LifeWiki:Project OmniOsci/Overview/Spaceships
Jump to navigation
Jump to search
This page tracks the minimal known examples for all kinetic symmetries and periods up to 24. The period cap will be expanded once every combination up to period 24 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 24, 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 | 3 | 3 | 4 |
| 2c/2 | 3 | 4 | 4 |
| c/3 | 3 | 3 | 4 |
| 2c/3 | 4 | 4 | 6 |
| 3c/3 | 3 | 4 | 4 |
| c/4 | 3 | 3 | 4 |
| 2c/4 | 3 | 3 | 4 |
| 3c/4 | 4 | 5 | 8 |
| 4c/4 | 3 | 4 | 4 |
| c/5 | 3 | 3 | 4 |
| 2c/5 | 3 | 3 | 4 |
| 3c/5 | 3 | 3 | 6 |
| 4c/5 | 5 | 5 | 8 |
| 5c/5 | 3 | 4 | 6 |
| c/6 | 3 | 3 | 4 |
| 2c/6 | 3 | 3 | 4 |
| 3c/6 | 3 | 3 | 4 |
| 4c/6 | 3 | 3 | 6 |
| 5c/6 | 5 | 5 | 10 |
| 6c/6 | 3 | 4 | 4 |
| c/7 | 3 | 3 | 4 |
| 2c/7 | 3 | 3 | 4 |
| 3c/7 | 3 | 3 | 4 |
| 4c/7 | 3 | 3 | 6 |
| 5c/7 | 3 | 3 | 6 |
| 6c/7 | 7 | ||
| 7c/7 | 3 | ||
| c/8 | 3 | 3 | 4 |
| 2c/8 | 3 | 3 | 4 |
| 3c/8 | 3 | ||
| 4c/8 | 9 | ||
| 5c/8 | 3 | ||
| 6c/8 | 3 | ||
| 7c/8 | 12 | ||
| 8c/8 | |||
| c/9 | 3 | 3 | 4 |
| 2c/9 | 3 | 3 | 4 |
| 3c/9 | 3 | ||
| 4c/9 | 3 | ||
| 5c/9 | 3 | ||
| 6c/9 | 3 | ||
| 7c/9 | 4 | ||
| 8c/9 | 12 | ||
| 9c/9 | 3 | ||
| c/10 | 3 | 3 | 4 |
| 2c/10 | 3 | 3 | 4 |
| 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 | 3 | 4 |
| 2c/11 | 3 | 3 | 4 |
| 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 | 3 | 4 |
| 2c/12 | 3 | 3 | 4 |
| 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 | 3 | 4 |
| 2c/13 | 3 | 3 | 4 |
| 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 | 3 | 4 |
| 2c/14 | 3 | 3 | 4 |
| 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 | 3 | 4 |
| 2c/15 | 3 | 3 | 4 |
| 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 | 3 | 4 |
| 2c/16 | 3 | 3 | 4 |
| 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 | |||
| c/17 | 3 | ||
| 2c/17 | 3 | ||
| 3c/17 | 3 | ||
| 4c/17 | 3 | ||
| 5c/17 | 3 | ||
| 6c/17 | 3 | ||
| 7c/17 | 3 | ||
| 8c/17 | 3 | ||
| 9c/17 | 3 | ||
| 10c/17 | |||
| 11c/17 | |||
| 12c/17 | |||
