Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-08-27
Physica A 388 (13), 2623-2639 (2009)
Physics
Condensed Matter
Statistical Mechanics
31 Elsart pages including 12 eps figures
Scientific paper
10.1016/j.physa.2009.03.023
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, {\em{i.e.}}, no preferred scaling ratio since the set of complex exponents spread 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.
Sornette Didier
Zhou Wei-Xing
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