Sierpinski triangles on an icosahedron, inspired by Ghee Beom Kim

#sierpinskitriangle #icosahedron #geometricart #fractal #fractalart #iteratedfunctionsystem #3dgraphics #raymarching #pythoncode #numpy #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Another blow-up view of the Apollonian spheres, now dropping on a concave surface to gather all the jetsam together. This is what I had in mind when writing the first drop demo, and the model just needed a bit of refinement for the differently sized balls.

New demo just dropped! Testing a basic elastic model with blocks of FCC, BCC and diamond lattice.

#particlesimulation #elasticcollision #hookeslaw #bodycenteredcubic #facecenteredcubic #diamondlattice #lattice #crystalstructure #3dgraphics #pythoncode #numpy #opengl

Deforming Apollonian spheres, again using some interesting math that Bluesky doesn't want me to explain in this limited space.

Making Apollonian gaskets usually follows a key rule of iterated function systems: each iteration should make the thing smaller. With inversions, this means going from the outside to the inside of inverting circles.

However, it's possible to make valid gaskets using a lopsided configuration, where

Another look at Apollonian spheres, cutting out the top half and showing a few iteration steps.

#apollonianspheres #apolloniangasket #iteratedfunctionsystem #inversion #sphereinversion

Apollonian spheres

New implementation of the Apollonian Gasket iteration

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.

Apollonian gaskets via circle inversion.

For more explanation, you should see my posts on Instagram, Youtube, Facebook or Mathstodon where the posting limits are more sensible.

Different views of iterating the Apollonian gasket

Truncated octahedron Apollonian gasket

Another style for regular 2D Apollonian gaskets

#apolloniancircles #apolloniangasket #relief #emblem #geometricart #fractal #fractalart #raymarching #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Apollonian gaskets based on Platonic solids. The vertices of a tetrahedron/octahedron/icosahedron are used for the centre positions of the initial circles.

Riemann sphere mappings of Apollonian gaskets.

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.

Another look at the Apollonian gasket. This shows that the process doesn't use simple inversion, since that would distort the image within each disc.

#apolloniancircles #apolloniangasket #geometricart #fractal #fractalart #biblicallyaccurateangels #weirdart #creepyart #horrorart

Back to basics: I made an Apollonian gasket generator based on Descartes' theorem, as explained on Wikipedia. The method involves some nontrivial details on the choice of +/- signs, which I had to figure out on my own.

#gasketcase