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 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.

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 None found 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 None found 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 98P25 98 26 pre-pulsar shuttle 26 200 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 92P33.1 92 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 None found 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 400 50 P50 traffic jam 92 51 112P51 112 52 35P52 35 53 None found 54 P54 shuttle 48 55 fumarole on Achim's p11 90 56 P56 B-heptomino shuttle 45 57 P57 Herschel loop 1 3004 58 P58 toadsucker 258 59 P59 Herschel loop 2 5822 60 mold on pentadecathlon 24 61 P61 herschel loop 2 1596 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

• List of common oscillators
• List of oscillators
• Omniperiodic

External links

• Oscillator at the Life Lexicon