Journal ArticleDOI
Negative fractal dimensions and multifractals
Reads0
Chats0
TLDR
In this article, a new notion of fractal dimension is defined, which measures the degree of emptiness of empty sets in random multifractals for which f(α) is constant.Abstract:
A new notion of fractal dimension is defined When it is positive, it effectively falls back on known definitions But its motivating virtue is that it can take negative values, which measure usefully the degree of emptiness of empty sets The main use concerns random multifractals for which f(α)read more
Citations
More filters
Journal ArticleDOI
A multifractal wavelet model with application to network traffic
TL;DR: A new multiscale modeling framework for characterizing positive-valued data with long-range-dependent correlations (1/f noise) using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, which provides a rapid O(N) cascade algorithm for synthesizing N-point data sets.
Journal ArticleDOI
Statistics of energy levels and eigenfunctions in disordered systems
TL;DR: In this article, a review of recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples is presented, with emphasis on low-dimensional (quasi-1D and 2D) systems.
Book
Multifractals: Theory and Applications
TL;DR: In this paper, the authors present an overview of the history of multifractal fractal sets and multi-fractal measures in dynamical systems, including the development of Generalised Renyi Dimensions, Point Centred Constructions, and Point-Centred Construction.
Journal ArticleDOI
Fractal geometry applications in description and analysis of patch patterns and patch dynamics
Bai-Lian Li,Bai-Lian Li +1 more
TL;DR: This paper summarizes the state of the art and introduces several updated developments in analysis and description of patch patterns and patch dynamics by means of Mandelbrot’s fractal analysis, with an emphasis on current research results and a personal view.
Journal ArticleDOI
Multifractal analysis of financial markets: a review.
TL;DR: The cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods is surveyed, and the sources ofMultifractality are discussed.
References
More filters
Book
The Fractal Geometry of Nature
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Journal ArticleDOI
Fractal measures and their singularities: The characterization of strange sets
TL;DR: A description of normalized distributions (measures) lying upon possibly fractal sets; for example those arising in dynamical systems theory, focusing upon the scaling properties of such measures, which are characterized by two indices: \ensuremath{\alpha}, which determines the strength of their singularities; and f, which describes how densely they are distributed.
Journal ArticleDOI
Fractal measures and their singularities: The characterization of strange sets
Journal ArticleDOI
Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier
TL;DR: In this article, it was shown that Kolmogorov's third hypothesis is logically inconsistent, save under assumptions that are extreme and unlikely, and a widely used justification of lognormality due to Yaglom and based on probabilistic argument involving a self-similar cascade, will also be discussed.