Spectrum Analysis Of Fractals Based On Orthogonal Decomposition

By connecting a fractal curve to the V-system which is a class of orthogonal function system with self-similar structure, the fractal curve can be represented as a V-series, which provides a new way of analyzing fractal objects in the frequency domain. Due to the self-similar structure of the V-system, a fractal shape and its details can be expressed in layers using this orthogonal decomposition method. Accordingly, the difference between different fractals can be precisely and easily quantified. Furthermore, this paper proposes a method to obtain the fractal variants or new fractal curves by changing the values of several adjustable parameters being introduced into the V-spectra of the arbitrary given fractal. Many illustrations are provided to interpret the proposed method and show its effect. In the end of the paper, some fractal curves describing changes in rivers are provided to illustrate the application prospect of the fractal orthogonal representation.