Although there is a growing interest in the application of fractal analysis in neurobiology, questions about the methodology have restricted its wider application. In this report we discuss some of the underlying principles for fractal analysis, we propose the cumulative-mass method as a standard method and we extend the applicability of fractal analysis to both 2 and 3 dimensions. We have exam...

The behavior of power-law shot noise, for which the associated impulse response functions assume a decaying power-law form, is explored. Expressions are obtained for the moments, moment generating functions, amplitude probability density functions, autoCorrelation functions, and power spectral densities for a variety of parameters of the process. For certain parameters the power spectral densit...

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...

The purpose of this study is the discrimination of 28 postmenopausal with osteoporotic femoral fractures from an agematched control group of 28 women using texture analysis based on fractals. Two pre-processing approaches are applied on radiographic images; these techniques are compared to highlight the choice of the pre-processing method. Furthermore, the values of the fractal dimension are co...

Partial discharge (PD) pattern recognition is an important tool in HV insulation diagnosis. A PD pattern recognition approach of HV power transformers based on a neural network is proposed in this paper. A commercial PD detector is firstly used to measure the 3-D PD patterns of epoxy resin power transformers. Then, two fractal features (fractal dimension and lacunarity) extracted from the raw 3...

In this paper a new hardware method for fast and low power fractal coding is presented. The introduced method is based on binary classification of domain and range blocks. The technique not only reduces power consumption and increases processing speed but also has minimal effect on the degradation of the output result compared to the available fractal techniques. In order to show the functional...

Recent studies by mathematicians and physicists have identified a close association between the distribution of prime numbers and quantum mechanical laws governing the subatomic dynamics of quantum systems such as the electron or the photon. It is now recognised that Cantorian fractal space-time fluctuations characterise dynamical systems of all space-time scales ranging from the microscopic su...

This paper seeks to check the validity of the apparent fractal conjecture (Ribeiro 2001ab), which states that the observed power-law behaviour for the average density of large-scale distribution of galaxies arises when some observational quantities, selected by their relevance in average density profile determination, are calculated along the past light cone. Since general relativity states tha...

Three-dimensional fractal models on grids of ∼ 200 pixels are generated from the inverse Fourier transform of noise with a power law cutoff, exponentiated to give a log normal distribution of density. The fractals are clipped at various intensity levels and the mass and size distribution functions of the clipped peaks and their subpeaks are determined. These distribution functions are analogous...