Genetic Algorithms (GAs) are direct searching methods which require little information from design space. This characteristic beside robustness of these algorithms makes them to be very popular in recent decades. On the other hand, while this method is employed, there is no guarantee to achieve optimum results. This obliged designer to run such algorithms more than one time to achieve more reli...

Since the last twenty years an increasing interest on the fractal approach on microphysics has been observed [1-9]. The Theory of fractal space-time or the Scale Relativity Theory (SRT) [1] extends Einstein’s principle of relativity to scale transformation of resolution. The introduction of non-differentiable trajectories in physics dates back to the pioneering works of Feynman, who demonstrate...

We study the problem of critical adsorption of piecewise directed random walks on a boundary of fractal lattices that belong to the Sierpinski gasket family. By applying the exact real space renormalization group method, we calculate the crossover exponent φ, associated with the number of adsorbed steps, for the complete fractal family. We demonstrate that our results are very close to the resu...

This is a study of the information evolution of complex systems by a geometrical consideration. We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement. Due to the incompleteness of the state number counting at any scale on fractal support, the incomplete normalizatio...

holds, then f is called a generalized convex function on I []. In α = , we have convex function, convexity is defined only in geometrical terms as being the property of a function whose graph bears tangents only under it []. The convexity of functions plays a significant role in many fields, for example, in biological system, economy, optimization, and so on [–]. In recent years, the fract...

The influence of stabilizing hydrostatic pressure gradients on the drainage of a fractal porous medium is studied. The invasion process is treated with invasion percolation (IP) in a gradient. Fractality is mimicked by randomly closing bonds of a network. Two length scales govern the problem: the characteristic length of the pore structure xi(s) and a length scale xi(g) above which buoyancy det...

Given a cloud of N points in an E-dimensional space, we often need to estimate the intrinsic dimensionality D of this cloud. For example, a set of points in 3-dimensional space all following along a straight line has intrinsic (or fractal) dimensionality D=1. Non-integer fractal dimensionality appears pervasively in nature. In this paper we give a very fast method to estimate the fractal dimens...

In this paper, a new concept of integration of fractal and the butterfly effect is proposed and implemented. A new fractal program was designed and developed to perform such integration. Among many existing fractal and chaos software programs, none of them allow us to achieve the resulting patterns demonstrated in this paper. Moreover, it is the first time that a fractal program provides functi...

In this paper we consider the topological aspects of sets defined by fractal geometry. Topology, as a geometry, is extended to the definition of fractal structures by characterising equivalences in different levels of detail. A group of distinct topological fractals are defined by taking the equipotence and multiplicity properties of sets. Additionally, we define fractal metamorphosis as the se...

Fractal array antennas are multiband arrays having ultra wide band and space filling facility. But Side lobe levels and large number of antenna elements are the major designing challenges of these arrays. In this paper, design and analysis of octagonal fractal array antenna is investigated with Morse-Thue fractal density tapering technique (MTFDT). Due to the proposed technique, a remarkable im...