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Structural characterization of chaos game fractals using small-angle scattering analysis

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  • Eugen Mircea Anitas
  • Azat Slyamov

Abstract

Small-angle scattering (SAS) technique is applied to study the nano and microstructural properties of spatial patterns generated from chaos game representation (CGR). Using a simplified version of Debye formula, we calculate and analyze in momentum space, the monodisperse scattering structure factor from a system of randomly oriented and non-interacting 2D Sierpinski gaskets (SG). We show that within CGR approach, the main geometrical and fractal properties, such as the overall size, scaling factor, minimal distance between scattering units, fractal dimension and the number of units composing the SG, can be recovered. We confirm the numerical results, by developing a theoretical model which describes analytically the structure factor of SG. We apply our findings to scattering from single scale mass fractals, and respectively to a multiscale fractal representing DNA sequences, and for which an analytic description of the structure factor is not known a priori.

Suggested Citation

  • Eugen Mircea Anitas & Azat Slyamov, 2017. "Structural characterization of chaos game fractals using small-angle scattering analysis," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-16, July.
    • Handle: RePEc:plo:pone00:0181385
    DOI: 10.1371/journal.pone.0181385
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    Cited by:

    1. Mohammad Hossein Olyaee & Alireza Khanteymoori & Khosrow Khalifeh, 2020. "A chaotic viewpoint-based approach to solve haplotype assembly using hypergraph model," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-19, October.

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