Spatial Statistics of Apollonian Gaskets. Issue 3 (3rd July 2019)

• Record Type: Journal Article
• Authors: Chen, Weiru; Jiao, Mo; Kessler, Calvin; Malik, Amita; Zhang, Xin
• Is Part Of: Experimental mathematics. Volume 28:Issue 3(2019)
• Page Start: 263
• Page End: 270
• Publication Date: 2019-07-03
• Subjects: Apollonian gaskets -- pair correlation -- spatial statistics; 52C26; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2017.1385037
• Languages: English
• ISSNs: 1058-6458

Abstract

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.