Spatial Statistics of Apollonian Gaskets

Weiru Chen; Mo Jiao; Calvin Kessler; Amita Malik; Xin Zhang

doi:10.1080/10586458.2017.1385037

Spatial Statistics of Apollonian Gaskets

Weiru Chen
, Mo Jiao
, Calvin Kessler
, Amita Malik
, Xin Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Apollonian gaskets are formed by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We experimentally study the nearest neighbor spacing, pair correlation, and electrostatic energy 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 certain interesting limiting behaviors.

Original language	English (US)
Pages (from-to)	263-270
Number of pages	8
Journal	Experimental Mathematics
Volume	28
Issue number	3
DOIs	https://doi.org/10.1080/10586458.2017.1385037
State	Published - Jul 3 2019

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1080/10586458.2017.1385037

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title = "Spatial Statistics of Apollonian Gaskets",

abstract = "Apollonian gaskets are formed by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We experimentally study the nearest neighbor spacing, pair correlation, and electrostatic energy 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 certain interesting limiting behaviors.",

author = "Weiru Chen and Mo Jiao and Calvin Kessler and Amita Malik and Xin Zhang",

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AU - Chen, Weiru

AU - Jiao, Mo

AU - Kessler, Calvin

AU - Malik, Amita

AU - Zhang, Xin

PY - 2019/7/3

Y1 - 2019/7/3

N2 - Apollonian gaskets are formed by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We experimentally study the nearest neighbor spacing, pair correlation, and electrostatic energy 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 certain interesting limiting behaviors.

AB - Apollonian gaskets are formed by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We experimentally study the nearest neighbor spacing, pair correlation, and electrostatic energy 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 certain interesting limiting behaviors.

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JO - Experimental Mathematics

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Spatial Statistics of Apollonian Gaskets

Abstract

All Science Journal Classification (ASJC) codes

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