# Spatial Statistics of Apollonian Gaskets

## TL;DR

This paper investigates the statistical properties of circle centers in Apollonian gaskets, revealing interesting limiting behaviors after normalization despite their non-uniform distribution.

## Contribution

It provides the first experimental analysis of pair correlation, electrostatic energy, and spacing statistics of Apollonian gasket circle centers.

## Key findings

- Centers exhibit non-uniform distribution in ambient space
- Normalized statistics show limiting behaviors
- Potential implications for understanding fractal circle packings

## 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.