The Apollonian Gasket
Constructing the Apollonian gasket fractal from Descartes' Circle Theorem and its complex extension. Includes an elementary algebraic proof, the Lagarias-Mallows-Wilks complex form, and a queue-based Python implementation.
A fractal of mutually tangent circles. The handout walks from Descartes’ 1643 theorem through Levrie’s elementary proof to the complex extension that determines not just the radii but the centres of the new tangent circles, then runs the resulting algorithm in Python with a queue-based traversal that processes each tangent triple exactly once.