International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 4, Pages 627-632
The dimension of the boundary of the Lévy Dragon
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 P. Duvall and J. Keesling. 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.
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 would have to be analyzed. It was possible to reduce the analysis to a
matrix. At last it was seen that if
was the largest eigenvalue of a
certain matrix, then Perron-Frobenius theory played an important role
in analyzing this matrix.