Cross-surface: Difference between revisions
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A '''cross-surface''' (or '''real projective plane''') is a possible finite [[Conway's Game of Life|Life]] [[universe]] (i.e. one of the [[bounded grids]]) 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]] (i.e. one of the [[bounded grids]]) 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 pattern demonstrates how diagonal and orthogonal | The following pattern demonstrates how diagonal and orthogonal [[spaceship]]s travel in a cross-surface universe. | ||
{{EmbedViewer | {{EmbedViewer | ||
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|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 4 WIDTH 600 HEIGHT 600 GPS 60 LOOP 801 ]] | |viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 4 WIDTH 600 HEIGHT 600 GPS 60 LOOP 801 ]] | ||
}} | }} | ||
Following from topology, any pattern on an m × n cross-surface bounded grid is equivalent to a pattern on a 2m × 2n toroidal bounded grid, where the upper left quadrant of the toroidal bounded grid contains the pattern on the cross-surface bounded grid, the upper right quadrant of the toroidal bounded grid contains the pattern on the cross-surface bounded grid mirrored vertically, the lower left quadrant is mirrored horizontally, and the lower right quadrant is mirrored both ways. | |||
==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}} | * {{LinkGollyHelp|bounded.html|title=Bounded grids}} | ||
[[Category:Topologies]] | [[Category:Topologies]] | ||
Latest revision as of 09:36, 23 August 2025
A cross-surface (or real projective plane) is a possible finite Life universe (i.e. one of the bounded grids) 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 pattern demonstrates how diagonal and orthogonal spaceships travel in a cross-surface universe.
| (click above to open LifeViewer) RLE: here Plaintext: here |
Following from topology, any pattern on an m × n cross-surface bounded grid is equivalent to a pattern on a 2m × 2n toroidal bounded grid, where the upper left quadrant of the toroidal bounded grid contains the pattern on the cross-surface bounded grid, the upper right quadrant of the toroidal bounded grid contains the pattern on the cross-surface bounded grid mirrored vertically, the lower left quadrant is mirrored horizontally, and the lower right quadrant is mirrored both ways.
External links
- Real projective plane at Wikipedia
- Bounded grids at Golly's online help