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Numerical problems with evaluating the fractal dimension of real data

  • Ada Szustalewicz

Abstract

A new program RIVER for evaluating the fractal dimension of real data sets was written. Its performance was compared with two programs HarFA — demo version and Coastline, available in Internet. The three programs were tested on about 50 data sets. The program RIVER yielded the maximal errors less than 3 percentages for all tested data sets, while the other tested programs gave more than 10 percentage errors.

Key words

Dimension Fractals Fractal dimension Box-counting Structure complexity 

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References

  1. [1]
    Buchnicek M., Nezadal M., Zmeskal O. 2000. ‘Numeric calculation of fractal dimension’. Nostradamus 2000. Prediction Conference.Google Scholar
  2. [2]
    Edgar G. 1990. ‘Measures, Topology and Fractal Geometry’. Springer-Verlag, New York.Google Scholar
  3. [3]
    Falconer K.J. 1985. ‘The Geometry of Fractal Sets’. Cambridge University Press. Cambridge.Google Scholar
  4. [4]
    Gonzato G., Mulargia F., Ciccotti M. 2000. ‘Measuring the fractal dimensions of ideal and actual objects: implications for application in geology and geophysics’. Geophys. J. Int. 142, 108–116.CrossRefGoogle Scholar
  5. [5]
    Gonzato G., Mulargia F., Marzochi W. 1998. ‘Practical application of fractal analysis: problems and solutions’. Geophys. J. Int. 132, 275–282.CrossRefGoogle Scholar
  6. [6]
    Har FA-Zmeskal O., Nezadal M., Buchnicek M. 2000. ‘Harmonic and Fractal Image Analyzer’. http://www.fch.vutbr.cz/lectures/imagesci/harfa.htm.Brno.Google Scholar
  7. [7]
    http://www.iamg.org/CGEditor/cgl998.htm. (look for Gonzato).Google Scholar
  8. [8]
    http://polymer.bu.edu/ogaf/html/chp211ab2.htm. Simulab 2: Covering a coastline.Google Scholar
  9. [9]
    Kolmogorov A. 1958. ‘Sur les proprietes des functions de concentrations de M.P. Levy’. Ann. Inst. H. Poincare. 16, 27–34.zbMATHMathSciNetGoogle Scholar
  10. [10]
    Kraft R. 1995. ‘Fractals and Dimensions’. HTTP-Protocol at www.weihenstephan.de. http://www.weihenstephan.de/ane/dimensions/dimensions.html.Google Scholar
  11. [11]
    Kraft R. ‘Test Images’. http://www.weihenstephan.de/dvs/idolon/idolonhtml/testimg.htmlGoogle Scholar
  12. [12]
    Mandelbrot B.B. 1977. ‘The fractal geometry of nature’. W.H.Freeman and Co., San Francisco.Google Scholar
  13. [13]
    Patzek Tad. W. 2003. E240 Lecture 3: ‘The Fractal Dimension’. 27 pp. http://patzek.berkeley.edu/indexold.html. main page. http://petroleum.berkeley.edu/patzek/e240/Lecture04Materials.htm. Coastline.Google Scholar
  14. [14]
    Peitgen H.O., Jurgens H., Saupe D. 1992. ‘Chaos and Fractals. New Frontiers of Science’. Springer-Verlag. New York.Google Scholar
  15. [15]
    Stromberg F. ‘Iterated function systems, the chaos game and invariant measures’. Uppsala Universitet. http://www.math.uu.se/staff/pages/?uname=fredrik.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Ada Szustalewicz
    • 1
  1. 1.Institute of Computer ScienceWrocław UniversityWrocław

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