Characterizing the lacunarity of random and deterministic fractal sets

C. Allain and M. Cloitre
Phys. Rev. A 44, 3552 – Published 1 September 1991
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Abstract

The notion of lacunarity makes it possible to distinguish sets that have the same fractal dimension but different textures. In this paper we define the lacunarity of a set from the fluctuations of the mass distribution function, which is found using an algorithm we call the gliding-box method. We apply this definition to characterize the geometry of random and deterministic fractal sets. In the case of self-similar sets, lacunarity follows particular scaling properties that are established and discussed in relation to other geometrical analyses.

  • Received 2 January 1991

DOI:https://doi.org/10.1103/PhysRevA.44.3552

©1991 American Physical Society

Authors & Affiliations

C. Allain and M. Cloitre

  • Laboratoire de Physique et Mécanique des Milieux Hétérogènes, Ecole Supérieure de Physique et de Chimie Industrielles de la Ville de Paris, 10 rue Vauquelin, 75231 Paris CEDEX, France

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Vol. 44, Iss. 6 — September 1991

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