Oblique spaceship
An oblique spaceship is a spaceship which moves neither orthogonally nor diagonally.
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 | Camelship |
| (4m,m)/n | giraffeship | giraffewise | (4,1)c/10 | none found |
| (5m,m)/n | ibisship | ibiswise | (5,1)c/12 | Gemini |
| (6m,m)/n | flamingoship | flamingowise | (6,1)c/14 | none found |
| (3m,2m)/n | zebraship | zebrawise | (3,2)c/10 | none found |
| (4m,3m)/n | antelopeship | antelopewise | (4,3)c/14 | none found |
| ... | ||||
| (23m,5m)/n | (23,5)c/56 | waterbear | ||
| (34m,7m)/n | (34,7)c/82 | Unnamed (34,7)c/156 spaceship | ||
*Spaceship is elementary
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.[1] The first oblique spaceship was Andrew Wade's ibisship Gemini, based on the Chapman-Greene construction arm.[2] 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 is the lowest-period oblique spaceship other than Sir Robin.
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.
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, which are either large engineered constructions or, in the case of Sir Robin, the result of extensive computer search.
See also
External links
- Oblique at the Life Lexicon
References
- ↑ 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