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.

The following LifeViewer demonstrates how diagonal and orthogonal spaceships travel in a Klein-bottle-shaped universe.

x = 98, y = 98, rule = B3/S23:K100,100* 73b2o9b2o$73b2o9b2o5$38b2o11b2ob2o11b2o$37bobo10bobobobo10bobo$36bobo 10bobo3bobo10bobo$35bobo10bobo5bobo10bobo$34bobo10bobo7b2o11b2o$34b2o 11b2o5$2ob2o85b2ob2ob2o$2ob2o85b2ob2ob2o10$2ob2o85b2ob2ob2o$2ob2o85b2o b2ob2o3$13b2o77b2o$12bobo77bobo$11bobo79bobo$11b2o81b2o10$13b2o77b2o$ 12bobo77bobo$11bobo79bobo$11b2o81b2o3$11b2o81b2o$11bobo65bo13bobo$12b 2o64b3o12b2o$77b2obo$77b3o$78b2o8$11b2o81b2o$11bobo79bobo$12b2o79b2o4$ 2ob2ob2o85b2ob2o$2ob2ob2o85b2ob2o4$31b2o$29b2ob2o$29b4o$30b2o3$2ob2ob 2o85b2ob2o$2ob2ob2o85b2ob2o2$37b3o$37bo$38bo$58b2o11b2o$35b2o11b2o7bob o10bobo$35bobo10bobo5bobo10bobo$36bobo10bobo3bobo10bobo$37bobo10bobobo bo10bobo$38b2o11b2ob2o11b2o5$73b2o9b2o$73b2o9b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 ZOOM 4 WIDTH 600 HEIGHT 600 GPS 60 LOOP 801 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here

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