Roughness Method to Estimate Fractal Dimension

• Authors: A. Błachowski , K. Ruebenbauer
• Languages of publication: EN

Abstracts

EN

A method based on the pattern roughness was introduced for determination of the fractal dimension and tested for fractals like the Sierpiński carpet, the Sierpiński triangle, standard Cantor set, the Menger sponge and the Sierpiński tetrahedron. It was tested for non-fractal pattern like two- and four-dimensional gray scale random dust as well. It was found that for all these patterns the Hausdorff dimension is reproduced with relatively high accuracy. Roughness method is based on simple, fast and easy to implement algorithm applicable in any topological dimension. It is particularly suited for patterns being composed of the hierarchy of structures having the same topological dimension as the space embedding them. It is applicable to "fuzzy" patterns with overlapping structures, where other methods are useless. It is designed for pixelized structures, the latter structures resulting as typical experimental data sets.

Keywords

EN

05.45.Df; 61.43.Hv

Discipline

• 05.45.Df: Fractals(see also 47.53.+n Fractals in fluid dynamics; 61.43.Hv Fractals; macroscopic aggregates in structure of solids)
• 61.43.Hv: Fractals; macroscopic aggregates (including diffusion-limited aggregates)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2009
• Volume: 115
• Issue: 3
• Pages: 636-640

Dates

published

2009-03

received

2009-01-30

(unknown)

2009-02-03

Contributors

author

A. Błachowski

• Mössbauer Spectroscopy Division, Institute of Physics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

author

K. Ruebenbauer

• Mössbauer Spectroscopy Division, Institute of Physics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

References

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Identifiers

DOI

10.12693/APhysPolA.115.636