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Fluctuations Fractal Nature

Posted on:2009-10-28Degree:MasterType:Thesis
Country:ChinaCandidate:S F TanFull Text:PDF
GTID:2208360245462658Subject:Basic mathematics
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Mandelbort studied the changes of market prices, and obtained the scale law ofprice changes. By using the scale law, he first studied prices of a lot of commodities,certain interest rates and the prices of securities. Based on Mandelbort's idea, thisthesis constructs an ideal pattern-fluctuating fractal to describe the law of the marketprice changes.This thesis consists of three chapters. In chapter one, we give the definition ofthe fluctuating fractal and its IFS expressions; In chapter two, we calculate thefluctuating fractal's box dimension, fractal dimension, Hausdorff dimension andHausdorff measure; In chapter three, we give the fractal's fractal interpolation and theinterpolation's fractal dimension.Main results:Theorem1.2.1 The IFS of the fluctuating fractal F is{R2;W1,W2,W3,W4,W5,W6}, whereTheorem2.1.1 The box demission of the fluctuating fractal F is log57.Theorem2.1.4 The box demission, fractal demission and Hausdorff demission ofF are the same to log57.Theorem2.2.1 The Hausdorff measure of the fluctuating fractal F is Theorem3.1.1 IFS{R2;W1,W2,W3,W4,W5,W6} is an attractor, and it is thefractal interpolation function of F.Theorem3.2.1 The fractal dimension of the fractal interpolation is D = log57...
Keywords/Search Tags:fractal, IFS(iterated function system), box dimension, fractal dimension, Hausdorff dimension, Hausdorff measure, fractal interpolation, attractor
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