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The Hausdorff dimension of the boundary of the Lévy Dragon

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Paul F. Duvall, Professor and Director of Graduate Study (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/

Abstract: 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 Lévy 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 × 752 matrix. Perron-Frobenius theory plays an important role in analyzing this matrix.

Additional Information

Publication
arXiv:math/9907145v1 [math.DS] 22 Jul 1999
Language: English
Date: 1999
Keywords
Hausdorff dimension, iterated function systems, attractors, fractal geometry, Lévy Dragon