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Morphological Features of Mathematical and Real-World Fractals: A Survey

Miguel Patiño-Ortiz, Julián Patiño-Ortiz

2024Englishfractalsmorphologyscale invariancemultifractalitylacunarityanisotropy

Abstract

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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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Cite This Work

@article{34ea0c8b-3c1f-45ad-bb57-8a60cb31da29,
  title={Morphological Features of Mathematical and Real-World Fractals: A Survey},
  author={Miguel Patiño-Ortiz and Julián Patiño-Ortiz},
  year={2024},
  language={English}
}
TY  - JOUR
TI  - Morphological Features of Mathematical and Real-World Fractals: A Survey
AU  - Miguel Patiño-Ortiz
AU  - Julián Patiño-Ortiz
PY  - 2024
LA  - English
ER  -

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