| 13c/17 | |||
| 14c/17 | |||
| 15c/17 | |||
| 16c/17 | |||
| 17c/17 | |||
| c/18 | 3 | ||
| 2c/18 | |||
| 3c/18 | 3 | ||
| 4c/18 | |||
| 5c/18 | 3 | ||
| 6c/18 | 3 | ||
| 7c/18 | 3 | ||
| 8c/18 | |||
| 9c/18 | 3 | ||
| 10c/18 | 3 | ||
| 11c/18 | |||
| 12c/18 | |||
| 13c/18 | |||
| 14c/18 | 13 | ||
| 15c/18 | |||
| 16c/18 | |||
| 17c/18 | |||
| 18c/18 | |||
| c/19 | 3 | ||
| 2c/19 | 3 | ||
| 3c/19 | 3 | ||
| 4c/19 | 3 | ||
| 5c/19 | 3 | ||
| 6c/19 | 3 | ||
| 7c/19 | 3 | ||
| 8c/19 | 3 | ||
| 9c/19 | 3 | ||
| 10c/19 | 3 | ||
| 11c/19 | |||
| 12c/19 | |||
| 13c/19 | |||
| 14c/19 | |||
| 15c/19 | |||
| 16c/19 | |||
| 17c/19 | |||
| 18c/19 | |||
| 19c/19 | |||
| c/20 | 3 | ||
| 2c/20 | |||
| 3c/20 | 3 | ||
| 4c/20 | 3 | ||
| 5c/20 | 3 | ||
| 6c/20 | |||
| 7c/20 | 3 | ||
| 8c/20 | |||
| 9c/20 | 3 | ||
| 10c/20 | 3 | ||
| 11c/20 | 3 | ||
| 12c/20 | |||
| 13c/20 | |||
| 14c/20 | |||
| 15c/20 | |||
| 16c/20 | 15 | ||
| 17c/20 | |||
| 18c/20 | |||
| 19c/20 | |||
| 20c/20 | |||
| c/21 | 3 | ||
| 2c/21 | 3 | ||
| 3c/21 | 3 | ||
| 4c/21 | 3 | ||
| 5c/21 | 3 | ||
| 6c/21 | 3 | ||
| 7c/21 | 3 | ||
| 8c/21 | 3 | ||
| 9c/21 | 4 | ||
| 10c/21 | 5 | ||
| 11c/21 | |||
| 12c/21 | |||
| 13c/21 | |||
| 14c/21 | |||
| 15c/21 | 6 | ||
| 16c/21 | |||
| 17c/21 | |||
| 18c/21 | |||
| 19c/21 | |||
| 20c/21 | |||
| 21c/21 | |||
| c/22 | 3 | ||
| 2c/22 | 3 | ||
| 3c/22 | 3 | ||
| 4c/22 | 3 | ||
| 5c/22 | 3 | ||
| 6c/22 | 3 | ||
| 7c/22 | 3 | ||
| 8c/22 | 3 | ||
| 9c/22 | 5 | ||
| 10c/22 | |||
| 11c/22 | 3 | ||
| 12c/22 | |||
| 13c/22 | |||
| 14c/22 | |||
| 15c/22 | |||
| 16c/22 | |||
| 17c/22 | |||
| 18c/22 | |||
| 19c/22 | |||
| 20c/22 | |||
| 21c/22 | |||
| 22c/22 | |||
| c/23 | 3 | ||
| 2c/23 | 3 | ||
| 3c/23 | 3 | ||
| 4c/23 | 3 | ||
| 5c/23 | 3 | ||
| 6c/23 | 3 | ||
| 7c/23 | 3 | ||
| 8c/23 | 4 | ||
| 9c/23 | 5 | ||
| 10c/23 | 5 | ||
| 11c/23 | 5 | ||
| 12c/23 | |||
| 13c/23 | |||
| 14c/23 | |||
| 15c/23 | |||
| 16c/23 | |||
| 17c/23 | |||
| 18c/23 | |||
| 19c/23 | |||
| 20c/23 | |||
| 21c/23 | |||
