https://www.youtube.com/watch?v=u-_vr7cPUtA

I wanted to know how to specify and create all possible Steiner chains in the extended complex plane.
This was made much easier by the fact that Steiner chains are closed under mobius transformations.

I wrote the code in R, rendered it to .png using Cairo, and then converted to .mp4 with ffmpeg.

I used these sources heavily while putting this together:

[1] Pedoe, D. (1970) Geometry, a Comprehensive Course, Cambridge University Press, Cambridge.

[2] https://en.wikipedia.org/wiki/Steiner_chain

[3] https://en.wikipedia.org/wiki/Generalised_circle

[4] https://en.wikipedia.org/wiki/M%C3%B6bius_transformation

#steinerchains #steinersporism #mobius #mobiustransforms

#introduction

Hi, I'm Sônia, 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