Fractal Geometry: Mathematical Foundations and ApplicationsThe seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applications of fractals in a way that is accessible to students and researchers from a wide range of disciplines. Fractal Geometry: Mathematical Foundations and Applications is an excellent course book for undergraduate and graduate students studying fractal geometry, with suggestions for material appropriate for a first course indicated. The book also provides an invaluable foundation and reference for researchers who encounter fractals not only in mathematics but also in other areas across physics, engineering and the applied sciences.
Leads onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth Falconer and available from Wiley) |
Contents
1 | |
Boxcounting dimension | |
List of Illustrations | |
Hausdorff and packing measures and dimensions | |
Techniques for calculating dimensions | |
Examples from pure mathematics | |
Dynamical systems | |
1 | |
1 | |
2 | |
3 | |
Iteration of complex functionsJulia sets and the Mandelbrot | |
1 | |
1 | |
Iterated function systemsselfsimilar and selfaffine sets | |
2 | |
Examples from number theory | |
Graphs of functions | |
1 | |
Random fractals | |
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Other editions - View all
Fractal Geometry: Mathematical Foundations and Applications Kenneth Falconer No preview available - 2014 |