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Inherent Features Of Fractal Sets And Key Attributes Of Fractal Models

Author

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  • ALEXANDER S. BALANKIN

    (ESIME-Zacatenco, Instituto Politécnico Nacional (IPN), Av. Luis Enrique Erro S/N, Unidad Profesional Adolfo López Mateos, Zacatenco, Alcaldía Gustavo A. Madero, C.P. 07738, Ciudad de México, Mexico)

  • JULIà N PATIÑO ORTIZ

    (ESIME-Zacatenco, Instituto Politécnico Nacional (IPN), Av. Luis Enrique Erro S/N, Unidad Profesional Adolfo López Mateos, Zacatenco, Alcaldía Gustavo A. Madero, C.P. 07738, Ciudad de México, Mexico)

  • MIGUEL PATIÑO ORTIZ

    (ESIME-Zacatenco, Instituto Politécnico Nacional (IPN), Av. Luis Enrique Erro S/N, Unidad Profesional Adolfo López Mateos, Zacatenco, Alcaldía Gustavo A. Madero, C.P. 07738, Ciudad de México, Mexico)

Abstract

The main goal of this work is to develop a robust framework for an exhaustive description of essential properties of a fractal object. For this purpose, the inherent features of fractal sets are scrutinized. The topological, metrological, morphological, and topographical attributes of fractal systems are delineated. The criteria of the fractal connectedness are established. The characteristics of the fractal connectivity and ramification are ascertained. The index of the fractal loopiness is introduced. The quantifications of the fractal heterogeneity, lacunarity, and anisotropy are briefly sketched out. A set of key attributes which enable a proper characterization of fractal system are suggested.

Suggested Citation

  • Alexander S. Balankin & Juliã N Patiã‘O Ortiz & Miguel Patiã‘O Ortiz, 2022. "Inherent Features Of Fractal Sets And Key Attributes Of Fractal Models," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-23, June.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:04:n:s0218348x22500827
    DOI: 10.1142/S0218348X22500827
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    Citations

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    Cited by:

    1. Balankin, Alexander S. & Mena, Baltasar, 2023. "Vector differential operators in a fractional dimensional space, on fractals, and in fractal continua," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Balankin, Alexander S., 2024. "A survey of fractal features of Bernoulli percolation," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    3. Didier Samayoa & Liliana Alvarez-Romero & José Alfredo Jiménez-Bernal & Lucero Damián Adame & Andriy Kryvko & Claudia del C. Gutiérrez-Torres, 2024. "Torricelli’s Law in Fractal Space–Time Continuum," Mathematics, MDPI, vol. 12(13), pages 1-13, June.
    4. Bevilacqua, Luiz & Barros, Marcelo M., 2023. "The inverse problem for fractal curves solved with the dynamical approach method," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    5. Balankin, Alexander S. & Ramírez-Joachin, Juan & González-López, Gabriela & Gutíerrez-Hernández, Sebastián, 2022. "Formation factors for a class of deterministic models of pre-fractal pore-fracture networks," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    6. Eduardo Reyes de Luna & Andriy Kryvko & Juan B. Pascual-Francisco & Ignacio Hernández & Didier Samayoa, 2024. "Generalized Kelvin–Voigt Creep Model in Fractal Space–Time," Mathematics, MDPI, vol. 12(19), pages 1-13, October.

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