How to calculate the Hausdorff dimension using fractal structures

DOI10.1016/j.amc.2015.04.059zbMath1410.28003OpenAlexW2219449664MaRDI QIDQ1659636

Miguel Angel Sánchez-Granero, Manuel Fernández-Martínez

Publication date: 22 August 2018

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.04.059

zbMATH Keywords

Hausdorff dimensionfractal dimensionfractalfractal structureself-similar setopen set condition

Mathematics Subject Classification ID

Topological spaces with richer structures (54E99) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (8)

Fractal dimension for IFS-attractors revisited ⋮ A survey on fractal dimension for fractal structures ⋮ Irreducible fractal structures for Moran type theorems ⋮ Counterexamples in theory of fractal dimension for fractal structures ⋮ A novel approach to improve the accuracy of the box dimension calculations: applications to trabecular bone quality ⋮ Calculating Hausdorff dimension in higher dimensional spaces ⋮ Theoretical properties of fractal dimensions for fractal structures ⋮ Generating pre-fractals to approach real IFS-attractors with a fixed Hausdorff dimension

Uses Software

• Scikit

Cites Work

• Fractal dimension for fractal structures
• Fractal dimension for fractal structures: A Hausdorff approach
• A new approach to metrization
• Hausdorff dimension of self-similar sets with overlaps
• Support-vector networks
• Fractal dimension for fractal structures: a Hausdorff approach revisited
• Fractal dimension for fractal structures: applications to the domain of words
• HAUSDORFF DIMENSION OF SELF-SIMILAR SETS WITH OVERLAPS
• A Computer Algorithm for Determining the Hausdorff Dimension of Certain Fractals
• On the Weierstrass-Mandelbrot fractal function
• Calculating Hausdorff dimension of Julia sets and Kleinian limit sets
• Completion of hyperspaces of compact subsets and topological completion of open-closed maps
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