We review recent findings of self-similarity in complex networks. Using the box-covering technique, it was shown that many networks present a fractal behavior, which is seemingly in contrast to their small-world property. Moreover, even non-fractal networks have been shown to present a self-similar picture under renormalization of the length scale. These results have an important effect in our ...

Michelitsch and Rossler in 1992 have applied seemingly small changes in complex analytic Mandelbrot set function and it makes a remarkable difference in the appearance of obtained fractal images. They named it burning ship as the image looks like a ship is going up in flame. The purpose of this paper is to explore the unidentified geometrical structure of various fractal images after applying i...

In this report, we present a simple geometric generation principle for the fractal that is obtained when applying Newton's method to nd the roots of a general complex polynomial with real coee-cients. For the case of symmetric polynomials z ? 1, the generation mechanism is derived from rst principles. We discuss the case of a general cubic and are able to give a description of the arising fract...

The blood vessel system has attracted attention as a typical biological complex adaptive system. In the present study, we investigate the properties of blood flow in terms of the fractal structure of retinal blood vessel systems, which are modeled by diffusion-limited aggregation (DLA). It is demonstrated from the study that there is a difference in the properties of blood flows between the art...

In this report, we present a complete theory for the fractal that is obtained when applying Newton's Method to nd the roots of a complex cubic. We show that a modiied Newton's Method improves convergence and does not yield a fractal, but basins of attraction with smooth borders. Extensions to higher-order polynomials and the numerical relevance of this fractal analysis are discussed. M. Drexler...

Fractal interpolation techniques provide good deterministic representations of complex phenomena. This paper approaches the Hermite interpolation using fractal procedures. This problem prescribes at each support abscissa not only the value of a function but also its first p derivatives. It is shown here that the proposed fractal interpolation function and its first p derivatives are good approx...

Spectral dimensions have been widely used to understand transport properties on regular and fractal lattices. However, they have received little attention with regard to complex networks such as scale-free and small-world networks. Here, we study the spectral dimension and the return-to-origin probability of random walks on hierarchical scale-free networks, which can be either fractal or nonfra...

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...

The fractal degree of adsorption on the multi-walled carbon nanotube has been investigated. The fractal-like Langmuir kinetics model has been used to obtain the fractal degree of ion adsorption on multi-walled carbon nanotube. The behavior of the fractal-like kinetics equation was compared with some famous rate equations like Langmuir, pseudo-first-order and pseudo-second-order equations. It is...

This essay concerns fractal geometry as a bridge between the imaginary and the real, mind and matter, conscious and unconscious. The logic rests upon Jung’s theory of number as the most primitive archetype of order for linking observers with the observed. Whereas Jung focused upon natural numbers as the foundation for order that is already conscious, I offer fractal geometry, with its endlessly...