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Record Nr. |
UNINA9910479922303321 |
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Autore |
Peitgen Heinz-Otto |
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Titolo |
Chaos and Fractals [[electronic resource] ] : New Frontiers of Science / / by Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe |
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Pubbl/distr/stampa |
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New York, NY : , : Springer New York : , : Imprint : Springer, , 1992 |
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ISBN |
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Edizione |
[1st ed. 1992.] |
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Descrizione fisica |
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1 online resource (XXXII, 999 p.) |
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Classificazione |
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Disciplina |
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Soggetti |
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Mathematics |
Mathematics, general |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Introduction: Causality Principle, Deterministic Laws and Chaos -- 1 The Backbone of Fractals: Feedback and the Iterator -- 2 Classical Fractals and Self-Similarity -- 3 Limits and Self-Similarity -- 4 Length, Area and Dimension: Measuring Complexity and Scaling Properties -- 5 Encoding Images by Simple Transformations -- 6 The Chaos Game: How Randomness Creates Deterministic Shapes -- 7 Recursive Structures: Growing of Fractals and Plants -- 8 Pascal’s Triangle: Cellular Automata and Attractors -- 9 Irregular Shapes: Randomness in Fractal Constructions -- 10 Deterministic Chaos: Sensitivity, Mixing, and Periodic Points -- 11 Order and Chaos: Period-Doubling and its Chaotic Mirror -- 12 Strange Attractors: The Locus of Chaos -- 13 Julia Sets: Fractal Basin Boundaries -- 14 The Mandelbrot Set: Ordering the Julia Sets -- A A Discussion of Fractal Image Compression -- A.1 Self-Similarity in Images -- A.2 A Special MRCM -- A.3 Encoding Images -- A.4 Ways to Partition Images -- A.5 Implementation Notes -- B Multifractal Measures -- B.1 Introduction -- B.2 The Binomial and Multinomial Measures -- B.5 Some Applications, and Advanced Multifractals. |
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Sommario/riassunto |
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For almost 15 years chaos and fractals have been riding a wave that has enveloped many areas of mathematics and the natural sciences in its power, creativity and expanse. Traveling far beyond the traditional |
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bounds of mathematics and science to the distant shores of popular culture, this wave captures the attention and enthusiasm of a worldwide audience. The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot Set, Julia Sets, Cellulair Automata, L- systems, Percolation and Strange Attractors. Each chapter is closed by a "Program of the Chapter" which provides computer code for a central experiment. Two appendices complement the book. The first, by Yuval Fisher, discusses the details and ideas of fractal images and compression; the second, by Carl J.G. Evertsz and Benoit Mandelbrot, introduces the foundations and implications of multifractals. |
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