LifeWiki:Project OmniOsci/Overview/Spaceships
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This page tracks the minimal known examples for all kinetic symmetries and periods up to 16. The period cap will be expanded once every combination up to period 16 is proven minimal.
Note that only orthogonal and diagonal spaceships are tracked in the spaceship sections, as these are the only types of spaceships which support kinetic symmetries other than n. For oblique spaceships and spaceships with periods higher then 16, refer to the 5s project.
For oscillators, see LifeWiki:Project OmniOsci/Overview/Oscillators.
This project has an associated forum thread: Project OmniOsci.
| Key |
|---|
| Provably optimal |
| Very likely to be optimal |
| Possibly optimal |
| Unoptimized; smaller examples must exist |
| Optimal, but a smaller example exists which is a pseudo-object |
| Current example is a pseudo-object |
| None currently known |
Square grid
Orthogonal
p/m = 1
| Velocity | n | ‑c | ‑e |
|---|---|---|---|
| c | 3 | 4 | 4 |
| c/2 | 4 | 3 | 4 |
| 2c/2 | 3 | 6 | 6 |
| c/3 | 3 | 3 | 6 |
| 2c/3 | 6 | 4 | 22 |
| 3c/3 | 3 | 4 | 4 |
| c/4 | 8 | 3 | 4 |
| 2c/4 | 15 | 3 | 18 |
| 3c/4 | 4 | 8 | 8 |
| 4c/4 | 6 | 12 | 12 |
| c/5 | 4 | 3 | 4 |
| 2c/5 | 10 | 3 | |
| 3c/5 | 7 | 3 | 10 |
| 4c/5 | 7 | 5 | 18 |
| 5c/5 | 3 | ||
| c/6 | 10 | 3 | |
| 2c/6 | 6 | ||
| 3c/6 | 3 | ||
| 4c/6 | 3 | ||
| 5c/6 | 5 | ||
| 6c/6 | 3 | ||
| c/7 | 10 | 3 | |
| 2c/7 | 3 | 6 | |
| 3c/7 | 3 | ||
| 4c/7 | 3 | ||
| 5c/7 | 3 | ||
| 6c/7 | 7 | ||
| 7c/7 | 3 | ||
| c/8 | 3 | 6 | |
| 2c/8 | 3 | ||
| 3c/8 | 3 | ||
| 4c/8 | 9 | ||
| 5c/8 | 3 | ||
| 6c/8 | 3 | ||
| 7c/8 | 12 | ||
| 8c/8 | |||
| c/9 | 3 | ||
| 2c/9 | 3 | ||
| 3c/9 | 3 | ||
| 4c/9 | 3 | ||
| 5c/9 | 3 | ||
| 6c/9 | 3 | ||
| 7c/9 | 4 | ||
| 8c/9 | 12 | ||
| 9c/9 | 3 | ||
| c/10 | 3 | 4 | |
| 2c/10 | 3 | ||
| 3c/10 | 3 | ||
| 4c/10 | |||
| 5c/10 | 3 | ||
| 6c/10 | 3 | ||
| 7c/10 | 3 | ||
| 8c/10 | 4 | ||
| 9c/10 | - | - | - |
| 10c/10 | 3 | ||
| c/11 | 3 | ||
| 2c/11 | 3 | ||
| 3c/11 | 3 | ||
| 4c/11 | 3 | ||
| 5c/11 | 3 | ||
| 6c/11 | 3 | ||
| 7c/11 | 3 | ||
| 8c/11 | 3 | ||
| 9c/11 | 4 | ||
| 10c/11 | - | - | - |
| 11c/11 | 3 | ||
| c/12 | 3 | ||
| 2c/12 | |||
| 3c/12 | 3 | ||
| 4c/12 | 3 | ||
| 5c/12 | 3 | ||
| 6c/12 | 3 | ||
| 7c/12 | 3 | ||
| 8c/12 | 3 | ||
| 9c/12 | 3 | ||
| 10c/12 | 5 | ||
| 11c/12 | - | - | - |
| 12c/12 | 3 | ||
| c/13 | 3 | ||
| 2c/13 | 3 | ||
| 3c/13 | 3 | ||
| 4c/13 | 3 | ||
| 5c/13 | 3 | ||
| 6c/13 | 3 | ||
| 7c/13 | 3 | ||
| 8c/13 | 3 | ||
| 9c/13 | 3 | ||
| 10c/13 | 3 | ||
| 11c/13 | 9 | ||
| 12c/13 | - | - | - |
| 13c/13 | 3 | ||
| c/14 | 3 | ||
| 2c/14 | 3 | ||
| 3c/14 | 3 | ||
| 4c/14 | 3 | ||
| 5c/14 | 3 | ||
| 6c/14 | 3 | ||
| 7c/14 | 3 | ||
| 8c/14 | 3 | ||
| 9c/14 | 3 | ||
| 10c/14 | 3 | ||
| 11c/14 | 4 | ||
| 12c/14 | - | - | - |
| 13c/14 | - | - | - |
