I played with paint today. The packing radii for n-dimensional spheres is $/sqrt{n} - 1$ and spiral of archimedes hypotenuses follows sqrt(n), so I subtracted 1 from each hypotenuse and then added color.

8x8in gouache on hot pressed cotton

#mathArt #mtbos #math #ndimensions #spiral #sphere

Watch at: https://youtu.be/Aob27X_M2Nw
Play at: https://www.desmos.com/3d/usxmf3y1sk

#youtube #youtuber #youtubechannel #desmos #desmos3d #math #mathart #maths #mathematics #desert #cactus #animation #animated #animator #animation3d #3d #3dart #3danimation #graph #equation #nerd #geek

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.

The result looks a lot like some of the inversion fractals I've done over the years, and they are certainly related. But writing this classical method on the CPU side was an attempt to do and learn something different. Using 6 iterations was a compromise between detail and rendering speed — at 5 or so FPS this wasn't quite realtime, though I guess it can be optimized further.

#apolloniancircles #circleinversion #indraspearls #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati