M. Patiño-Ortiz, J. Patiño-Ortiz, M. Martínez-Cruz, Fernando René Esquivel-Patiño, A. Balankin
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引用次数: 0
Abstract
The aim of this review paper is to survey the fractal morphology of scale-invariant patterns. We are particularly focusing on the scale and conformal invariance, as well as on the fractal non-uniformity (multifractality), inhomogeneity (lacunarity), and anisotropy (succolarity). We argue that these features can be properly quantified by the following six adimensional numbers: the fractal (e.g., similarity, box-counting, or Assouad) dimension, conformal dimension, degree of multifractal non-uniformity, coefficient of multifractal asymmetry, index of lacunarity, and index of fractal anisotropy. The difference between morphological properties of mathematical and real-world fractals is especially outlined in this review paper.
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