Apollonian depth and the accidental fractal

Abstract

The depth function of three numbers representing curvatures of three mutually tangent circles is introduced. Its 2D plot leads to a partition of the moduli space of the triples of mutually tangent circles/disks that is unexpectedly a beautiful fractal, the general form of which resembles that of an Apollonian disk packing, except that it consists of ellipses instead of circles.

31+4 pages, 20+4 figures

References in corpus (1)

• A note on unbounded Apollonian disk packings

Cited by in corpus (2)

• Apollonian depth, spinors, and the super-Dedekind tessellation
• Integral spinors, Apollonian disk packings, and Descartes groups