| 22c/23 | |||
| 23c/23 | |||
| c/24 | 3 | ||
| 2c/24 | 3 | ||
| 3c/24 | 3 | ||
| 4c/24 | |||
| 5c/24 | 3 | ||
| 6c/24 | |||
| 7c/24 | 3 | ||
| 8c/24 | |||
| 9c/24 | 3 | ||
| 10c/24 | 3 | ||
| 11c/24 | 5 | ||
| 12c/24 | |||
| 13c/24 | |||
| 14c/24 | |||
| 15c/24 | |||
| 16c/24 | |||
| 17c/24 | |||
| 18c/24 | |||
| 19c/24 | |||
| 20c/24 | 21 | ||
| 21c/24 | |||
| 22c/24 | |||
| 23c/24 | |||
| 24c/24 | |||
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 | |
| 2c/18 | 3 | |
| 4c/18 | 3 | |
| 6c/18 | ||
| 8c/18 | 3 | |
| 10c/18 | ||
| 12c/18 | 4 | |
| 14c/18 | ||
| 16c/18 | ||
| 18c/18 | 3 | |
| 2c/20 | 3 | |
| 4c/20 | ||
| 6c/20 | 3 | |
| 8c/20 | 3 | |
| 10c/20 | ||
| 12c/20 | 5 | |
| 14c/20 | ||
| 16c/20 | ||
| 18c/20 | ||
| 20c/20 | 3 | |
| 2c/22 | ||
| 4c/22 | ||
| 6c/22 | ||
| 8c/22 | ||
| 10c/22 | 3 | |
| 12c/22 | 4 | |
| 14c/22 | 6 | |
| 16c/22 | 5 | |
| 18c/22 | ||
| 20c/22 | ||
| 22c/22 | 5 | |
| 2c/24 | ||
| 4c/24 | 3 | |
| 6c/24 | 3 | |
| 8c/24 | 3 | |
| 10c/24 | ||
| 12c/24 | 3 | |
| 14c/24 | 3 | |
| 16c/24 | 4 | |
| 18c/24 | 4 | |
| 20c/24 | ||
| 22c/24 | ||
| 24c/24 | 4 | |
Diagonal spaceships
p/m = 1
| Velocity | n | / |
|---|---|---|
| c/2 | 5 | 4 |
| c/3 | 3 | 3 |
| c/4 | 3 | 14 |
| 2c/4 | 4 | |
| c/5 | 3 | 3 |
| 2c/5 | 7 | 3 |
| c/6 | 3 | |
| 2c/6 | 3 | |
| 3c/6 | 4 | |
| c/7 | 3 | 3 |
| 2c/7 | 3 | |
| 3c/7 | 3 | |
| c/8 | 3 | |
| 2c/8 | ||
| 3c/8 | 3 | |
| 4c/8 | 4 | |
| c/9 | 3 | 3 |
| 2c/9 | 3 | |
| 3c/9 | 3 | |
| 4c/9 | 3 | |
| c/10 | 3 | |
| 2c/10 | ||
| 3c/10 | ||
| 4c/10 | 3 | |
| 5c/10 | ||
| c/11 | 3 | 3 |
| 2c/11 | 3 | |
| 3c/11 | 3 | |
| 4c/11 | 3 | |
| 5c/11 | 3 | |
| c/12 | 3 | 3 |
| 2c/12 | 3 | |
| 3c/12 | 3 | |
| 4c/12 | 3 | |
| 5c/12 | 3 | |
| 6c/12 | 4 | |
| c/13 | 3 | 3 |
| 2c/13 | 3 | |
| 3c/13 | 3 | |
| 4c/13 | 3 | |
| 5c/13 | 3 | |
| 6c/13 | 3 | |
| c/14 | 3 | 3 |
| 2c/14 | ||
| 3c/14 | ||
| 4c/14 | ||
| 5c/14 | 3 | |
| 6c/14 | 3 | |
| 7c/14 | ||
| c/15 | 3 | 3 |
| 2c/15 | 3 | |
| 3c/15 | 3 | |
| 4c/15 | 3 | |
| 5c/15 | 3 | |
| 6c/15 | 3 | |
