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

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

Jan 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002ap.....45...79t&link_type=abstract

Astrophysics (English translation of Astrofizika), v. 45, Issue 1, p. 79-87 (2002).

Astronomy and Astrophysics

Astrophysics

3

Scientific paper

This investigation indicates an ambiguity in interpreting the results of applying the apparatus of the correlation gamma function [(r) and *(r)] to analyze the spatial distribution of objects from some sample. The presence of a linear section in the dependences of log() on log(r) and of log(*) 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() on log(r) and of log(Γ*) on log(r).

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