The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a cross-over to homogeneity. Fractal properties maybe studied with methods which do not assume homogeneity a priori as the standard statistical methods do. We show...

The task of object recognition in image processing and machine vision problems relies on nding good algorithms for one particular low-level processing task: image segmentation. In this report, we apply the concept of fractal dimension to this problem. In particular, we introduce the notion of a local fractal operator that can \measure" the fractal dimension of a single pixel; we investigate thr...

Fractal Interpolation Function is the attractor of Iterated Function System (IFS), to overcome the weakness of IFS that IFS only reflect the similarity between global region and local region of a graph, Barnsley put forward the Recurrent Iterated Function System and the Recurrent Fractal Interpolation Function. RIFS reflect the similarity between local and local, it can make more complicated gr...

Assuming that the motions of a complex system structural units take place on continuous, but non-differentiable curves of a space-time manifold, the scale relativity model with arbitrary constant fractal dimension (the hydrodynamic and wave function versions) is built. For non-differentiability through stochastic processes of the Markov type, the non-differentiable entropy concept on a space-ti...

The novel concept of a microfluidic chip with an integrated three-dimensional fractal geometry with nanopores, acting as a gas transport membrane, is presented. The method of engineering the 3D fractal structure is based on a combination of anisotropic etching of silicon and corner lithography. The permeation of oxygen and carbon dioxide through the fractal membrane is measured and validated th...

With advancement in communication technology over the past decade, there is an increasing demand for miniaturization, cost effective, multiband and wideband antennas. Fractal antenna designs can support in meeting these requirements. Though these antennas provide several advantages but at the same time miniaturization and performance of the fractal antennas can be further enhanced using reconfi...

Fractal, which means broken or irregular fragments, was originally coined by Dr B. Mandelbrot in the year the 1970. Fractals describe a family of complex shapes that possess an inherent self-similarity in their geometrical structure usually in nature, since the pioneering work of Mandelbrot and others, a wide variety of applications for fractals has been found in many branches of science and en...

Abstract: In this paper, a type-2 fuzzy adaptive controller of a Lotak-Volterra system is considered. For bettering the active system properly, the approximated error is introduced into the design of the controller. By using Lyapunov synthesis approach, we attain an adaptive law adjusting the free parameters in the controller such that the closed-loop system follows a desired trajectory. The no...

In this paper we work with nonparametric methods in modeling and analyzing the financial times series. We use the concept of fractal dimension for measuring the complexity of time series of observed financial data. The aim of this paper is to distinguish between the randomness and determinism of the financial information. We will compare the fractal analysis of the selected forward exchange rat...

in this work, sio2 –zro2 mixed oxides was prepared by the polymeric sol–gel route. the characterization of pore structure, which determines the permeation process of membrane, is of great importance. so far, most investigations have focused on such pore structure as specific surface area and pore size distribution, but the surface fractal, the important parameter reflecting the roughness of por...