Numerical investigations of discrete scale invariance in fractals and multifractal measures

Wei-Xing Zhou and Didier Sornette

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 13, 2623-2639

Abstract: Fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems. Here, we focus on lattice multifractals which exhibit complex exponents associated with observable log-periodicity. We perform detailed numerical analyses of lattice multifractals and explain the origin of three different scaling regions found in the moments. A novel numerical approach is proposed to extract the log-frequencies. In the non-lattice case, there is no visible log-periodicity, i.e., no preferred scaling ratio since the set of complex exponents spreads irregularly within the complex plane. A non-lattice multifractal can be approximated by a sequence of lattice multifractals so that the sets of complex exponents of the lattice sequence converge to the set of complex exponents of the non-lattice one. An algorithm for the construction of the lattice sequence is proposed explicitly.

Keywords: Fractal and multifractal; Discrete scale invariance; Log-periodicity; Complex dimensions; Numerical simulations (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:13:p:2623-2639

DOI: 10.1016/j.physa.2009.03.023

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