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Minimal Coverage of Investigated Object when Seeking for its Fractal Dimension

  • Adam Szustalewicz

Abstract

The measuring of the complexity of river shapes is very important in erosion problems. A perfectly useful way for it is calculating the fractal dimension of curves representing rivers on maps. The shapes of rivers vary in form from smooth to very complicated and algorithm for calculating their fractal dimension should be universal and give good results for both. The paper considers the essence of fulfilling the very difficult and numerically very expensive assumption of the fractal theory about the minimal coverage of the measured objects. The actual version of the algorithm taking care to fulfill the assumption is compared, using 59 objects of different kinds and known fractal dimensions, with four easier and cheaper algorithms of covering. For some objects the obtained results are similar, but generally the elaborated algorithm is the best.

Keywords

Fractal Dimension Hausdorff Dimension Special Subset Minimal Coverage True Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Adam Szustalewicz
    • 1
  1. 1.Institute of Computer Science Wroclaw Universityul. Joliot-Curie 15Wrocńaw

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