PL EN


Preferences help
enabled [disable] Abstract
Number of results
2009 | 115 | 3 | 636-640
Article title

Roughness Method to Estimate Fractal Dimension

Content
Title variants
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
Year
Volume
115
Issue
3
Pages
636-640
Physical description
Dates
published
2009-03
received
2009-01-30
(unknown)
2009-02-03
References
  • 1. B.B. Mandelbrot, The Fractal Geometry of Nature, Freeman, New York 1982
  • 2. L.S. Liebovitch, T. Toth, Phys. Lett. A 141, 386 (1989)
  • 3. P. Grassberger, I. Procaccia, Phys. Rev. Lett. 50, 346 (1983)
  • 4. C.W. Lung, J. Jiang, E.K. Tian, C.H. Zhang, Phys. Rev. E 60, 5121 (1999)
  • 5. J.L. Zubimendi, M.E. Vela, R.C. Salvarezza, L. Vázquez, J.M. Vara, A.J. Arvia, Phys. Rev. E 50, 1367 (1994)
  • 6. B.B. Mandelbrot, A Theory of Roughness, in: Edge Foundations Inc., Ed. J. Brockman: www.edge.org/3rd_culture/mandelbrot04/mandelbrot04_index.html
  • 7. B.B. Mandelbrot, Phys. Scr. 32, 257 (1985)
  • 8. A. Błachowski, K. Ruebenbauer, J. Przewoźnik, J. Żukrowski, J. Alloys Comp. 458, 96 (2008)
  • 9. A. Błachowski, K. Ruebenbauer, A. Rakowska, in: Problems of Modern Techniques in Engineering and Education, Eds. P. Kurtyka, P. Malczewski, K. Mroczka, I. Sulima, IT Monograph, Kraków 2007, p. 161; see also: www.elektron.ap.krakow.pl/fractal.pdf
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.bwnjournal-article-appv115n307kz
Identifiers
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.