| Summary: | This thesis introduces fractal interpolation functions, exposes advantages of fractal interpolation of real world objects and presents some newly developed procedures, associated with fractal interpolation process.
The work briefly presents the context needed for introduction of fractal approach and relevant definitions. Also, the detailed description of fractal generating algorithms (deterministic, random iteration, “escape time”) as well as fractal classifications is presented. Since the research object is theoretical and practical aspects of fractal interpolation function analysis, special attention is paid to geometric fractals, obtained using systems of iterated functions (IFS).
The notion of a fractal interpolation function is introduced in the work. The author shows that it is possible to generate fractal interpolation functions for various types of data. The generated functions are “close” (in the sense of Housdorf dimension) to the data under processing, i.e., it is possible to ensure that the fractal interpolation graph dimension were equal to the fractal dimension of experimental data (graph). The random iteration algorithm is used for the analysis of fractal interpolation functions, since it is relatively simple and fast enough. The author makes an attempt to analyze and solve the problem of choosing interpolation points (general case). A few approaches are proposed, namely the uniform distribution of interpolation points (for the interactive use) and collage. On... [to full text]
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