Monday, September 28, 2015

[rmlkabxb] Space filling curves on spheres

Do space filling curves that uniformly fill the surface of a sphere exist?

It's probably possible to adapt an open space filling curve of a polygon and tile it, with connecting bits, onto a polyhedron, then project it on a sphere.  There are a few polyhedra whose faces can be traversed with a Hamiltonian circuit.  This seems a boring construction, though.

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