List of oscillators by present frequencies

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Oscillators of each period by which cell frequency values are present. Frequency-0 cells are not counted as part of the oscillator.

Blue This oscillator is proven to be the smallest of the given type.
Green This oscillator is the smallest known example of the given type.
Yellow This oscillator may be the smallest known example of the given type; checking of other pattern collections may be advisable.
Orange It is not known whether there is a known oscillator of this type; checking of pattern collections advisable.
Red Oscillators of this type are currently unknown.
Gray Oscillators of this type have been proven impossible.

p2

Freqs. Oscillator Cells
1 only phoenix 1 12
1, 2 blinker 3

p3

Freqs. Oscillator Cells
1 only proven impossible[1]
1,2 Statorless p3 140[2]
1,3 open cuphook 18[3]
1,2,3 caterer 12
2 only proven impossible[4]
2,3 stillater (stator variant) 20[3]

p4

Freqs. Oscillator Cells
1 only proven impossible[1]
1,2 proven impossible[5]
1,3 proven impossible[4]
1,2,3 mazing 12
1,4 proven impossible[4]
1,2,4 lightweight emulator 30
1,3,4 unnamed 30
1,2,3,4 mold 12
2 only proven impossible[4]
2,3 proven impossible[6]
2,4 unnamed 25
2,3,4 1-2-3-4 25
3 only proven impossible[4]
3,4 unnamed 33

p5

Freqs. Oscillator Cells
1 only proven impossible[1]
1,2 proven impossible[7]
1,3 proven impossible[7]
1,2,3 none known
1,4 proven impossible[7]
1,2,4 none known
1,3,4 proven impossible[8]
1,2,3,4 statorless p5 68
1,5 proven impossible[7]
1,2,5 none known
1,3,5 none known
1,2,3,5 pseudo-barberpole 15
1,4,5 proven impossible[5]
1,2,4,5 hooks 21
1,3,4,5 unnamed 38
1,2,3,4,5 Silver's p5 17
2 only proven impossible[7]
2,3 proven impossible[7]
2,4 proven impossible[7]
2,3,4 none known
2,5 proven impossible[6]
2,3,5 mathematician 35
2,4,5 none known
2,3,4,5 Elkies' p5 20
3 only proven impossible[7]
3,4 proven impossible[7]
3,5 proven impossible[9]
3,4,5 unnamed 72
4 only proven impossible[7]
4,5 proven impossible[7]

p6

Freqs. Oscillator Cells Freqs. Oscillator Cells
1 only proven impossible[1] 1,3,4,5,6 unnamed 34
1,2 none known 1,2,3,4,5,6 blonker 20
1,3 none known 2 only proven impossible[5]
1,2,3 none known 2,3 none known
1,4 none known 2,4 none known
1,2,4 none known 2,3,4 none known
1,3,4 none known 2,5 none known
1,2,3,4 statorless p6 36 2,3,5 none known
1,5 none known 2,4,5 none known
1,2,5 none known 2,3,4,5 none known
1,3,5 none known 2,6 proven impossible[5]
1,2,3,5 none known 2,3,6 unnamed 38
1,4,5 none known 2,4,6 unnamed 28
1,2,4,5 none known 2,3,4,6 unnamed 52
1,3,4,5 none known 2,5,6 unnamed 32
1,2,3,4,5 Jason's p6 28 2,3,5,6 unnamed 38
1,6 proven impossible[5] 2,3,4,5,6 unnamed 40
2,4,5,6 unnamed 28 3 only proven impossible[5]
1,2,6 none known 3,4 none known
1,3,6 none known 3,5 none known
1,2,3,6 unnamed 56 3,4,5 none known
1,4,6 none known 3,6 unnamed 66
1,2,4,6 unnamed 38 3,4,6 unnamed 32
1,3,4,6 unnamed 67 3,5,6 none known
1,2,3,4,6 p6 thumb 27 3,4,5,6 unnamed 36
1,5,6 none known 4 only proven impossible[5]
1,2,5,6 A for all 28 4,5 none known
1,3,5,6 unnamed 65 4,6 unnamed 69
1,2,3,5,6 unix 16 4,5,6 none known
1,4,5,6 unnamed 33 5 only proven impossible[5]
1,2,4,5,6 30P6.1 30 5,6 proven impossible[5]
Frequencies 1 1 1 1
2 2 2 2
3 3 3 3
n/a [1] [5] ? [5] ? ? ?
4 [5] ? ? ? ? ? ? 36
5 [5] ? ? ? ? ? ? ?
4 5 ? ? ? ? ? ? ? 28
6 p1 [5] [5] ? 66 ? 38 56
4 6 69 ? 28 38 32 67 52 27
5 6 [5] ? 32 28 ? 65 38 16
4 5 6 ? 33 28 30 36 34 40 20
Frequencies 1 1 1 1
2 2 2 2
3 3 3 3
n/a [1] ? [5] ? ? ? [5]
5 [5] ? ? ? ? ? ? ?
4 5 ? ? ? ? ? 28 ? ?
4 [5] ? ? ? ? 36 ? ?
4 6 69 ? 38 28 52 27 67 32
4 5 6 ? 33 30 28 40 20 34 36
5 6 [5] ? 28 32 38 16 65 ?
6 p1 [5] ? [5] 38 56 ? 66

References

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 "Every finite phoenix has period 2". Complex Projective 4-Space. Retrieved on January 20, 2024.
  2. ↑ Keith Amling (July 31, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  3. ↑ 3.0 3.1 Keith Amling (September 14, 2025). Re: amling search program principles discussion / brain dump (discussion thread) at the ConwayLife.com forums
  4. ↑ 4.0 4.1 4.2 4.3 4.4 Keith Amling (September 14, 2025). Re: amling search program principles discussion / brain dump (discussion thread) at the ConwayLife.com forums
  5. ↑ 5.00 5.01 5.02 5.03 5.04 5.05 5.06 5.07 5.08 5.09 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18 5.19 5.20 5.21 5.22 Matthias Merzenich (September 21, 2025). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  6. ↑ 6.0 6.1 Matthias Merzenich (September 18, 2025). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  7. ↑ 7.00 7.01 7.02 7.03 7.04 7.05 7.06 7.07 7.08 7.09 7.10 Matthias Merzenich (September 15, 2025). Re: amling search program principles discussion / brain dump (discussion thread) at the ConwayLife.com forums
  8. ↑ Keith Amling (December 21, 2025). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  9. ↑ Keith Amling (September 15, 2025). Re: amling search program principles discussion / brain dump (discussion thread) at the ConwayLife.com forums
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