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Bo Söderberg

Teaching staff

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Apollonian tiling, the Lorentz group, and regular trees

Author

  • Bo Söderberg

Summary, in English

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.

Department/s

  • Computational Biology and Biological Physics - Has been reorganised

Publishing year

1992

Language

English

Pages

1859-1866

Publication/Series

Physical Review A (Atomic, Molecular and Optical Physics)

Volume

46

Issue

4

Document type

Journal article

Publisher

American Physical Society

Status

Published

ISBN/ISSN/Other

  • ISSN: 1050-2947