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...

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of t...

We put the theory of Dirichlet series and integrals in the geometric setting of`fractal strings' (one-dimensional drums with fractal boundary). The poles of a Dirichlet series thus acquire the geometric meaning of`complex dimensions' of the associated fractal string, and they describe the geometric and spectral oscillations of this string by means of anèxplicit formula'. We deene thèspectral op...

in this work, sio2 –zro2 mixed oxides was prepared by the polymeric sol–gel route. the characterization of pore structure, which determines the permeation process of membrane, is of great importance. so far, most investigations have focused on such pore structure as specific surface area and pore size distribution, but the surface fractal, the important parameter reflecting the roughness of por...

The most significant aspect of a geochemical exploration program is to define and separate the anomalous values from the background. In the past decades, geochemical anomalies have been identified by means of various methods. Most of the conventional statistical methods aiming at defining the geochemical concentration thresholds for separating anomalies from the background have limited the effi...

The extension of the concepts of the Fractal Geometry [Mandelbrot 1983] toward the life sciences has brought a significant progress in understanding complex functional properties and morphological features that characterise cells and tissues. It has even be argued that fractal geometry might provide a coherent description of the design principle underlying living organisms. Fractals fulfil a ce...

The components of complex bioelectrical activity – action potential (AP), interspike interval (ISI) and the quiet interburst interval (IBI), along with the effects of 2.7 mT and 10 mT static magnetic fields, were identified and examined in the spontaneously active Br neuron of the subesophageal ganglion complex of the garden snail Helix pomatia by fractal analysis using Higuchi’s fractal dimens...

We present a fractal technique for addressing geometric analogy problems from the Raven's Standard Progressive Matrices test of general intelligence. In this method, an image is represented fractally, capturing its inherent selfsimilarity. We apply these fractal representations to problems from the Raven's test, and show how these representations afford a new method for solving complex geometri...

The current experiments investigated the fractal structure in the nested actions of tapping behavior. The results revealed that task constraints (e.g., tapping to a metronome) alter the fractal structure of a given aspect of the behavior (e.g., intertap interval) and decouple its long-term interactions with other aspects of the behavior (e.g., key-press duration). These results support the idea...

The fractal and the small-world properties of complex networks are systematically studied both in the box-covering (BC) and the cluster-growing (CG) measurements. We elucidate that complex networks possessing the fractal (small-world) nature in the BC measurement are always fractal (small world) even in the CG measurement and vice versa, while the fractal dimensions d{B} by the BC measurement a...