Sphere: Difference between revisions
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{{Glossary}} | {{Glossary}} | ||
A '''sphere''' is a possible finite [[Conway's Game of Life|Life]] universe in the form of a sphere. The simplest way to do this is to use an | A '''sphere''' is a possible finite [[Conway's Game of Life|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 [[spaceship]]s travel in a spherical universe. | |||
{{EmbedViewer | |||
|position = center | |||
|pname = sphere | |||
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 4 WIDTH 600 HEIGHT 600 GPS 60 LOOP 801 ]] | |||
}} | |||
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== | ==External links== | ||
{{LinkWikipedia|Sphere}} | * {{LinkWikipedia|Sphere}} | ||
* | * {{LinkGollyHelp|bounded.html|title=Bounded grids}} | ||
[[Category:Topologies]] | [[Category:Topologies]] | ||
Latest revision as of 20:44, 26 August 2025
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.
| (click above to open LifeViewer) RLE: here Plaintext: here |
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