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Determination of fractal dimensions for geometrical multifractals

✍ Scribed by Tamás Tél; Ágnes Fülöp; Tamás Vicsek

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
706 KB
Volume
159
Category
Article
ISSN
0378-4371

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✦ Synopsis

Two independent approaches, the box counting and the sand box methods are used for the determinatiov of the generalized dimensions (Dq) associated with, the geometrical structure of growing deterministic fractals. We find that the muitifractal nature of the geometry results in an unusually slow convergence of the numerically calculated Dq's to their true values. Our study demonstrates that the above-mentioned two methods are equivalent only if the sand box method is applied with an averaging over randomly selected centres. In this case the latter approach provides better estimates of the generalized dimensions.

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