Torus

A glider travelling on an 8 × 8 torus

A torus, as it applies to Life, usually refers to a finite Life universe (i.e. one of the bounded grids) that takes the form of an m × n rectangle with the bottom edge considered to be joined to the top edge and the left edge joined to the right edge, so that the universe is topologically a torus. There are also other less obvious ways of obtaining a toroidal universe.

The following pattern demonstrates how diagonal and orthogonal spaceships travel in a toroidal universe.

x = 98, y = 98, rule = B3/S23:T100,100 10b2o6bo4b2o8b2o9b2o$10bobo4b2o4bobo7b2o9b2o$11b2o4bobo4b2o50$38b3o$ 38bo2bo$38bo$38bo$39bobo15$94b2o$94bobo$95bobo$96b2o3$2o$obo$bobo$2b2o 4$94b2o$94bobo$95bobo$96b2o3$2o$obo$bobo$2b2o2$5b2o11b2o$5bobo10bobo 12b2o9b2o$6b2o11b2o12b2o9b2o! #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

Toruses not aligned to the grid

A torus not aligned to the grid can be embedded in a larger gird aligned torus with additional translation symmetry.

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THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 ZOOM 4 WIDTH 600 HEIGHT 600 GPS 60 LOOP 1100 ]]

Soup with an additional (40,20) symmetry embedded in a 100 × 100 torus. (click above to open LifeViewer)

See also

• Achim Flammenkamp's census

External links

• Torus at the Life Lexicon
• Torus at Wikipedia
• Bounded grids at Golly's online help
• Small Tori in B3/S23 (discussion thread) at the ConwayLife.com forums