Fractal theory has been used widely for studying the scaling properties of different biological and ecological time series [1-3]. A phenomenon showinga repeating pattern at every scale is called fractal [4]. Fractals can be regular or complex [5]. In fact, fractal objects can be characterized using a scaling exponent that is called fractal dimension. Regular and complex fractals have integer an...

Fractal growth is a kind of allometric growth, and the allometric scaling exponents can be employed to describe growing fractal phenomena such as cities. The spatial features of the regular fractals can be characterized by fractal dimension. However, for the real systems with statistical fractality, it is incomplete to measure the structure of scaling invariance only by fractal dimension. Somet...

The Fourier transform and spectral analysis are employed to estimate the fractal dimension and explore the fractal parameter relations of urban growth and form using mathematical experiments and empirical analyses. Based on the models of urban density, two kinds of fractal dimensions of urban form can be evaluated with the scaling relations between the wave number and the spectral density. One ...

It was proved in [6] that the trinomial arcs N (p, k, r, n) are mono-tonic. Through this result, we will estimate the fractal dimension of the union N of all these arcs.

This paper describes the preliminary work of image separation between natural and artificial objects using fractal dimensions by noting that most of natural images have non-integer dimensions while artificial ones have integer dimensions.

The free-energy landscape of two peptides is evaluated at various temperatures and an estimate for its fractal dimension at these temperatures calculated. We show that monitoring this quantity as a function of temperature allows to determine the glass transition temperature.

Recent results from a number of redshift surveys suggest that the Universe is well described by an inhomogeneous, fractal distribution on the largest scales probed. This distribution has been found to have fractal dimension, D, approximately equal to 2.1, in contrast to a homogeneous distribution in which the dimension should approach the value 3 as the scale is increased. In this paper we demo...

Particle size distribution of gravelly soil plays a crucial role in debris flow initiation. For better understanding the mechanism of debris flow formation, two crucial mechanical property parameters of the gravelly soil are required to be studied meticulously: hydraulic conductivity and strength. With the aim of measuring the composition of the gravelly soil, 182 soil samples were taken from d...

PURPOSE Fractal analysis is a mathematical method used to describe the internal architecture of complex structures such as trabecular bone. Fractal analysis of panoramic radiographs of implant recipient sites could help to predict the quality of the bone prior to implant placement. This study investigated the correlations between the fractal dimension values obtained from panoramic radiographs ...

The river patterns comprise of straight, meandering, braided and wandering river. They are formed and developed under the action of the long-term certain sediment-water assembly and the geological condition. There are many traditional methods such as single parameter including bend coefficient, width-depth ration and multipleparameters discrimination methods, to distinguish the river pattern. I...