THE FRACTAL DIMENSION OF THE APOLLONIAN SPHERE PACKING-Reference-Cited by-同舟云学术

THE FRACTAL DIMENSION OF THE APOLLONIAN SPHERE PACKING

Published:1994-12 Issue:04 Volume:02 Page:521-526
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

BORKOVEC M.¹,DE PARIS W.¹,PEIKERT R.²

Affiliation:

1. Institute of Terrestrical Ecology, Federal Institute of Technology ETH, Grabenstrasse 3, 8952 Schlieren, Switzerland

2. Interdisciplinary Project Center for Supercomputing, Federal Institute of Technology ETH, Clausiusstrasse 59, 8092 Zürich, Switzerland

Abstract

The fractal dimension of the Apollonian sphere packing has been computed numerically up to six trusty decimal digits. Based on the 31 944 875 541 924 spheres of radius greater than 2−19 contained in the Apollonian packing of the unit sphere, we obtained an estimate of 2.4739465, where the last digit is questionable. Two fundamentally different algorithms have been employed. Outlines of both algorithms are given.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X94000739

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