Is a Power-Law Form of the Correlation Gamma Function Sufficient to State that a Distribution Has Fractal Properties? (Englisch)

Nationallizenz
in Astrophysics ; 45 , 1 ; 79-87
Astrophysics

Abstract

This investigation indicates an ambiguity in interpreting the results of applying the apparatus of the correlation gamma function [Γ(r) and Γ*(r)] to analyze the spatial distribution of objects from some sample. The presence of a linear section in the dependences of log(Γ) on log(r) and of log(Γ*) on log(r) proves to be insufficient to state that the distribution has fractal properties (self-similarity). It is shown that a change in the geometrical boundaries of the sample may influence the form of the dependences of log(Γ) on log(r) and of log(Γ*) on log(r).

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