Oblique spaceship
An oblique spaceship is a spaceship which moves neither orthogonally nor diagonally. By definition, such a spaceship must be statically and kinetically asymmetric.
The simplest type is a knightship, so called because it moves parallel to a knight in chess. By analogy with the corresponding fairy chess pieces, the following other terms may be used to designate spaceships with different slopes:
| Type | Ship | Movement | Maximum speed (Life) |
Example |
|---|---|---|---|---|
| (2m,m)/n | knightship | knightwise | (2,1)c/6 | Sir Robin* |
| (3m,m)/n | camelship | camelwise | (3,1)c/8 | Solifuge |
| (4m,m)/n | giraffeship | giraffewise | (4,1)c/10 | Giraffe weevil |
| (5m,m)/n | ibisship | ibiswise | (5,1)c/12 | Gemini |
| (6m,m)/n | flamingoship | flamingowise | (6,1)c/14 | Carotenoid[1] |
| (3m,2m)/n | zebraship | zebrawise | (3,2)c/10 | none found |
| (4m,3m)/n | antelopeship | antelopewise | (4,3)c/14 | none found |
| ... | ||||
| (15m,11m)/n | (15,11)c/52 | Silk moth | ||
| (23m,5m)/n | (23,5)c/56 | Waterbear | ||
| (34m,7m)/n | (34,7)c/82 | Much smaller (34,7)c/156 spaceship | ||
*Spaceship is elementary
The slopes (0,m)/n and (m,m)/n respectively correspond to orthogonal spaceships and diagonal spaceships, which are not considered oblique.
A full list of spaceships in Life can be seen at List of spaceships. Further spaceships in arbitrary isotropic non-totalistic rules are catalogued at the 5s project; these can be emulated to produce a spaceship with equivalent slope in Life using the 0E0P metacell, but no examples have been explicitly constructed yet.
History
In 1982, Berlekamp showed that there must exist spaceships of any given rational slope in Life, although no explicit oblique examples were constructed.[2] The first oblique spaceship was Andrew Wade's ibisship Gemini, based on the Chapman-Greene construction arm.[3] Dave Greene proceeded to build variants, called Geminoids, travelling in a variety of directions.
In early 2014, a collaborative effort was launched to build a half-baked knightship, which translates itself by (6, 3) each period and is therefore a knightship. Chris Cain optimised the construction to yield a smaller and faster parallel HBK.
In December 2014, Brett Berger constructed the first fast oblique spaceship in Conway's Game of Life, the waterbear, moving at a velocity of (23,5)c/79. It has a bounding box very slightly smaller than the parallel HBK. With a period of 158, it was the lowest-period oblique spaceship other than Sir Robin until the construction of the unnamed (34,7)c/156 spaceship.
In March 2018, Adam P. Goucher and Tomas Rokicki discovered Sir Robin, the first elementary oblique ship. It is the fastest knightship and lowest-period oblique ship possible, and also the smallest known oblique ship.
In December 2018, Chris Cain completed a new diagonal loop design for a small-step oblique spaceship, a true camelship with a (3,1) step size in each cycle instead of the (3072,1024) step distance of the adjusted Gemini spaceship.
On November 30, 2025, Nora Brown completed a (12,4)c/62 camelship using a LOM-based reaction,[4] reducing it over the following days.[5] The latter ship is the smallest engineered spaceship that is not a stabilized puffer engine.
Other rules
Many automata extremely similar to Life have oblique ships and related technology. For example, Pedestrian Life has a naturally-occurring family of (5,2)c/190 ships, as well as a natural (101,3)c/1884 puffer; tDryLife has a slope 3 ship puffer that can be stabilized into a spaceship.
These natural spaceships and puffers are qualitatively different from any in Life (to the point where certain rulestrings allow oblique ships to travel faster than (2,1)c/6), which are either large engineered constructions or, in the case of Sir Robin, the result of extensive computer search.
Other grids
On grids other than the square tiling, it is possible to define specific "symmetric" directions as orthogonal, diagonal, and even more for higher dimensions. On the hexagonal tiling and triangular tiling, for example, orthogonal directions and diagonal directions are rather well-defined, so an oblique spaceship would be one that simply travels in neither such direction.
| A knightship in B256/S256H, possibly the first known in any 2-state isotropic hexagonal rule[6] (click above to open LifeViewer) |
For n-dimensional hypercubic honeycombs, an oblique spaceship is one that does not travel across the diagonals of any element. In the 3D case, this means it cannot travel across one of a cube's edges (orthogonal), face diagonals (diagonal) or space diagonals (paragonal). Note that 2D oblique displacements are more symmetric in 3D: (2,1) is unambiguously oblique on a square grid, but a spaceship that travels in the (2,1,0) direction in a cubic honeycomb can only have 24 distinct orientations (as -0 is equal to 0), whereas one that travels in the (3,2,1) direction can move in all 48 directions. This also applies when moving from 3D to 4D, and so on.
The 24-cell honeycomb and 16-cell honeycomb are harder to visualize, but nonetheless follow the similar such rules.
See also
External links
- Oblique at the Life Lexicon
References
- ↑ ElijahKen (March 17, 2026). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ D. Eppstein, Searching for Spaceships (2000, p.4). Accessed 11 September 2022.
- ↑ Dave Greene (February 4, 2022). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
- ↑ Nora Brown (November 30, 2025). Re: Crawlers (discussion thread) at the ConwayLife.com forums
- ↑ Nora Brown (December 1, 2025). Re: Crawlers (discussion thread) at the ConwayLife.com forums
- ↑ https://conwaylife.com/forums/viewtopic.php?p=155640#p155640