文摘
英文文摘
独创性声明及学位论文版权使用授权书
Chapter 1 introduction
§1. Historical background and literature review
§2. Hausdorff measure and Hausdorff dimension
§3. Hausdorff distance and Iterated Function Sys-tem
Chapter 2 Three Geometric Forms and fractal interpolation
§1. Geometric representation of function and fractal interpolation problem
§2. Local double Lipschitz transformation of polar coordinate and orthogonal coordinate
§3. Generalization of the properties of self-similarity and classification of self-similar set
Chapter 3 Affine IFS Fractal Interpolation
§1. Three kinds of fractal interpolation curve of affine IFS
§2. The dimension relation of affine fractal interpolation curves
§3. The range control of affine fractal interpolation curve
§4. Plotting examples of affine interpolation curve
Chapter 4 Holographic Fractal Interpolation
§1. Three kinds of fractal interpolation curve of holographic IFS
§2. The dimension relation of holographic fractal interpolation curves
§3. The range control of holographic fractal interpolation curve
§4. Plotting examples of holographic interpolation curve
Chapter 5 Intergraphic Fractal Interpolation
§1. Three kinds of fractal interpolation curve of intergraphic IFS
§2. The dimension relation of holographic fractal interpolation curves
§3. The range control of intergraphic fractal interpolation curve
§4. Plotting examples of intergraphic interpolation curve
References
Aknowledgements