A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and spatial network proved to be associated with one another. This paper is devoted to exploring the theory of fractal analysis of complex systems by means of hierar...

In this survey we give a report on some recent results obtained in the studies of hyperbolic manifolds by means of fractal geometry. Emphasis has been put on results derived in the quantitative and qualitative fractal analysis of long term geodesic dynamics on hyperbolic manifolds.

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...

The fractal features including fractal dimension (FD) and lacunarity measures are often used as indicators of texture. Several FD and lacunarity estimation methods leading to different results have been proposed in the literature. This paper is devoted mainly to show the need to combine the lacunarity with fractal dimension for the discrimination between different textures and especially to che...

Reliable online monitoring of wear remains a challenge to tribology research as well as to the industry. This paper presents a new method for monitoring of dry sliding wear using digital imaging and fractal analysis. Fractal values, namely fractal dimension and intercept, computed from the power spectrum of the images of a wearing surface, are adopted as indicators of the dynamic wear process. ...

Biological reactions of individuals of a testing animal to toxic substance are unique and can be used as an indication of the existing of toxic substance. However, to distinguish such phenomenon need a very complicate system and even more complicate to analyze data in 3 dimensional. In this paper, a system to evaluate in vitro biological activities to acute toxicity of stochastic self-affine no...

WHEN INVESTIGATING FRACTAL PHENOMENA, THE FOLLOWING QUESTIONS ARE FUNDAMENTAL FOR THE APPLIED RESEARCHER: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. Fi...

A brain computer interface (BCI) enables direct communication between a brain and a computer translating brain activity into computer commands usi ng preprocessing, feature extraction and classification operations. Feature extraction is crucial as it has a substantial effect on the classification accuracy and speed. While fractal dimension has been successfully used in various domains to charac...

The latest research works have revealed that fractal geometry, a measure of irregular contours, inconvenient for describing the various pathological architectures like tumors (for yielding insights into the tumor growth), different MR (magnetic-response) image analysis, neuro imaging analysis, bone fracture measurement and many more. Researchers major attraction towards fractal geometry lie in ...