| 14c/14 | 3 | ||
| c/15 | 3 | ||
| 2c/15 | 3 | ||
| 3c/15 | 3 | ||
| 4c/15 | 3 | ||
| 5c/15 | 3 | ||
| 6c/15 | 3 | ||
| 7c/15 | 3 | ||
| 8c/15 | 3 | ||
| 9c/15 | 3 | ||
| 10c/15 | 3 | ||
| 11c/15 | 3 | ||
| 12c/15 | 4 | ||
| 13c/15 | - | - | - |
| 14c/15 | - | - | - |
| 15c/15 | 3 | ||
| c/16 | 3 | ||
| 2c/16 | 3 | ||
| 3c/16 | 3 | ||
| 4c/16 | 3 | ||
| 5c/16 | 3 | ||
| 6c/16 | 3 | ||
| 7c/16 | 3 | ||
| 8c/16 | |||
| 9c/16 | 3 | ||
| 10c/16 | |||
| 11c/16 | 3 | ||
| 12c/16 | 3 | ||
| 13c/16 | 4 | ||
| 14c/16 | - | - | - |
| 15c/16 | - | - | - |
| 16c/16 | |||
p/m = 2
| Velocity | n-c | n-e |
|---|---|---|
| 2c/2 | 4 | 3 |
| 2c/4 | 5 | 9 |
| 4c/4 | 4 | 3 |
| 2c/6 | 3 | 5 |
| 4c/6 | ||
| 6c/6 | ||
| 2c/8 | ||
| 4c/8 | 3 | |
| 6c/8 | 10 | |
| 8c/8 | 3 | |
| 2c/10 | ||
| 4c/10 | 3 | |
| 6c/10 | ||
| 8c/10 | ||
| 10c/10 | ||
| 2c/12 | 3 | 5 |
| 4c/12 | ||
| 6c/12 | ||
| 8c/12 | ||
| 10c/12 | ||
| 12c/12 | ||
| 2c/14 | ||
| 4c/14 | ||
| 6c/14 | ||
| 8c/14 | ||
| 10c/14 | ||
| 12c/14 | - | - |
| 14c/14 | ||
| 2c/16 | ||
| 4c/16 | ||
| 6c/16 | ||
| 8c/16 | 3 | |
| 10c/16 | 4 | |
| 12c/16 | ||
| 14c/16 | - | - |
| 16c/16 | 3 | |
Diagonal spaceships
p/m = 1
| Velocity | n | / |
|---|---|---|
| c/2 | 20 | 9 |
| c/3 | 9 | 3 |
| c/4 | 10 | 14 |
| 2c/4 | 4 | |
| c/5 | 10 | 3 |
| 2c/5 | 7 | 3 |
| c/6 | ||
| 2c/6 | 3 | |
| 3c/6 | 4 | |
| c/7 | 3 | |
| 2c/7 | 3 | |
| 3c/7 | 3 | |
| c/8 | ||
| 2c/8 | ||
| 3c/8 | 3 | |
| 4c/8 | 4 | |
| c/9 | 3 | |
| 2c/9 | 3 | |
| 3c/9 | 3 | |
| 4c/9 | 3 | |
| c/10 | ||
| 2c/10 | ||
| 3c/10 | ||
| 4c/10 | 3 | |
| 5c/10 | ||
| c/11 | 3 | |
| 2c/11 | 3 | |
| 3c/11 | 3 | |
| 4c/11 | 3 | |
| 5c/11 | 3 | |
| c/12 | 3 | |
| 2c/12 | 3 | |
| 3c/12 | 3 | |
| 4c/12 | 3 | |
| 5c/12 | 3 | |
| 6c/12 | 4 | |
| c/13 | 3 | |
| 2c/13 | 3 | |
| 3c/13 | 3 | |
| 4c/13 | 3 | |
| 5c/13 | 3 | |
| 6c/13 | 3 | |
| c/14 | 3 | |
| 2c/14 | ||
| 3c/14 | ||
| 4c/14 | ||
| 5c/14 | 3 | |
| 6c/14 | 3 | |
| 7c/14 | ||
| c/15 | 3 | |
| 2c/15 | 3 | |
| 3c/15 | 3 | |
| 4c/15 | 3 | |
| 5c/15 | 3 | |
| 6c/15 | 3 | |
| 7c/15 | 3 | |
| c/16 | ||
| 2c/16 | ||
| 3c/16 | ||
| 4c/16 | 3 | |
| 5c/16 | ||
| 6c/16 | 3 | |
| 7c/16 | 3 | |
| 8c/16 | 4 | |
p/m = 2
Note: this table does not distinguish between "n/" and "n/e" symmetries, as these only arise depending on the displacement of the spaceship.
| Velocity | n/ | |
|---|---|---|
| c/2 | 4 | |
| c/4 | 3 | |
| 2c/4 | ||
| c/6 | 3 | |
| 2c/6 | ||
| 3c/6 | ||
| c/8 | 333 | |
| 2c/8 | 3 | |
| 3c/8 | ||
| 4c/8 | ||
| c/10 | 3 | |
| 2c/10 | 3 | |
| 3c/10 | 3 | |
| 4c/10 | ||
| 5c/10 | 4 | |
| c/12 | ||
| 2c/12 | ||
| 3c/12 | ||
| 4c/12 | ||
| 5c/12 | ||
| 6c/12 | ||
| c/14 | ||
| 2c/14 | 3 | |
| 3c/14 | 3 | |
| 4c/14 | 3 | |
| 5c/14 | ||
| 6c/14 | ||
| 7c/14 | 4 | |
| c/16 | 3 | |
| 2c/16 | 3 | |
| 3c/16 | 3 | |
| 4c/16 | ||
| 5c/16 | 3 | |
| 6c/16 | ||
| 7c/16 | ||
| 8c/16 | ||