Multi-fractal patterns occur widely in nature. In developing new algorithms to determine multi-fractal spectra of experimental data I am lead to the conclusion that generalised dimensions Dq of order q ≤ 0, including the Hausdorff dimension, are effectively irrelevant. The reason is that these dimensions are extraordinarily sensitive to regions of low density in the multi-fractal data. Instead,...

Shape is one of the most important visual attributes used to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape analysis is the complexity, and Fractal Dimension and Multi-Scale Fractal Dimension are both well-known methodologies to estimate it. This papers presents a co...

Multi-fractal scaling in the transition to the dissipative regime for compressible turbulence is considered. The multi-fractal power law scaling behavior breaks down for very small length scales thanks to viscous effects. However, the effect of compressibility is found to extend the single-scaling multi-fractal regime further into the dissipative range. This result appears to be consistent with...

one of the important aspects of soil is, knowing the relationships between spatial features of soil and quantity in statistical model. the goal of this research is to estimate saturated hydraulic conductivity by regression and co-active neuro-fuzzy inference system (anfis) with using the parameters of bulk density, real density, porosity, fractal dimension of particle size, and clay percent, si...

Long memory (long-term dependence) seems to be as widespread in financial time series as in nature. Inspired by the long memory property, Multi-fractal processes have recently been introduced as a new tool for modeling the stylized facts in financial time series. In this paper, we attempt to construct a bivariate multi-fractal model, and implement its estimation via both GMM and likelihood appr...

A Monte Carlo model of radiative transfer in multi-phase dusty media is applied to the situation of stars and clumpy dust in a sphere or a disk. The distribution of escaping and absorbed photons are shown for various filling factors and densities. Analytical methods of approximating the escaping fraction of radiation, based on the Mega-Grains approach [4], are discussed. Comparison with the Mon...

Fractal antennas have been shown to demonstrate repetitive multi-band or logperiodic behavior that has been attributed to the self-similar scale factor of the antenna’s geometry. This geometry, which has been used to model complex objects found in nature such as clouds and coastlines, has space filling properties that can be utilized to miniaturize antennas. These unique properties of fractals ...

In this paper we describe the design of a multiagent system based on simple interaction rules that can generate different overall behaviours, from asymptotically stable to chaotic, verified by the corresponding largest Lyapunov exponent. We show that very small perturbations can have a great impact on the evolution of the system, and we investigate some methods of controlling such perturbations...