P18 61
96 caterer on 68P32 80
99 extended snacker on Achim's p11 124
100 centinal 70
104 figure eight on 34P13 46
105 pentadecathlon on 37P7.1 49
108 T-nosed p4 on 56P27 87
110 pseudo-barberpole on 36P22 51
120 figure eight on pentadecathlon 24
138 Gabriel's p138 36
144 Achim's p144 42
156 92P156 92
177 104P177 104
312 60P312 60

See also

External links

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