Abstract
A two-step procedure for the analysis of different-type fractals is proposed for the PaC and SePaC methods. An advantage of the two-step procedures of the PaC and SePaC methods over the basic and modified PaC and SePaC methods is shown. Results of comparative analysis of the unified data set using different approaches (the BC method and two-step procedures of the PaC and SePaC methods) are given. It is shown that the two-step procedure of the SePaC method is most efficient in reconstructing the overall data set.
Similar content being viewed by others
References
T. G. Dedovich and M. V. Tokarev, “Comparison of fractal analysis methods in the study of fractals with independent branching,” Phys. Part. Nucl. Lett. 10, 481 (2013).
T. G. Dedovich and M. V. Tokarev, “Analysis of fractals with dependent branching by box counting, P-adic coverages, and systems of equations of P-adic coverages,” Phys. Part. Nucl. Lett. 10, 491 (2013).
T. G. Dedovich and M. V. Tokarev, “Analysis of fractals with combined branching,” Preprint No. JINR P2-2015-92 (Dubna, 2015).
E. Feder, Fractals (Plenum, New York, 1988).
F. Hausdorff, “Dimension Und Ausseres Mass,” Math. Ann. 79, 157–179 (1919).
B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
A. Barabasi and H. Stanley, Fractal Concepts in Surface Growth (Cambridge Univ. Press, New York, USA, 1995).
F. Roueff and J. L. Vehel, “A regularization approach to fractional dimension estimation,” in Proceedings of the Conference on Fractals 98, Malta, 1998.
A. N. Pavlov and V. S. Anishchenko, “Multifractal analysis of complex signals,” Phys. Usp. 50, 819 (2007).
T. G. Dedovich and M. V. Tokarev, “P-adic coverage method in fractal analysis of showers,” Phys. Part. Nucl. Lett. 8, 521 (2011).
T. G. Dedovich and M. V. Tokarev, “Method of systems of equations of P-adic coverages for fractal analysis of events,” Phys. Part. Nucl. Lett. 9, 552 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © T.G. Dedovich, M.V. Tokarev, 2016, published in Pis’ma v Zhurnal Fizika Elementarnykh Chastits i Atomnogo Yadra, 2016.
Rights and permissions
About this article
Cite this article
Dedovich, T.G., Tokarev, M.V. A two-step procedure of fractal analysis. Phys. Part. Nuclei Lett. 13, 178–189 (2016). https://doi.org/10.1134/S1547477116020072
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1547477116020072