# Oscillator

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. 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* | David Buckingham | ≤1991 | p18 bi-block hassler | 43 | |

19 | None found | |||||

20 | 145P20* | Noam Elkies | 1995 | mold on fumarole | 30 | |

21 | 124P21* | Robert Wainwright | 1995 | caterer on 28P7.3 | 40 | |

22 | 168P22.1 | Noam Elkies | 1997 | Jason's p22 | 36 | |

23 | David Hilbert | Luka Okanishi, Aidan F. Pierce | 2019 | David Hilbert | 122 | |

24 | 186P24* | Bill Gosper | 1994 | caterer on figure eight | 24 | |

25 | 134P25 | Noam Elkies | 1994 | p25 honey farm hassler | 88 | |

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 | gourmet | 66 | |

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* | Dean Hickerson | 1995 | p35 honey farm hassler | 44 | |

36 | p36 toad hassler* | Robert Wainwright | 1984 | 22P36 | 22 | |

37 | Beluchenko's p37 | Nicolay Beluchenko | 2009 | Beluchenko's p37 | 124 | |

38 | None found | |||||

39 | 134P39.1 | David Buckingham, Noam Elkies | 2000 | caterer on Beluchenko's p13 | 46 | |

40 | p40 B-heptomino shuttle* | David Buckingham | ≤1991 | Beluchenko's p40 | 26 | |

41 | None found | |||||

42 | p42 glider shuttle* | Noam Elkies | 1994 | unix on 34P14 shuttle | 50 | |

43 | p43 glider loop | Mike Playle | 2013 | p43 glider loop | 228 | |

44 | p44 pi-heptomino hassler | David Buckingham | 1992 | mold on rattlesnake | 45 | |

45 | pentadecathlon on snacker | ? | ≤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 | unix on Rich's p16 | 52 | |

49 | p49 glider shuttle | Noam Elkies | 1999 | p49 bumper loop | 206 | |

50 | p50 glider shuttle | Dean Hickerson | 1992 | p50 traffic jam | 92 | |

51 | Beluchenko's p51 | Nicolay Beluchenko | 2009 | 92P51 | 92 | |

52 | Four eaters hassling lumps of muck | David Buckingham | 1977 | Four eaters hassling lumps of muck | 35 | |

53 | p53 glider loop | Mike Playle | 2013 | p53 glider 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* | David Buckingham | ≤1991 | p56 B-heptomino shuttle | 45 | |

57 | p57 Herschel loop 1 | Dietrich Leithner | 1997 | p57 bumper loop | 152 | |

58 | p58 toadsucker | Bill Gosper | 1994 | p58 pre-pulsar shuttle | 104 | |

59 | p59 Herschel loop 1 | David Buckingham | 1997 | p59 glider loop | 228 | |

60 | p60 glider shuttle | David Buckingham | ≤ 1971 | mold on pentadecathlon | 24 | |

61 | p61 Herschel loop 1 | David Buckingham | 1996 | p61 glider loop | 228 | |

62 | ? | ? | ? | 110P62 | 110 | |

63 | ? | ? | ? | snacker on 38P7.2 | 78 | |

64 | ? | ? | ? | Merzenich's p64 | 34 | |

65 | ? | ? | ? | fumarole on Beluchenko's p13 | 52 | |

66 | ? | ? | ? | caterer on 36P22 | 48 | |

67 | ? | ? | ? | ? | ? | |

68 | ? | ? | ? | ? | ? | |

69 | ? | ? | ? | ? | ? | |

70 | ? | ? | ? | fumarole on 34P14 shuttle | 52 | |

71 | ? | ? | ? | ? | ? | |

72 | two blockers hassling R-pentomino | Robert Wainwright | 1990 | figure eight on 22P36 | 36 | |

73 | ? | ? | ? | ? | ? | |

74 | ? | ? | ? | ? | ? | |

75 | ? | ? | ? | 6 bits | 49 | |

76 | ? | ? | ? | ? | ? | |

77 | ? | ? | ? | 77P77 | 77 | |

78 | ? | ? | ? | p6 thumb on Beluchenko's p13 | 61 | |

79 | ? | ? | ? | ? | ? | |

80 | ? | ? | ? | fumarole on Rob's p16 | 39 | |

81 | ? | ? | ? | ? | ? | |

82 | ? | ? | ? | ? | ? | |

83 | ? | ? | ? | ? | ? | |

84 | ? | ? | ? | 52P84 | 52 | |

85 | ? | ? | ? | ? | ? | |

86 | ? | ? | ? | ? | ? | |

87 | ? | ? | ? | 84P87 | 84 | |

88 | p88 pi-heptomino hassler | Dean Hickerson | 1994 | figure eight on rattlesnake | 45 | |

89 | ? | ? | ? | ? | ? | |

90 | ? | ? | ? | fumarole on 43P18 | 61 | |

91 | ? | ? | ? | ? | ? | |

92 | ? | ? | ? | twin bees shuttle on 22P4.3 | 50 | |

93 | ? | ? | ? | caterer on Merzenich's p31 | 60 | |

94 | ? | ? | ? | capped AK-94 | 110 | |

95 | ? | ? | ? | ? | ? | |

96 | ? | ? | ? | caterer on 68P32 | 80 | |

97 | ? | ? | ? | ? | ? | |

98 | ? | ? | ? | ? | ? | |

99 | ? | ? | ? | ? | ? | |

100 | centinal | Bill Gosper | ≤1987 | centinal | 70 | |

104 | ? | ? | ? | figure eight on Beluchenko's p13 | 46 | |

105 | ? | ? | ? | pentadecathlon on 37P7.1 | 49 | |

108 | ? | ? | ? | 22P4.3 on 56P27 | 78 | |

110 | p110 traffic jam | Bill Gosper | 1994 | pseudo-barberpole on 36P22 | 51 | |

120 | ? | ? | ? | figure eight on pentadecathlon | 24 | |

124 | p124 lumps of muck hassler | Dean Hickerson | 1994 | mold on Merzenich's p31 | 60 | |

132 | p132 pi-heptomino hassler | David Buckingham | ≤1994 | ? | ? | |

135 | 106P135 | Bill Gosper | 1989 | pentadecathlon on 56P27 | 68 | |

138 | ? | ? | ? | Gabriel's p138 | 36 | |

144 | Achim's p144 | Achim Flammenkamp | 1994 | Achim's p144 | 42 | |

156 | p156 Hans Leo hassler | Noam Elkies | 1995 | Jason's p156 | 92 | |

177 | ? | ? | ? | Karel's p177 | 104 | |

200 | p200 traffic jam | Bill Gosper | 1994 | figure eight on centinal | 82 | |

312 | period-tripled p104 gun | Dave Greene | 2004 | 60P312 | 60 |

## See also

- List of common oscillators
- List of oscillators
- Omniperiodic
- Table of oscillators by period
- Oscillator periods status table