Sphere

A sphere is a possible finite Life universe (i.e. one of the bounded grids) in the form of a sphere. The simplest way to do this is to use an n × n rectangle with the top edge joined to the left edge and the bottom edge joined to the right edge. It is similar to a torus except that it has adjacent pairs of sides joined instead of opposite pairs. With this configuration, the top-left and bottom-right corner cells become the "poles" of the sphere which have themselves as three of their neighbors. The other two corner cells have only one of themselves as a neighbor.

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

x = 98, y = 98, rule = B3/S23:S100 11b2o9b2o$11b2o9b2o5$29b2o11b2ob2o11b2o$28bobo10bobobobo10bobo$27bobo 10bobo3b2o11b2o$26bobo10bobo$26b2o11b2o$2o91b2ob2o$2o91b2ob2o10$2o91b 2ob2o$2o91b2ob2o5$7b2o$6bobo$6b2o4$86b2o$86bobo$87bobo$88bobo$89bobo$ 90b2o2$7b2o$6bobo$6b2o2$6b2o$6bobo$7bobo76b2o$8bobo75bobo$9b2o76bobo$ 88bobo$89bobo$90b2o2$90b2o$89bobo$88bobo$17bo70b2o$6b2o8b3o$6bobo7bob 2o$7bobo7b3o$8bobo6b2o$9b2o5$90b2o$89bobo$88bobo$88b2o9$34b2o$34bobo$ 34bo5$58b2o11b2o$57bobo10bobo$36b2o11b2o5bobo10bobo$36bobo10bobo3bobo 10bobo$37bobo10bobobobo10bobo$38b2o11b2ob2o11b2o2$11b2o9b2o$11b2o9b2o 2$11b2o9b2o$11b2o9b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 ZOOM 4 WIDTH 600 HEIGHT 600 GPS 60 LOOP 801 ]]

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Following from topology, any pattern on an n × n sphere bounded grid is equivalent to a pattern on a 2n × 2n toroidal bounded grid, where the upper left quadrant of the toroidal bounded grid contains the pattern on the sphere bounded grid, and each other quadrant contains that pattern rotated about the central vertex.

External links

• Sphere at Wikipedia
• Bounded grids at Golly's online help