Paddy is one of major crops grown in China. Fractal dimension is an important parameter used to describe geometrical characteristics of many natural objects. The objective of this study is to investigate mathematical relationships between the fractal dimension and the yield of the paddy spike based on the fractal theory and the image processing technologies. The color images of paddy spikes wer...

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...

The texture of the surface of individual fiber is an important characteristic. The fibers can be classified and recognized using the surface texture by a specific parameter. To describe the texture, the fractal parameter (or Hurst coefficient) is a proper value. In this study, we use the Fractional Brownian Motion (FBM) to model the texture of the fiber surface. And we apply a Fourier-domain Ma...

As a new modeling procedure of geothermal energy extraction systems, the authors present two dimensional and three dimensional modeling techniques of subsurface fracture network, based on fractal geometry. Fluid flow in fractured rock occurs primarily through a connected network of discrete fractures. The fracture network approach, therefore, seeks to model fluid flow and heat transfer through ...

The fractal dimension has been employed as a useful parameter in the diagnosis of retinal disease. Avakian et al. (Curr Eye Res 2002; 24: 274-280), comparing the vascular pattern of normal patients with mild to moderate non-proliferative diabetic retinopathy (NPDR), found a significant difference between them only in the macular region. This significant difference in the box-counting fractal di...

This dissertation examines the theory and applications of fractal interpolation. Its main contribution is the parameter identification, algorithmic construction and applications of fractal interpolation. We focus on the self-affine and piecewise self-affine fractal interpolation functions that are based on the theory of iterated function systems. Specifically, we present two novel methods for p...

Weak interactions of solitary waves in the generalized nonlinear Schrödinger equations are studied. It is first shown that these interactions exhibit similar fractal dependence on initial conditions for different nonlinearities. Then by using the Karpman-Solov'ev method, a universal system of dynamical equations is derived for the velocities, amplitudes, positions, and phases of interacting sol...

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...

Digital image databases represent huge amount of data, automatic indexing and content base retrieval are crucial factors. IFS ( Iterated function system ) fractal code can be used to retrieve image and the position parameter of IFS code is replaced with the relative distance and direction parameter. A new algorithm of IFS fractal code for image retrieval on compression domain is presented in th...