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.