Apollonian depth, spinors, and the super-Dedekind tessellation

2020/09/06 by Jerzy Kocik, Kocik, Jerzy
Materials Science · Mathematics · Physics and Astronomy · #11F06 #15A66 #28A80 #51M15 #52C26 #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Metric Geometry (math.MG) #Number Theory (math.NT) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2009.02680

openalex publication_date 2020/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• A theorem on circle configurations
• A note on unbounded Apollonian disk packings
• Proof of Descartes circle formula and its generalization clarified
• On the Dedekind tessellation
• Spinors, lattices, and classification of integral Apollonian disk\n packings
• Apollonian depth and the accidental fractal

Related

• Apollonian depth and the accidental fractal
• Spinors, lattices, and classification of integral Apollonian disk\n packings
• Spinors and Descartes configurations of disks
• Integral spinors, Apollonian disk packings, and Descartes groups
• The sensual Apollonian circle packing