Spatial Statistics of Apollonian Gaskets
Metric Geometry
2017-05-19 v2 Mathematical Physics
Dynamical Systems
math.MP
Abstract
Apollonian gaskets are formed by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We experimentally study the pair correlation, electrostatic energy, and nearest neighbor spacing of centers of circles from Apollonian gaskets. Even though the centers of these circles are not uniformly distributed in any `ambient' space, after proper normalization, all these statistics seem to exhibit some interesting limiting behaviors.
Cite
@article{arxiv.1705.06212,
title = {Spatial Statistics of Apollonian Gaskets},
author = {Weiru Chen and Mo Jiao and Calvin Kessler and Amita Malik and Xin Zhang},
journal= {arXiv preprint arXiv:1705.06212},
year = {2017}
}
Comments
8 pages, 13 figures