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...

Kolmogorov introduced a concept of ε-entropy to analyze information in classical continuous system. The fractal dimension of geometrical sets was introduced by Mandelbrot as a new criterion to analyze the complexity of these sets. The ε-entropy and the fractal dimension of a state in general quantum system were introduced by one of the present authors in order to characterize chaotic properties...

The purpose of this paper is to introduce the concept of fractals and its use in antenna arrays for obtaining multiband property. One type of fractals namely, Cantor set is investigated. Cantor set is used in linear array antenna design. Therefore, this array know fractal Cantor linear array antenna. A comparison with conventional non-fractal linear array antenna is made regarding the beamwidth...

Introduction Central to fractal geometryy3] is the concept of self-similarity.

Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical propertie...

We consider the concept of fractons, i.e. particles or quasiparticles which obey specific fractal statistics and for each universal class h of particles we obtain a fractal-deformed Heisenberg algebra. This one takes into account the braid group structure of these objects which live in two-dimensional multiply connected space. PACS numbers: 05.30.-d; 02.20.-a; 11.25.Hf

From a “strange” case-Koch curve in Euclidean space, we introduce the concept of fractal geometry, and meanwhile, give the MATLAB programs and their operational results. Since a variety of phenomena in nature have fractal characteristics, yet it is difficult to simulate the natural features with fractal characteristics in Euclidean space. Therefore, in order to solve this problem, we apply frac...

We consider the concept of fractons, i.e. particles or quasiparticles which obey specific fractal distribution function and for each universal class h of particles we obtain a fractal-deformed Heisenberg algebra. This one takes into account the braid group structure of these objects which live in twodimensional multiply connected space. PACS numbers: 05.30.-d; 02.20.-a; 11.25.Hf

The fractal protein is a new concept for improving evolvability, scalability, exploitability and providing a rich medium for evolution. Here the idea of fractal proteins is introduced, and a series of experiments showing how evolution can design and exploit them within gene regulatory networks is described.

A Fractal model equipped with detail concept like that used in wavelet transforms is introduced and used to perform global and local deformations to objects. This fractal model based on Projected IFS attractors allows the definition of free form fractal shapes controlled by a set of points. The details concept taken from wavelet theory represents the geometric texture of the object. An approxim...