The Hausdorff dimension of the boundary of the Lévy dragon

Details The Hausdorff dimension of the boundary of the Lévy dragon The Hausdorff dimension of the boundary of the Lévy dragon

1999-07-22

arxiv.org/abs/math/9907145v1

Mathematics

Dynamical Systems

12 pages, 4 figures

Scientific paper

A theoretical approach to computing the Hausdorff dimension of the topological boundary of attractors of iterated function systems is developed. The curve known as the L\'evy Dragon is then studied in detail and the Hausdorff dimension of its boundary is computed using the theory developed. The actual computation is a complicated procedure. It involves a great deal of combinatorial topology as well as determining the structure and certain eigenvalues of a $752 \times 752$ matrix. Perron-Frobenius theory plays an important role in analyzing this matrix.

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