Today Fractal geometry is completely new area of research in the field of computer science and engineering. It has wide range of applications. Fractals in nature are so complicated and irregular that it is hopeless to model them by simply using classical geometry objects. Benoit Mandelbrot, the father of fractal geometry, from his book The Fractal Geometry of Nature, 1982. This paper explor var...

Keywords: Fractal structure Fractal dimension Box-counting dimension Domain of words Language Regular expression Binary-coded decimal Search tree a b s t r a c t A fractal structure is a tool that is used to study the fractal behavior of a space. In this paper, we show how to apply a new concept of fractal dimension for fractal structures, extending the use of the box-counting dimension to new ...

Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a...

We introduce and investigate numerically a minimal class of dynamical triangulations of two-dimensional gravity on the sphere in which only vertices of order five, six or seven are permitted. We show firstly that this restriction of the local coordination number, or equivalently intrinsic scalar curvature, leaves intact the fractal structure characteristic of generic dynamically triangulated ra...

Critical path analysis and percolation theory are known to predict accurately dc and low frequency ac electrical conductivity in strongly heterogeneous solids, and have some applications in statistics. Much of this work is dedicated to review the current state of these theories. Application to heterogeneous porous media has been slower, though the concept of percolation was invented in that con...

In statistical mechanics, observables are usually related to local degrees of freedom such as the Q < 4 distinct states of theQ-state Potts models or the heights of the restricted solid-on-solid models. In the continuum scaling limit, these models are described by rational conformal field theories, namely the minimal models M(p, p ′) for suitable p, p ′. More generally, as in stochastic Loewner...

In scientiic studies objects are often very rough. Mathematically these rough objects are modeled by fractal functions, and fractal dimension is usually used to measure their roughness. The present paper investigates fractal function estimation by wavelet shrinkage. It is shown that wavelet shrinkage can estimate fractal functions with their fractal dimensions virtually preserved.

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...

This paper puts forward the concept of fractal company is in the process of online shopping. According to the characteristics of the network shopping, the paper establishes the mathematical model of fractal clustering, and uses the fractal dimension to describe and depict Fractal Company. Online shopping is actually the management of the entire supply chain. Based on similar structure of fracta...

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...