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 ...

The multifractal nature of solar photospheric magnetic structures are studied using the 2D wavelet transform modulus maxima (WTMM) method. This relies on computing partition functions from the wavelet transform skeleton defined by the WTMM method. This skeleton provides an adaptive spacescale partition of the fractal distribution under study, from which one can extract the multifractal singular...

In this work we perform a fractal analysis of 160 pieces of music belonging to six different genres. We show that the majority of the pieces reveal characteristics that allow us to classify them as physical processes called the 1/f (pink) noise. However, this is not true for classical music represented here by Frederic Chopin’s works and for some jazz pieces that are much more correlated than t...

Recent studies have shown that TCP traffic displays strong multifractal scaling. However, a physical explanation of why such a behavior occurs is still eluding. In this paper, we propose a cascade model that is based on the retransmission and congestion avoidance mechanisms of TCP. At the same time, it relates to the physical, tree-like organization of networks. This model allows to relate the ...

On the one hand, the large scale structure of matter is arguably scale invariant, and, on the other hand, halos and voids are recognized as prominent features of that structure. To unify both approaches, we propose to model the dark matter distribution as a set of fractal distributions of halos of different kinds. This model relies on the concept of multifractal as the most general scaling dist...

Context. Large simulations of dark matter and gas structure formation allow us to separate the pure gravitational dynamics from other processes and, hence, to better compare them with observations. Aims. Our objective is to analyse the recent MareNostrum simulation from a new perspective, regarding the geometry of the dark matter and gas distributions in it. We intend to find the fractal geomet...

Although there is increasing evidence of criticality in the brain, the processes that guide neuronal networks to reach or maintain criticality remain unclear. The present research examines the role of neuronal gain plasticity in time-series of simulated neuronal networks composed of integrate-and-fire stochastic spiking neurons, and the utility of fractal methods in assessing network criticalit...

In this paper, we describe a new multiscale model for characterizing positive-valued and long-range dependent data. The model uses the Haar wavelet transform and puts a constraint on the wavelet coefficients to guarantee positivity, which results in a swift O ( N ) algorithm to synthesize N-point data sets. We elucidate our model’s ability to capture the covariance structure of real data, study...

Fractal approach is successfully implemented in many applications within 2D signal processing. Fractal synthetical concept is applied for image compression with high compression ratios while fractal and multifractal descriptors provide classification of textural images with high occuracy. Various multifractal models are presented in literature. This paper summarizes them and illustrates new mul...