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arXiv · 1705.06212

Spatial Statistics of Apollonian Gaskets

Weiru Chen·Mo Jiao·Calvin Kessler·Amita Malik·Xin Zhang
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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.

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Weiru Chen, Mo Jiao, Calvin Kessler, Amita Malik, Xin Zhang. 2017-05-17. Spatial Statistics of Apollonian Gaskets. https://arxiv.org/abs/1705.06212

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