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

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

Chaos, Solitons & Fractals, 2020, vol. 133, issue C

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.

Keywords: Morphology; Scaling; Fractality; Transitions; Universality (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077920300485

DOI: 10.1016/j.chaos.2020.109649

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