Numerical investigations of discrete scale invariance in fractals and multifractal measures

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dc.creatorZhou, W. -X.
dc.creatorSornette, D.
dc.date2004-08-27
dc.date2007-04-17
dc.date.accessioned2026-07-07T13:03:27Z
dc.date.available2026-07-07T13:03:27Z
dc.descriptionFractals 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.
dc.description31 Elsart pages including 12 eps figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0408600
dc.identifierhttp://arxiv.org/abs/cond-mat/0408600
dc.identifierPhysica A 388 (13), 2623-2639 (2009)
dc.identifierdoi:10.1016/j.physa.2009.03.023
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/226811
dc.subjectStatistical Mechanics
dc.titleNumerical investigations of discrete scale invariance in fractals and multifractal measures
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