Apollonian gaskets based on Platonic solids. The vertices of a tetrahedron/octahedron/icosahedron are used for the centre positions of the initial circles. These are Riemann-sphere-mapped to the complex plane, where the gasket is iterated for more circles, and the result is mapped back onto the sphere. It's a little roundabout, but it works for me, and the heaviest part by far is drawing the visuals.

#apolloniancircles #apolloniangasket #riemannsphere #complexmath #platonicsolid #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Riemann sphere mappings of Apollonian gaskets. After the 2D gaskets, I'd been thinking of some kind of 3D versions for a while, but the final inspiration came from Antti Immonen's sculptures I saw on Friday at the opening of his exhibition here in Jyväskylä. As a real-life sculptor who incorporates fractals and other math ideas in his works, he's a pretty rare specimen at least by national standards.

Since my 2D gaskets are fitted to the unit circle, they cover exactly half of the Riemann sphere, as seen in the first part. My lazy solution to covering the entire sphere was a simple copy-paste, and the result doesn't seem too bad.

#apolloniancircles #apolloniangasket #riemannsphere #complexmath #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati