We study the behaviour of the power spectrum (PS) in the case of fractal structures. We show that in this case the main observational features of the PS, the large scale flattening and the scaling of the amplitude with sample depth, are related to finite size effects, due to the fractal nature of galaxy distribution in the sample. Comparing with the recent results of the PS for the CfA2 we conc...

It is shown that the observed fractal distribution of galaxies is, in fact, consistent with homogeneity of the Universe and observational limits on ∆T /T , if the presence of dark matter and dark charge predicted by the Modified Field Theory is taken into account. It is discussed a new scenario of structure formation in which observed structures appear as a result of decay of the primordial fra...

We report an algorithm for the partition of a line segment according to a given ratio ν. At each step the length distribution among sets of the partition follows a binomial distribution. We call k-set to the set of elements with the same length at the step n. The total number of elements is 2 and the number of elements in a same k-set is C n. In the limit of an infinite partion this object beco...

The fractal nature of heterogeneity of myocardial blood flow and its implications for the healthy and diseased heart is not yet understood. The main hindrance for investigation of blood flow heterogeneity and its role in physiology and pathophysiology is that conventional methods for determination of myocardial perfusion have severe limitations concerning temporal and spatial resolution and inv...

In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...

We propose a dynamical model in which a network structure evolves in a self-organized critical (SOC) manner and explain a possible origin of the emergence of fractal and small-world networks. Our model combines a network growth and its decay by failures of nodes. The decay mechanism reflects the instability of large functional networks against cascading overload failures. It is demonstrated tha...

We determined the changes in fractal dimensions and spatial correlations of regional pulmonary blood flow with increasing exercise in race horses (n = 4) by using 15-microm fluorescent microspheres. Fluorescence was measured to quantitate regional blood to 1.3-cm(3) samples (n = 1,621-2,503). Perfusion distributions were characterized with fractal dimensions (a measure of spatial variability) a...

In recent work, various fractal image coding methods are reported, which adopt the selfsimilarity of images to compress the size of images. However, till now, no solutions for the security of fractal encoded images have been provided. In this paper, a secure fractal image coding scheme is proposed and evaluated, which encrypts some of the fractal parameters during fractal encoding, and thus, pr...

BACKGROUND AND AIMS Fractal analysis allows calculation of fractal dimension, fractal abundance and lacunarity. Fractal analysis of plant roots has revealed correlations of fractal dimension with age, topology or genotypic variation, while fractal abundance has been associated with root length. Lacunarity is associated with heterogeneity of distribution, and has yet to be utilized in analysis o...

We introduce the notion of entanglement measure for the universal classes of fractons as an entanglement between ocuppation-numbers of fractons in the lowest Landau levels and the rest of the many-body system of particles. This definition came as an entropy of the probability distribution à la Shannon. Fractons are charge-flux systems classified in universal classes of particles or quasiparticl...