Klein bottle

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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.

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