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An improved method to estimate the fractal dimension of physical fractals based on the Hausdorff definition

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  • Martı́nez-López, F.
  • Cabrerizo-Vı́lchez, M.A.
  • Hidalgo-Álvarez, R.

Abstract

In this paper we present an algorithm to estimate the Hausdorff fractal dimension. The algorithm uses a recursive formula with a fast enough convergence. The accuracy of results is independent on the size, i.e., degree of definition of the fractal set. This fact is particularly useful when studying real physical fractals with a low definition, such as colloidal aggregates of small size. The different tests reveal no dependence of the results on the irregularities of the fractal. Thus, self-similarity or statistical similarity of the fractal set does not affect results. The proposed algorithm gives correct values for all the fractal dimension of the tested sets. Finally, the algorithm was used to evaluate the Hénon attractor fractal dimension and was applied to an experimental system obtained from a two-dimensional aggregation of latex colloidal particles.

Suggested Citation

  • Martı́nez-López, F. & Cabrerizo-Vı́lchez, M.A. & Hidalgo-Álvarez, R., 2001. "An improved method to estimate the fractal dimension of physical fractals based on the Hausdorff definition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 387-399.
    • Handle: RePEc:eee:phsmap:v:298:y:2001:i:3:p:387-399
    DOI: 10.1016/S0378-4371(01)00255-2
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    Cited by:

    1. Carletti, Timoteo & Galatolo, Stefano, 2006. "Numerical estimates of local dimension by waiting time and quantitative recurrence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 120-128.
    2. Spodarev, Evgeny & Straka, Peter & Winter, Steffen, 2015. "Estimation of fractal dimension and fractal curvatures from digital images," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 134-152.

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