The fractal dimension is considered on several examples; the method of its calculation shown. possibilities using fractals in study complex signals are proposed

We investigate whether fractal markets hypothesis and its focus on liquidity and investment horizons give reasonable predictions about dynamics of the financial markets during the turbulences such as the Global Financial Crisis of late 2000s. Compared to the mainstream efficient markets hypothesis, fractal markets hypothesis considers financial markets as complex systems consisting of many hete...

Fractal modulation is obtained by forming a power weighted superposition of scaled and modulated versions of the signal. The resulting signal is self-similar with fractal characteristics. In this paper we explore fractal modulation as a powerful method to generate rich signals, useful both for the synthesis of complex sounds, like the sounds from natural events or ecological sounds, or as contr...

Characterization of a digitized image is often required in nondestructive evaluation. Apart from the existing image processing techniques, a recent method to analyze and quantify complex images has been developed based on the fractal theory. As reported, it is possible to get salient information from any digitized image by evaluating the fractal dimension, the defining characteristic of a fract...

In this paper, we introduce an L-system based on the fractal geometry to study complex fracture networks. Comparing with other simulation models, the fractal fracture could not only maintain the bifurcation of the fracture geometry but also represent the multi-level feature of the complex fracture networks according to its fractal characteristics. Since the fractal geometry is always connected ...

We investigate in this work a local version of the theory of fractal strings and associated geometric zeta functions. Such a generalization allows to describe the asymptotic behaviour of a “fractal” set in the neighborhood of any of its points. We give basic properties and several examples illustrating the possible range of situations concerning in particular the evolution of the local complex ...

BACKGROUND/AIM Fractal dimension (FD) is widely used in medicine and biology as a tool for defining features of structure. This study aimed to compare pathological endometrium (simple-complex hyperplasia and endometrial carcinoma), as well as the endometrial changes, during the phases of the menstrual cycle. The main goal was the objective measurement of fractal dimension and to refrain from su...