Numerical investigations of discrete scale invariance in fractals and multifractal measures Export

@article{citeulike:5940246, 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.}, author = {Zhou, Wei-Xing and Sornette, Didier}, citeulike-article-id = {5940246}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.physa.2009.03.023}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0378437109002222}, day = {01}, doi = {10.1016/j.physa.2009.03.023}, issn = {03784371}, journal = {Physica A: Statistical Mechanics and its Applications}, keywords = {2009, pdf, scale-invariance, statistics}, month = {July}, number = {13}, pages = {2623--2639}, posted-at = {2009-10-14 18:18:48}, priority = {2}, title = {Numerical investigations of discrete scale invariance in fractals and multifractal measures}, url = {http://dx.doi.org/10.1016/j.physa.2009.03.023}, volume = {388}, year = {2009} }

TY - JOUR ID - citeulike:5940246 L3 - citeulike-article-id:5940246 N2 - 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. IS - 13 JF - Physica A: Statistical Mechanics and its Applications SN - 03784371 EP - 2639 TI - Numerical investigations of discrete scale invariance in fractals and multifractal measures VL - 388 SP - 2623 KW - 2009 KW - pdf KW - scale-invariance KW - statistics AU - Zhou, Wei-Xing AU - Sornette, Didier PY - 2009/07/01/ UR - http://dx.doi.org/10.1016/j.physa.2009.03.023 ER -