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基本説明
複雑な図形を数学的に理論化するフラクタル幾何学を解説した、同著者のFractal Every where (1998 Academic)に続く著作。４色刷。
"...colourfully conveys to the reader this next step in chaotic harmony, highlighting the unification of information theory and physics. ..a superb addition to the bookshelves of any scientists who use fractal analysis techniques in their research, be they physicist, biologist or economist.." J. R. Mureika Nature (Vol.445 18 Jan.,2007)
Full Description
SuperFractals, first published in 2006, is the successor to Fractals Everywhere, in which the power and beauty of Iterated Function Systems were introduced and applied to producing startling and original images that reflect complex structures found for example in nature. This provoked the question of whether there is a deeper connection between topology, geometry, IFS and codes on the one hand and biology, DNA and protein development on the other. Now, 20 years later, Barnsley explains how IFS have developed in order to address this issue. Ideas such as fractal tops and superIFS are introduced, and the classical deterministic approach is combined with probabilistic ideas to produce new mathematics and algorithms that open a whole theory that could have applications in computer graphics, bioinformatics, economics, signal processing and beyond. For the first time these ideas are explained in book form, and illustrated with breathtaking pictures.
Contents
Part I. Geometries and Transformations: 1. Codes, metrics and topologies; 2. Transformations of points, sets, pictures and measures; 3. Semigroups on sets, measures and pictures; Part II. Iterated Function Systems: 4. IFS acting on measures; 5. More on IFS; Part III. Applications to Graphics: 6. Digital content production; 7. Image compression; 8. Super IFS.
