We introduce the mathematical concept of multifractality and describe various multifractal spectra for dynamical systems, including spectra for dimensions and spectra for entropies. We support the study by providing some physical motivation and describing several nontrivial examples. Among them are subshifts of finite type and one-dimensional Markov maps. An essential part of the article is dev...

The crossing tree of a signal has been recently used to construct monofractal and multifractal processes. In this paper, we use the crossing tree of a signal for the purpose of analysis. Given a realisation of a signal, its crossing tree is calculated, whose characteristics are used to estimate the multifractal spectrum. More precisely, a partition function is evaluated at each resolution to su...

This paper investigates new properties concerning the multifractal structure of a class of statistically self-similar measures. These measures include the well-known Mandelbrot multiplicative cascades, sometimes called independent random cascades. We evaluate the scale at which the multifractal structure of these measures becomes discernible. The value of this scale is obtained through what we ...

Fractality, represented as self-similar repeating patterns, is ubiquitous in nature and the brain. Dynamic patterns of hippocampal spike trains are known to exhibit multifractal properties during working memory processing; however, it is unclear whether the multifractal properties inherent to hippocampal spike trains reflect active cognitive processing. To examine this possibility, hippocampal ...

There are strong reasons to believe that the multifractal spectrum of DLA shows anomalies which have been termed left sided ME, M]. In order to show that this is compatible with strictly multiplicative structures Mandelbrot et al. M, MEH] introduced a one parameter family of multifractal measures invariant under innnitely many linear maps on the real line. Under the assumption that the usual mu...

The rank-ordered multifractal analysis (ROMA), a recently developed technique that combines the ideas of parametric rank ordering and one-parameter scaling of monofractals, has the capabilities of deciphering the multifractal characteristics of intermittent fluctuations. The method allows one to understand the multifractal properties through rank-ordered scaling or nonscaling parametric variabl...

The major goal of this article was to evaluate the efficiency of Linux operating system using statistical self-similarity and multifractal analysis. In order to collect the necessary data, the tools available in Linux such as vmstat, top and iostat were used. The measurement data collected with those tools had to be converted into a format acceptable by applications which analyze statistical se...

We performed multifractal analysis of fetal heart rate (FHR) variability in fetuses with and without acidosis during labor. Multifractal analysis was performed on fetal electrocardiograms in 10-minute sliding windows within the last 2 hours before delivery in 45 term fetuses divided in three groups according to umbilical arterial pH and FHR pattern: group A had pH ≥7.30 and normal FHR, group B ...

We study auto-correlations and cross-correlations of daily price changes and daily volume changes of thirteen global stock market indices, using multifractal detrended fluctuation analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DXA). We find rather distinct multifractal behavior of price and volume changes. Our results indicate that the time series of price changes a...

Fractal dimension has been found not suitable to be used solely in classifying natural earth terrain. This is due to the fact that surfaces with different texture may portray similar fractal dimensions. Evertsz and Mandelbrot [Evertsz, et. al. 1992] suggested that multifractal dimension may be a more appropriate parameter than fractal dimension in describing geometrical properties of a fractal ...