{
  "id": "cond-mat/0408600",
  "version": "v2",
  "published": "2004-08-27T11:09:20.000Z",
  "updated": "2007-04-17T04:53:16.000Z",
  "title": "Numerical investigations of discrete scale invariance in fractals and multifractal measures",
  "authors": [
    "W. -X. Zhou",
    "D. Sornette"
  ],
  "comment": "31 Elsart pages including 12 eps figures",
  "journal": "Physica A 388 (13), 2623-2639 (2009)",
  "doi": "10.1016/j.physa.2009.03.023",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "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, {\\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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-04-17T04:53:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete scale invariance",
      "multifractal measures",
      "numerical investigations",
      "lattice multifractals",
      "scale invariant complex systems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}