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The dynamics of the angular and radial density correlation scaling exponents in fractal to non-fractal morphodynamics

Author

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  • Nicolás-Carlock, J.R.
  • Solano-Altamirano, J.M.
  • Carrillo-Estrada, J.L.

Abstract

Fractal/non-fractal morphological transitions allow for the systematic study of the physics behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and equivalently computed from the scaling of the two-point radial- or angular-density correlations. However, these two quantities lead to discrepancies during the analysis of basic systems, such as in the diffusion-limited aggregation fractal. Hence, the corresponding clarification regarding the limits of the radial/angular scaling equivalence is needed. In this work, considering three fundamental fractal/non-fractal transitions in two dimensions, we show that the unavoidable emergence of growth anisotropies is responsible for the breaking-down of the radial/angular equivalence. Specifically, we show that the angular scaling behaves as a critical power-law, whereas the radial scaling as an exponential that, under the fractal dimension interpretation, resemble first- and second-order transitions, respectively. Remarkably, these and previous results can be unified under a single fractal dimensionality equation.

Suggested Citation

  • Nicolás-Carlock, J.R. & Solano-Altamirano, J.M. & Carrillo-Estrada, J.L., 2020. "The dynamics of the angular and radial density correlation scaling exponents in fractal to non-fractal morphodynamics," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077920300485
    DOI: 10.1016/j.chaos.2020.109649
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    References listed on IDEAS

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    1. Philip Ball, 2013. "In retrospect: On Growth and Form," Nature, Nature, vol. 494(7435), pages 32-33, February.
    2. Tolman, Susan & Meakin, Paul, 1989. "Two, three and four-dimensional diffusion-limited aggregation models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 158(3), pages 801-816.
    3. Filipe Leoncio Braga & Alexandre Barbosa de Souza, 2017. "Pair-Pair Angular Correlation Function," Chapters, in: Fernando Brambila (ed.), Fractal Analysis - Applications in Health Sciences and Social Sciences, IntechOpen.
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    Cited by:

    1. García-Sandoval, J.P., 2020. "Fractals and discrete dynamics associated to prime numbers," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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