Fractal Functions, Fractal Surfaces, and Wavelets

Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets. The book is based on Massopust’s work on and contributions to the theory of fractal interpolation, and the author uses a number of tools—including analysis, topology, algebra, and probability theory—to introduce readers to this exciting subject.

Though much of the material presented in this book is relatively current (developed in the past decades by the author and his colleagues) and fairly specialized, an informative background is provided for those entering the field. With its coherent and comprehensive presentation of the theory of univariate and multivariate fractal interpolation, this book will appeal to mathematicians as well as to applied scientists in the fields of physics, engineering, biomathematics, and computer science. In this second edition, Massopust includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, further develops the connections to wavelets and wavelet sets, and deepens and extends the pedagogical content.

Offers a comprehensive presentation of fractal functions and fractal surfacesIncludes latest developments in fractal interpolationConnects fractal geometry with wavelet theoryIncludes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, and further develops the connections to wavelets and wavelet setsDeepens and extends the pedagogical content

Part I: Foundations 1. Mathematical preliminaries 2. Construction of fractal sets 3. Dimension theory 4. Dynamical systems and dimension

Part II: Fractal Functions and Fractal Surfaces 5. Construction of fractal functions 6. Fractels and self-referential functions 7. Dimension of fractal functions 8. Fractal functions and wavelets 9. Fractal surfaces 10. Fractal surfaces and wavelets in ℝⁿ