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 the smallest possible example for the subperiod combination of this period.
Green This oscillator is the smallest known example for the subperiod combination of this period.
Yellow This oscillator may be the smallest known example for the subperiod combination of this period; checking of other pattern collections may be advisable.
Orange Whether this subperiod combination is known for this period is unknown; checking of pattern collections advisable.
Red This subperiod combination is currently unknown for this period.
Gray This subperiod combination is provably impossible for this period.

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 none known
1,3 proven impossible[4]
1,2,3 mazing 12
1,4 proven impossible[4]
1,2,4 lightweight emulator 30
1,3,4 boss 42
1,2,3,4 mold 12
2 only proven impossible[4]
2,3 proven impossible[5]
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[6]
1,3 proven impossible[6]
1,2,3 none known
1,4 proven impossible[6]
1,2,4 none known
1,3,4 none known
1,2,3,4 statorless p5 68
1,5 proven impossible[6]
1,2,5 none known
1,3,5 none known
1,2,3,5 pseudo-barberpole 15
1,4,5 none known
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[6]
2,3 proven impossible[6]
2,4 proven impossible[6]
2,3,4 none known
2,5 proven impossible[5]
2,3,5 mathematician 35
2,4,5 none known
2,3,4,5 Elkies' p5 20
3 only proven impossible[6]
3,4 proven impossible[6]
3,5 proven impossible[7]
3,4,5 unnamed 72
4 only proven impossible[6]
4,5 proven impossible[6]

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 none known
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 none known
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 none known 2,3,4,5,6 unnamed 40
2,4,5,6 unnamed 28 3 only none known
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 none known
1,2,4,6 unnamed 38 3,4,6 unnamed 32
1,3,4,6 none known 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 none known
1,2,5,6 A for all 28 4,5 none known
1,3,5,6 none known 4,6 none known
1,2,3,5,6 unix 16 4,5,6 none known
1,4,5,6 unnamed 33 5 only none known
1,2,4,5,6 30P6.1 30 5,6 none known
1 1 1 1
2 2 2 2
3 3 3 3
- [1] ? ? ? ? ? ?
4 ? ? ? ? ? ? ? 36
5 ? ? ? ? ? ? ? ?
4 5 ? ? ? ? ? ? ? 28
6 - ? ? ? ? ? 38 56
4 6 ? ? 28 38 32 ? 52 27
5 6 ? ? 32 28 ? ? 38 16
4 5 6 ? 33 28 30 36 34 40 20

References

  1. 1.0 1.1 1.2 1.3 1.4 "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. 5.0 5.1 Matthias Merzenich (September 18, 2025). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  6. 6.00 6.01 6.02 6.03 6.04 6.05 6.06 6.07 6.08 6.09 6.10 Matthias Merzenich (September 15, 2025). Re: amling search program principles discussion / brain dump (discussion thread) at the ConwayLife.com forums
  7. Keith Amling (September 15, 2025). Re: amling search program principles discussion / brain dump (discussion thread) at the ConwayLife.com forums