We study numerically multifractal properties of two models of one-dimensional quantum maps: a map with pseudointegrable dynamics and intermediate spectral statistics and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of tw...

Multifractal scaling analysis is applied to the growing surfaces of random deposition model. The effect of number of deposited particles and lattice size on multifractal spectra is studied. Three cases of the growing surfaces are considered: (1) Same total number of particles deposited on different square lattice so that the number of particles deposited per surface site is different. (2) Diffe...

The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of nonstationary time series and the long-range correlations of fractal surfaces, which contains a parameter θ determining the position of the detrending window. We develop multifractal detrending moving average (MFDMA) algorithms for the analysis of one-dimensional multifractal measu...

The multifractal detrended fluctuation analysis of time series is able to reveal the presence of longrange correlations and, at the same time, to characterize the self-similarity of the series. The rich information derivable from the characteristic exponents and the multifractal spectrum can be further analyzed to discover important insights about the underlying dynamical process. In this paper...

We discuss a general concept of multifractality, and give a complete description of the multifractal spectra for Gibbs measures on two-dimensional horseshoes. We discuss a multifractal characterization of surface diffeomorphisms.

For hyperbolic diffeomorphisms, we describe the variational properties of the dimension spectrum of equilibrium measures on locally maximal hyperbolic sets, when the measure or the dynamical system are perturbed. We also obtain explicit expressions for the first derivative of the dimension spectra and the associated Legendre transforms. This allows us to establish a local version of multifracta...

Most results in multifractal analysis are obtained using either a thermodynamic approach based on existence and uniqueness of equilibrium states or a saturation approach based on some version of the specification property. A general framework incorporating the most important multifractal spectra was introduced by Barreira and Saussol, who used the thermodynamic approach to establish the multifr...

Fractal structures are found in biomedical time series from a wide range of physiological phenomena. The multifractal spectrum identifies the deviations in fractal structure within time periods with large and small fluctuations. The present tutorial is an introduction to multifractal detrended fluctuation analysis (MFDFA) that estimates the multifractal spectrum of biomedical time series. The t...

It is now clear that natural texture images can be discriminated by multifractal exponents. Most natural images, such as geographical images , are all textural in nature. In remote sensing images, different regions possess different texture and have different multifractal exponents. These properties are thus ideal for use in image segmentation. Like fractal dimensions, multifractal exponents ar...

Long-range dependence (LRD) or second-order self-similarity has been found to be an ubiquitous feature of internet traffic. In addition, several traffic data sets have been shown to possess multifractal behavior. In this paper, we present an algorithm to generate traffic traces that match the LRD and multifractal properties of the parent trace. Our algorithm is based on the decorrelating proper...