Chaos and fractals : new frontiers of science
著者
書誌事項
Chaos and fractals : new frontiers of science
Springer-Verlag, c1992
- : us
- : gw
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注記
Includes bibliographical references and index
内容説明・目次
- 巻冊次
-
: us ISBN 9780387979038
内容説明
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 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.
- 巻冊次
-
: gw ISBN 9783540979036
内容説明
For almost ten 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. Travelling far beyond the traditional bounds of mathematics and science to 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, cellular 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.
目次
- Preface
- Authors
- Foreword
- Introduction: Causality Principle, Deterministic Laws and Chaos
- The Backbone of Fractals: Feedback and the Iterator
- Classical Fractals and Self-Similarity
- Limits and Self- Similarity
- Length, Area and Dimension: Measuring Complexity and Scaling Properties
- Encoding Images by Simple Transformations
- The Chaos Game: How Randomness Creates Deterministic Shapes
- Recursive Structures: Growing of Fractals and Plants
- Pascal's Triangle: Cellular Automata and Attractors
- Irregular Shapes: Randomness in Fractal Constructions
- Deterministic Chaos: Sensitivity, Mixing, and Periodic Points
- Order and Chaos: Period-Doubling and its Chaotic Mirror
- Strange Attractors: The Locus of Chaos
- Julia Sets: Fractal Basin Boundaries
- The Mandelbrot Set: Ordering the Julia Sets
- A: A Discussion of Fractal Image Compression
- B: Multifractal Measures
- Bibliography
- Index.
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