Characterizing the lacunarity of random and deterministic fractal sets
- 1 September 1991
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 44 (6) , 3552-3558
- https://doi.org/10.1103/physreva.44.3552
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.Keywords
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