Fractals and chaos
著者
書誌事項
Fractals and chaos
Springer-Verlag, c1991
- : us
- : gw
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注記
Includes bibliographical references and index
内容説明・目次
- 巻冊次
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: us ISBN 9780387973623
内容説明
This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot in the late 1970s, but objects now defined as fractal in form have been known to artists and mathematicians for centuries.
Mandelbrot's definition-"a set whose Hausdorff dimension is not an integer" -is clear in mathematical terms. In addition, related concepts are those of self-similarity and sub-divisibility. A fractal object is self-similar in that subsections of the object are similar in some sense to the whole object.
目次
1 Fractals.- 1 Jones: Fractals Before Mandelbrot.- 2 Reeve: Mandelbrot, Julia Sets and Nonlinear Mappings.- 3 Batty: Cities as Fractals: Simulating Growth and Form.- 4 Kaandorp: Modelling Growth Forms of Sponges with Fractal Techniques.- 5 Saupe: Random Fractals in Image Synthesis.- 6 Horn: IFSs and the Interactive Design of Tiling Structures.- 7 Bressloff and Stark: Neural Networks, Learning Automata and Iterated Function Systems.- 2 Chaos.- 8 Crilly: The Roots of Chaos-A Brief Guide.- 9 Lansdown: Chaos, Design and Creativity.- 10 Novak: Relativistic Particles in a Magnetic Field.- 11 Mullin: Chaos in Physical Systems.- 12 Darbyshire and Price: Phase Portraits from Chaotic Time Series.- 13 Pottinger: Data Visualisation Techniques for Nonlinear Systems.
- 巻冊次
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: gw ISBN 9783540973621
内容説明
This volume brings together a number of contributions in the areas of fractals, chaos and the interrelationship between the two domains. These contributions cover a wide variety of application areas, and this indicates the extent to which fractals and chaotic phenomena are being studied in the various disciplines. It is anticipated that the interdisciplinary nature of the subject will increase, which in turn will yield useful information on the potential (and also limitations in some cases) of fractals and chaos as modelling tools for the investigation of various natural and scientific phenomena. It is hoped that an understanding of fractals and chaos will lead to a common basis for examining the growth, development, organization, and behaviour of complex dynamical systems, many of which make up the natural world of fractal structure associated with phase portraits.
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