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Apollonian tiling, the Lorentz group, and regular trees

Söderberg, Bo LU (1992) In Physical Review A - Atomic, Molecular, and Optical Physics 46(4). p.1859-1866
Abstract

The Apollonian tiling of the plane into circles is analyzed with respect to its group properties. The relevant group, which is noncompact and discrete, is found to be identical to the symmetry group of a particular geometric tree graph in hyperbolic three-space. A linear recursive method to compute the radii is obtained. Certain modifications of the problem are investigated, and relations to other problems, such as the universal scaling of circle maps, are pointed out. © 1992 The American Physical Society.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
in
Physical Review A - Atomic, Molecular, and Optical Physics
volume
46
issue
4
pages
8 pages
publisher
American Physical Society (APS)
external identifiers
  • scopus:0010050835
ISSN
1050-2947
DOI
10.1103/PhysRevA.46.1859
language
English
LU publication?
yes
id
02f06279-b1d0-447b-a32e-4c48a11d3929
date added to LUP
2016-10-03 19:23:17
date last changed
2017-02-26 04:41:32
@article{02f06279-b1d0-447b-a32e-4c48a11d3929,
  abstract     = {<p>The Apollonian tiling of the plane into circles is analyzed with respect to its group properties. The relevant group, which is noncompact and discrete, is found to be identical to the symmetry group of a particular geometric tree graph in hyperbolic three-space. A linear recursive method to compute the radii is obtained. Certain modifications of the problem are investigated, and relations to other problems, such as the universal scaling of circle maps, are pointed out. © 1992 The American Physical Society.</p>},
  author       = {Söderberg, Bo},
  issn         = {1050-2947},
  language     = {eng},
  number       = {4},
  pages        = {1859--1866},
  publisher    = {American Physical Society (APS)},
  series       = {Physical Review A - Atomic, Molecular, and Optical Physics},
  title        = {Apollonian tiling, the Lorentz group, and regular trees},
  url          = {http://dx.doi.org/10.1103/PhysRevA.46.1859},
  volume       = {46},
  year         = {1992},
}