User:Pifricted/Omniperiodicity
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Life-like rules
List of omniperiodic life-like rules
| Rules | Reason |
|---|---|
| Life | P41 found in July 21,2023 |
| Eightlife | P41 works |
| Pedestrian Life | P41 works |
| B3/S123 to B38/S0123678 | Signal loop[1] |
| B3/S234 to B38/S023478 | Signal loop[1] |
| B36/S123 to B368/S012378 | Signal loop[1] |
| B4/S35678 to B4678/S01235678 [1] | W150 emulator |
| B7/S234568 to B457/S01234568 [1] | W150 emulator |
| B27/S234568 to B257/S01234568 [1] | W150 emulator |
| B37/S234568 to B357/S01234568 [1] | W150 emulator |
| B2/S125 to B278/S01245678 [1] | W150 emulator |
| B5/S23458 to B24568/S01234578 [1] | W150 emulator |
| B3/S24567 to B3/S01245678 [1] | W150 emulator |
List of nearly omniperiodic rules
| Rules | Reason |
|---|---|
| HoneyLife | P29 not known[2] |
List of non-omniperiodic life-like rules
| From...to... | Reason |
|---|---|
| B/S to B012345678/S | No still life |
| B/S to B/S012345678 | No oscillator |
| B1/S to B12345678/S012345678 | Too explosive |
| B/S4(8) to B02345678/S4(8) | No still life |
| B/S012345678 to B012345678/S012345678 | No death |
| B/S5678 to B012345678/S5678 [note 1] | No still life |
Isotropic non-totalistic rules
List of omniperiodic isotropic non-totalistic rules
| Rules | Reason |
|---|---|
| Tflock 2 | Spaceship loop[citation needed] |
| B35y6a/S34-a56c | Spaceship loop[citation needed] |
| Fource(B3aijk4y7c/S2c34aijkqry5-cj6ac7c) | Spaceship loop[citation needed] |
| B3-k/S234w | W150 emulator[3] |
| B3/S234y5k | W150 emulator[4] |
| B2ce4t6-i/S145-r6-ei7c8 | Spaceship loop[5] |
Others
List of non-omniperiodic CAs
| CAs | Reason |
|---|---|
| Strobing rules | No odd periods |
| Generations, Reverse generations | No periods between 1 and Cn |
Note
- ↑ No still life without S0,S1,S2,S3 and S4
References
- ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 May13 (July 19, 2023). Re: Which Life-like CA have been proven omniperiodic? (discussion thread) at the ConwayLife.com forums
- ↑ yujh (July 22, 2023). Re: Which Life-like CA have been proven omniperiodic? (discussion thread) at the ConwayLife.com forums
- ↑ affamatodidio (September 18, 2023). Re: Miscellaneous Discoveries in Other Cellular Automata (discussion thread) at the ConwayLife.com forums
- ↑ Period1GliderGun (September 18, 2023). Re: Miscellaneous Discoveries in Other Cellular Automata (discussion thread) at the ConwayLife.com forums
- ↑ pifricted (September 6, 2024). Re: B2ce4t6-i/S145-r6-ei7c8 (discussion thread) at the ConwayLife.com forums