Bo Söderberg
Teaching staff
Apollonian tiling, the Lorentz group, and regular trees
Author
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