| 7c/15 | 3 | |
| c/16 | 3 | |
| 2c/16 | ||
| 3c/16 | ||
| 4c/16 | 3 | |
| 5c/16 | ||
| 6c/16 | 3 | |
| 7c/16 | 3 | |
| 8c/16 | 4 | |
| c/17 | 3 | |
| 2c/17 | 3 | |
| 3c/17 | 3 | |
| 4c/17 | 3 | |
| 5c/17 | 3 | |
| 6c/17 | 3 | |
| 7c/17 | 3 | |
| 8c/17 | 3 | |
| c/18 | ||
| 2c/18 | ||
| 3c/18 | ||
| 4c/18 | ||
| 5c/18 | ||
| 6c/18 | 3 | |
| 7c/18 | 3 | |
| 8c/18 | 3 | |
| 9c/18 | ||
| c/19 | 3 | |
| 2c/19 | 3 | |
| 3c/19 | 3 | |
| 4c/19 | 3 | |
| 5c/19 | 3 | |
| 6c/19 | 3 | |
| 7c/19 | 3 | |
| 8c/19 | 3 | |
| 9c/19 | 3 | |
| c/20 | ||
| 2c/20 | ||
| 3c/20 | 3 | |
| 4c/20 | ||
| 5c/20 | ||
| 6c/20 | ||
| 7c/20 | 3 | |
| 8c/20 | 3 | |
| 9c/20 | 3 | |
| 10c/20 | 4 | |
| c/21 | 3 | |
| 2c/21 | 3 | |
| 3c/21 | 3 | |
| 4c/21 | 3 | |
| 5c/21 | 3 | |
| 6c/21 | 3 | |
| 7c/21 | 3 | |
| 8c/21 | 3 | |
| 9c/21 | 3 | |
| 10c/21 | 3 | |
| c/22 | ||
| 2c/22 | ||
| 3c/22 | 3 | |
| 4c/22 | ||
| 5c/22 | 3 | |
| 6c/22 | ||
| 7c/22 | ||
| 8c/22 | 3 | |
| 9c/22 | 3 | |
| 10c/22 | 3 | |
| 11c/22 | 4 | |
| c/23 | 3 | |
| 2c/23 | 3 | |
| 3c/23 | 3 | |
| 4c/23 | 3 | |
| 5c/23 | 3 | |
| 6c/23 | 3 | |
| 7c/23 | 3 | |
| 8c/23 | 3 | |
| 9c/23 | 3 | |
| 10c/23 | 3 | |
| 11c/23 | 3 | |
| c/24 | ||
| 2c/24 | 3 | |
| 3c/24 | ||
| 4c/24 | ||
| 5c/24 | ||
| 6c/24 | ||
| 7c/24 | ||
| 8c/24 | 3 | |
| 9c/24 | 3 | |
| 10c/24 | 3 | |
| 11c/24 | 3 | |
| 12c/24 | 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 | ||
| c/18 | 3 | |
| 2c/18 | 3 | |
| 3c/18 | 3 | |
| 4c/18 | 3 | |
| 5c/18 | 3 | |
| 6c/18 | ||
| 7c/18 | ||
| 8c/18 | ||
| 9c/18 | 4 | |
| c/20 | 3 | |
| 2c/20 | 3 | |
| 3c/20 | ||
| 4c/20 | 3 | |
| 5c/20 | 3 | |
| 6c/20 | 3 | |
| 7c/20 | ||
| 8c/20 | ||
| 9c/20 | ||
| 10c/20 | ||
| c/22 | 3 | |
| 2c/22 | 3 | |
| 3c/22 | ||
| 4c/22 | 3 | |
| 5c/22 | ||
| 6c/22 | 3 | |
| 7c/22 | 3 | |
| 8c/22 | ||
| 9c/22 | ||
| 1c/22 | ||
| 11c/22 | ||
| c/24 | 3 | |
| 2c/24 | ||
| 3c/24 | 3 | |
| 4c/24 | 3 | |
| 5c/24 | 3 | |
| 6c/24 | 3 | |
| 7c/24 | 3 | |
| 8c/24 | ||
| 9c/24 | ||
| 10c/24 | ||
| 11c/24 | ||
| 12c/24 | ||