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...

Software development is difficult to model, particularly the noisy, non-stationary signals of changes per time unit, extracted from version control systems (VCSs). Currently researchers are utilizing timeseries analysis tools such as ARIMA to model these signals extracted from a project’s VCS. Unfortunately current approaches are not very amenable to the underlying power-law distributions of th...

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...

This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequ...

Long term power load has a big impact on the development of industry of power. The forecasting models of linear systems even a single forecasting model of the nonlinear systems can not forecast the long term power load greatly. In the study, the combined forecasting model of nonlinear systems including chaos and fractal was established to improve the accuracy of the forecast. First, the charact...

spatial analysis of aeolian landforms by fractal theory (case study: ardestan rig) abstract natural sciences face to a great revolution, nowadays. now, scientists think the world as a collection of complex systems which prediction of consequences of this complex systems is so difficult. in this situation the systems have rotational act so irregularly lead to regular and regularly lead to irregu...

The α predominant electroencephalographic (EEG) recording of the human brain during eyes-closed and-open is studied using the zero-crossing time statistics. We found evidence of fractal characteristics which is otherwise ambiguous from the power spectrum or detrend fluctuation analysis. Our results indicate a reverse relationship between the degree of fractal fluctuation and the α rhythm intens...

The scaling and surface area properties of the wrinkled surface separating turbulent from nonturbulent regions in open shear flows are important to our understanding of entrainment mechanisms at the boundaries of turbulent flows. Particle image velocimetry data from high Reynolds number turbulent boundary layers covering three decades in scale are used to resolve the turbulent-nonturbulent inte...

The basic rules of central place networks are abstracted and formulated as three geometric series scaling laws, which can be transformed into several power laws associated with fractal structure. The scaling laws might be the Rosetta Stone to understand the complexity of human geographical systems because they take the form of Horton and Strahler's laws in geomorphology and Gutenberg and Richte...

introduction: soil hydraulic conductivity is considered as one of the most important hydraulic properties in water and solutionmovement in porous media. in recent years, variousmodels as pedo-transfer functions, fractal models and scaling technique are used to estimate the soil saturated hydraulic conductivity (ks). fractal models with two subset of two (solid and pore) and three phases (solid,...