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...

Recent analyses of real data/internet tra c indicate that data tra c exhibits long-range dependence as well as self-similar or multi-fractal properties. By using mathematical models of Internet tra c that share these properties we can perform analytical studies of network tra c. This gives us an opportunity to analyse potential bottlenecks and estimate delays in the networks. Processes with mul...

In order to describe the phenomenon of intermittency in wall turbulence and, more particularly, the behaviour of moments p r V δ and p r ε and intermittency exponents ζP with the order p and distance to the wall, we developed a new geometrical framework called “entropic-skins geometry” based on the notion of scale-entropy which is here applied to an experimental database of boundary layer flows...

This paper proposes a moment based encoding algorithm for iterated function system (IFS) coding of high order nonhomogeneous fractal images. The proposed algorithm employs a quasi-Newton method combined with a multi-start steepest descent technique in order to solve the simultaneous algebraic equations for IFS codes. Experimental results show that the average computational time for encoding the...

Three aspects of texture are considered by the fractal geometry: Fractal Dimension (FD), Lacunarity and Succolarity. Fractal Dimension has been well studied; a great number of approaches have been presented to extract it from images. It can be computed from black-white to multi-band image. There are many approaches also, from the simple Box-Dimension to the most complex Hausdorff Dimension. The...

In this paper, a forward-looking infrared (FLIR) video surveillance system is presented for collision avoidance of moving ships to bridge piers. An image pre-processing algorithm is proposed to reduce clutter noises by multi-scale fractal analysis, in which the blanket method is used for fractal feature computation. Then, the moving ship detection algorithm is developed from image differentials...

This paper presents a method for the quantification of cellular rejection in endomyocardial biopsies of patients submitted to heart transplant. The model is based on automatic multilevel thresholding, which employs histogram quantification techniques, histogram slope percentage analysis and the calculation of maximum entropy. The structures were quantified with the aid of the multi-scale fracta...

Two-point correlation function of galaxy distribution shows that the structure in the present Universe is scale-free up to a certain scale (at least several tens Mpc), which suggests that a fractal structure may exist. If small primordial density fluctuations have a fractal structure, the present fractal-like nonlinear structure below the horizon scale could be naturally explained. We analyze a...

Fractal behavior has been observed in both ion-channel gating and neuronal spiking patterns, but a causal relationship between the two has not yet been established. Here, we examine the effects of fractal ion-channel activity in modifications of two classical neuronal models: Fitzhugh-Nagumo (FHN) and Hodgkin-Huxley (HH). For the modified FHN model, the recovery variable was represented as a po...