Generalized Wave Fractal

Mandelbrot studied a lot of commodity market price changes found price changes have scale constant rule.Tanshufen use this thought to construct a ideal model of fluc-tuation fractal.But this model simplistic, only studied market fluctuations in the price of the special circumstances.In order to research the market price fluctuation rule, need to construct a universally applicable model, thus this article introduces two parame-ters was constructed fractal, and generalized fluctuations of generalized fluctuations are fractal iterated function system and the fractal dimension, the box counting dimension and Hausdorff dimension, discussed the fractal interpolation generalized fluctuations.The article consists of three chapters. The first chapter one,we use the set of generalized fluctuations constructed fractal and the generalized fluctuation fractal iter-ated function system;In second chapter,we calculated the generalized fluctuation frac-tal's box dimension,fractal dimension.Hausdorff dimension and Hausdorff measure;In chapter three,we give the fractal's fractal interpolation and the interpolation's fractal dimension.This paper mainly results:Theorem 1.2.1 The IFS of the fluctuating fractal F is{R2;ω1,ω2,ω3,ω4,ω5,ω6}, where Theorem2.1.1 The box dimension of the fluctuating fractal F isTheorem 2.1.2 The fractal dimension of the fluctuating fractal F is theTheorem 2.1.3 The Hausdorff dimension of the fluctuating fractal F is theTheorem 2.2.1 The Hausdorff measure of the fluctuating fractal F(1/2)P-1(2P+1+4P), whereTheorem 3.1.1 In R2,IFS{ω1,ω2,ω3,ω4,ω5,ω6} is an attractor,and it is the fractal interpolation function of F.Theorem 3.2.1 The Fractal dimension of the fractal interpolation is...