A Klein bottle, as an alternative to a torus, is a possible finite Life universe 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 LifeViewer demonstrates how diagonal and orthogonal spaceships travel in a Klein-bottle-shaped universe.
| (click above to open LifeViewer)|
RLE: here Plaintext: here