#riemannsphere — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #riemannsphere, aggregated by home.social.
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2D circle inversion fractals on the spherical surface. This was a fun offshoot of my recent Apollonian endeavours, again using the Riemann sphere mapping to go from 3D to 2D for the iterations.
The inversion circle centres come from a tetrakis hexahedron and a triakis icosahedron, so the circles form approximations of a truncated octahedron and a truncated dodecahedron.
#apolloniancircles #apolloniangasket #inversion #circleinversion #riemannsphere #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati
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The set of polyhedra that can be converted into Apollonian gaskets via sphere-plane mapping is quite limited. The face polygons should be regular, the edge midpoints should all lie on the same sphere, and the vertices should be 3-fold. There are some Platonic solids that work, and I've showed all of these earlier. It turns out that Archimedean solids with 3-fold vertices work too. So here's a truncated octahedron, also showing a progressive view of the gasket iteration.
#apolloniancircles #apolloniangasket #riemannsphere #archimedeansolid #truncatedoctahedron #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati