Comparison of fractal analysis methods in the study of fractals with independent branching
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The notion of dimension as a quantitative characteristic of space geometry is discussed. It is supposed that hadrons created in interactions between particles and nuclei can be considered sets of points possessing fractal properties in the three-dimensional phase space (p T , η, ϕ). The Hausdorff-Besicovich dimension D F is considered the most natural characteristic for determining the fractal dimension. Different methods for determining the fractal dimension are compared: box counting (BC), P-adic coverage (PaC), and system of equations of P-adic coverage (SePaC). A procedure for choosing optimum values of parameters of the considered methods is presented. These parameters are shown to be able to reconstruct the fractal dimension D F , number of levels N lev, and fractal structure with maximal efficiency. The features of the PaC- and SePaC-methods in the analysis of fractals with independent branching are noted.
KeywordsFractal Dimension Nucleus Letter Reconstruction Error Parton Shower Admissible Range
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