1999/07/22 by P. Duvall, P. F. Duvall, Duvall, P. +3
Computer Science · Mathematics · Physics and Astronomy · #28A20 #54E40 #57Nxx (Primary) #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Theoretical and Computational Physics #math.DS #msc:28A20 #msc:54E40 #msc:57Nxx
paper · pdf · doi:10.48550/arxiv.math/9907145
12 pages, 4 figures
arxiv created 1999/07/22 · openalex publication_date 1999/07/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.