Apollonian depth and the accidental fractal (original) (raw)

Jerzy Kocik

2020, arXiv:2002.04135

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35 pages

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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.

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