Apollonian depth and the accidental fractal

Apollonian depth, spinors, and the super-Dedekind tessellation

The configuration space of tricycles (triples of disks in contact) is shown to coincide with the complex plane resulting as a projective space costructed from the tangency and Pauli spinors. Remarkably, the fractal of the depth functions assumes a particularly simple and elegant form. Moreover, the factor space due to a certain symmetry group provides a parametrization of the Apollonian disk packings.

阿波罗尼奥斯垫片的豪斯多夫维数

Hausdorff dimension of the Apollonian gasket

本文针对阿波罗尼奥斯垫片豪斯多夫维数缺乏闭形式且难以严格计算的问题，提出一种高效估计抛物极限集维数的方法，首次将其计算至128位小数并给出严格误差界，且有望推广至其他抛物分形。