International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 4, Pages 627-632
doi:10.1155/S0161171297000872

The dimension of the boundary of the Lévy Dragon

P. Duvall1 and J. Keesling2

1Department of Mathematical Sciences, University of North Carolina at Greensboro, Greensboro 27412, NC, USA
2Department of Mathematics, University of Florida, P.O Box 118105, 358 Little Hall, Gainesville 32611-8105, FL, USA

Received 7 April 1997

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper we describe the computations done by the authors in determining the dimension of the boundary of the Lévy Dragon. A general theory was developed for calculating the dimension of a self-similar tile and the theory was applied to this particular set. The computations were challenging. It seemed that a matrix which was 215×215 would have to be analyzed. It was possible to reduce the analysis to a 752×752 matrix. At last it was seen that if λ was the largest eigenvalue of a certain 734×734 matrix, then dimH(K)=ln(λ)ln((2)) Perron-Frobenius theory played an important role in analyzing this matrix.