ZenoRogue | Cat Portal: Non-Euclidean Portal in Solv @ZenoRogue | Uploaded March 2021 | Updated October 2024, 34 minutes ago.
Yet another non-Euclidean portal, this time in Solv geometry (the honecomb based on the mapping torus of Arnold's cat mapping).
As usual, the algorithm works as follows:
* we start with a basic scene (here, a 8x8x3 manifold with a loop put in it)
* create all possible paths not hitting the walls in this space
* two paths are the same if they are homotopic (one can be continuously deformed into another)
* two paths are the same under some extra rules (here, we identify paths which go 6 times around the loop)
* create a new space where every group of paths which are "the same" becomes a cell
Wihout extra rules we get the universal cover; with extra rules we get just a cover. Can you guess the extra rules here?
Made with the HyperRogue engine aka RogueViz
Source code: github.com/zenorogue/hyperrogue/blob/master/rogueviz/notknot.cpp
A playable Windows exe at roguetemple.com/z/sims/notknot.zip (works in VR too!)
Yet another non-Euclidean portal, this time in Solv geometry (the honecomb based on the mapping torus of Arnold's cat mapping).
As usual, the algorithm works as follows:
* we start with a basic scene (here, a 8x8x3 manifold with a loop put in it)
* create all possible paths not hitting the walls in this space
* two paths are the same if they are homotopic (one can be continuously deformed into another)
* two paths are the same under some extra rules (here, we identify paths which go 6 times around the loop)
* create a new space where every group of paths which are "the same" becomes a cell
Wihout extra rules we get the universal cover; with extra rules we get just a cover. Can you guess the extra rules here?
Made with the HyperRogue engine aka RogueViz
Source code: github.com/zenorogue/hyperrogue/blob/master/rogueviz/notknot.cpp
A playable Windows exe at roguetemple.com/z/sims/notknot.zip (works in VR too!)