Klein bottle
A Klein bottle, as an alternative to a torus, is a possible finite Life universe (i.e. one of the bounded grids) in the form of a Klein bottle. The simplest way to do this is to use an m × n rectangle with the top edge joined to the bottom edge (as with a torus) and the left edge twisted and joined to the right edge.
While interesting topologically, it was of historical importance as a technique for gaining space for limited computer memory; wraparound from the northeast on a torus appeared in the southwest, liberating the diagonal instead of closing in on the middle columns of a rectangle.
The Klein bottle is similar to the Möbius strip, in that a configuration travelling off of the left edge will appear on the right edge, but vertically reflected.
The following pattern demonstrates how diagonal and orthogonal spaceships travel in a Klein-bottle-shaped universe.
| (click above to open LifeViewer) RLE: here Plaintext: here |
Following from topology, any pattern on an m × n Klein bottle bounded grid is equivalent to a pattern on a 2m × n toroidal bounded grid, where the left half of the toroidal bounded grid contains the pattern on the Klein bottle bounded grid, and the right half of the toroidal bounded grid contains the pattern on the Klein bottle bounded grid, mirrored vertically.
External links
- Klein bottle at the Life Lexicon
- Klein bottle at Wikipedia
- Bounded grids at Golly's online help