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

#ArtAdventCalendar Day 10

Continuing to progress through the algorithms in "Indra's Pearls". I got "grandma's recipe" implemented in #Python and used it to draw a swirly-thing.

I cheated and manually filled the color inside the swirl using Gimp; my code doesn't do that (not yet anyway).

#fractal #indraspearls #swirly

#ArtAdventCalendar Day 4.

I started working through the book "Indra's Pearls" by David Mumford, Caroline Series, and David Wright. And by working, I mean implementing the pseudo-code in #python. It's fun when you recognize that a messy triple-nested loop algorithm in the book can be replaced by a single `itertools.product` followed by a `filter` call - which makes one appreciate the ease of coding in Python!

This is a "Theta-Schottky group" fractal inspired by Exercise 4.2 in the book.

#indraspearls #fractal #schottkygroup #itertools

#introduction

Hi, I'm Sônia (she/her), and this is my hobbyist computational-math account. I decided to invest some time into _Indra's Pearls_ by Mumford, Series, Wright a little over a decade ago, and a quest that started out with "do all the assignments" has turned into a personal research and artistic program.

I spend a lot of time thinking about sets of tangent circles. So much so that if I got a "revive an ancient mathematician for a day" boon, I'd spend it on Apollonius. I'm pretty sure that my guy from Perga would a) be fascinated by the beauty of Kleinian double-cusp groups and b) tell me we were cheating by using calculations instead of construction. Sorry, fans of Euclid, Brahmagupta, and person-who-invented-zero. #academicnecromancy

This account is intended to be primarily used to post artwork/videos and links to interactive demos, explanations of the techniques used to render them, and engaging with any discussions prompted by the preceding.

#kleiniangroups #steinerchains #fractionallineartransforms #mobius #fractals #R #glsl #shadertoy #indraspearls #mobiustransforms