# Difference between revisions of "Cross-surface"

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A '''cross-surface''' (or '''real projective plane''') is a possible finite [[Conway's Game of Life|Life]] universe in the form of a real projective plane. The simplest way to do this is to use an m × n rectangle with the top edge twisted and joined to the bottom edge and the left edge twisted and joined to the right edge. It is similar to the [[Klein bottle]] except it has both pairs of sides twisted instead of just one. | A '''cross-surface''' (or '''real projective plane''') is a possible finite [[Conway's Game of Life|Life]] universe in the form of a real projective plane. The simplest way to do this is to use an m × n rectangle with the top edge twisted and joined to the bottom edge and the left edge twisted and joined to the right edge. It is similar to the [[Klein bottle]] except it has both pairs of sides twisted instead of just one. | ||

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+ | The following [[LifeViewer]] demonstrates how diagonal and orthogonal spaceships travel in a cross-surface universe. | ||

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+ | {{EmbedViewer | ||

+ | |position = center | ||

+ | |pname = crosssurface | ||

+ | |viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 4 WIDTH 600 HEIGHT 600 GPS 60 LOOP 801 ]] | ||

+ | }} | ||

==See also== | ==See also== | ||

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*[[Klein bottle]] | *[[Klein bottle]] | ||

*[[Sphere]] | *[[Sphere]] | ||

+ | *[[Bounded grids]] | ||

==External links== | ==External links== | ||

{{LinkWikipedia|Real_projective_plane|name=Real projective plane}} | {{LinkWikipedia|Real_projective_plane|name=Real projective plane}} | ||

− | + | {{LinkGollyHelp|bounded.html|title=Bounded grids}} | |

[[Category:Topologies]] | [[Category:Topologies]] |

## Latest revision as of 01:00, 4 October 2019

A **cross-surface** (or **real projective plane**) is a possible finite Life universe in the form of a real projective plane. The simplest way to do this is to use an m × n rectangle with the top edge twisted and joined to the bottom edge and the left edge twisted and joined to the right edge. It is similar to the Klein bottle except it has both pairs of sides twisted instead of just one.

The following LifeViewer demonstrates how diagonal and orthogonal spaceships travel in a cross-surface universe.

(click above to open LifeViewer)RLE: here Plaintext: here |

## See also

## External links

- Real projective plane at Wikipedia

- Bounded grids at Golly's online help