The dimension of the boundary of the Lévy Dragon

P. Duvall and J. Keesling

International Journal of Mathematics and Mathematical Sciences, 1997, vol. 20, 1-6

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 2 15 × 2 15 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 dim H ( K ) = ln ( λ ) ln ( ( 2 ) ) Perron-Frobenius theory played an important role in analyzing this matrix.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:850947

DOI: 10.1155/S0161171297000872

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