Determination of fractal dimensions for geometrical multifractals

T. Tél, Ágnes Fülöp, T. Vicsek

Research output: Contribution to journalArticle

109 Citations (Scopus)

Abstract

Two independent approaches, the box counting and the sand box methods are used for the determination of the generalized dimensions (Dq) associated with the geometrical structure of growing deterministic fractals. We find that the multifractal 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.

Original languageEnglish
Pages (from-to)155-166
Number of pages12
JournalPhysica A: Statistical Mechanics and its Applications
Volume159
Issue number2
DOIs
Publication statusPublished - Aug 15 1989

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Fractal Dimension
Generalized Dimensions
boxes
fractals
sands
Averaging
Fractal
Counting
counting
estimates
geometry
Estimate
Demonstrate

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Determination of fractal dimensions for geometrical multifractals. / Tél, T.; Fülöp, Ágnes; Vicsek, T.

In: Physica A: Statistical Mechanics and its Applications, Vol. 159, No. 2, 15.08.1989, p. 155-166.

Research output: Contribution to journalArticle

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