Entropy of fractal systems

Computers and Mathematics with Applications

Volumn 66, Issue 2, 2013, Pages 135-146

  Zmeskal, Oldrich ^a   Dzik, Petr ^a   Vesely, Michal ^a  

^a BRNO UNIVERSITY OF TECHNOLOGY   (Czech Republic)

Author keywords

Fractal dimension; Fractal geometry; Fractal measure; Fractal physics; Kolmogorov entropy; R nyi entropy; Shannon entropy; Thermodynamic entropy

Indexed keywords

FRACTAL GEOMETRY; FRACTAL MEASURES; KOLMOGOROV ENTROPIES; SHANNON ENTROPY; THERMODYNAMIC ENTROPY;

ALGORITHMS; MATHEMATICAL MODELS;

FRACTAL DIMENSION;

EID: 84880216441     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2013.01.017     Document Type: Article

References (18)

1. C.E. Shannon A mathematical theory of communication Bell Syst. Tech. J. 27 1948 379 423 623-656
2. A. Rényi Probability Theory 1970 Elsevier
3. A. Garrido Classifying entropy measures Symmetry 3 2011 487 502 10.3390/sym3030487
4. M. Higashi, and G.J. Klir Measures of uncertainty and information based on possibility distributions Int. J. General Syst. 9 1982 43 58
5. T.S. Han, and K. Kobayashi Mathematics of Information and Coding 2002 American Mathematical Society 978-0-8218-4256-0 pp. 19-20
6. P. Grassberger, and I. Procaccia Characterization of strange attractors Physical Review Letters 50 5 1983 346 349 10.1103/PhysRevLett.50.346
7. P. Grassberger, and I. Procaccia Estimation of the Kolmogorov entropy from a chaotic signal Phys. Rev. A 28 4 1983 2591 2593 10.1103/PhysRevA.28.2591
8. H. Trochet A History of Fractal Geometry 2009 MacTutor History of Mathematics
9. L.F. Richardson, O.M. Ashford, H. Charnock, P.G. Drazin, J.C.R. Hunt, P. Smoker, I. Sutherland, The Collected Papers of Lewis Fry Richardson, Cambridge, 1993. ISBN 978-0-521-38297-7; ISBN 978-0-521-38298-4.
10. B.B. Mandelbrot How long is the coast of britain? statistical self-similarity and fractional dimension Science, New Series 156 1967 636 638 10.1126/science.156.3775.636
11. B.B. Mandelbrot Fractal Geometry of Nature 1983 W. H. Freeman and Co. New York
12. O. Zmeskal, M. Nezadal, and M. Buchnicek Fractal-Cantorian geometry, Hausdorff dimension and the fundamental laws of physics Chaos, Solitons & Fractals 17 2003 113 119
13. B.B. Mandelbrot A fractal set is one for which the fractal (Hausdorff-Besicovitch) dimension strictly exceeds the topological dimension Fractals and Chaos 2004 Springer 978-0-387-20158-0
14. P. Jerabkova, O. Zmeskal, and J. Haderka Fractal analysis of the images using wavelet transformation In Complexus Mundi - Emergent Patterns in Nature 2006 World Scientific Singapore 300 312
15. K. Tomankova, P. Jerabkova, O. Zmeskal, M. Vesela, and J. Haderka Use of the image analysis to study growth and division of yeastcells J. Imaging Sci. Technology. 50 2006 583 589
16. © 1997-2012.
17. O. Zmeskal, M. Nezadal, and M. Buchnicek Fractal analysis of printed structures J. Imaging Sci. Technol. 46 2002 453 456
18. Wikipedia, the free encyclopedia, http://en.wikipedia.org (Accessed May 2012).