Ebook: Fractals and Chaos

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.

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This volume brings together a number of distinctive 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 modeling 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 which we are part. It is anticipated that the investigations of fractal structure associated with phase portraits will be an exciting area for future work.

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This volume brings together a number of distinctive 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 modeling 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 which we are part. It is anticipated that the investigations of fractal structure associated with phase portraits will be an exciting area for future work.
Content:
Front Matter....Pages i-ix
Introduction Fractals and Chaos....Pages 1-4
Front Matter....Pages 5-5
Fractals Before Mandelbrot A Selective History....Pages 7-33
Mandelbrot, Julia Sets and Nonlinear Mappings....Pages 35-42
Cities as Fractals: Simulating Growth and Form....Pages 43-69
Modelling Growth Forms of Sponges with Fractal Techniques....Pages 71-88
Random Fractals in Image Synthesis....Pages 89-118
IFSs and the Interactive Design of Tiling Structures....Pages 119-144
Neural Networks, Learning Automata and Iterated Function Systems....Pages 145-190
Front Matter....Pages 191-191
The Roots of Chaos—A Brief Guide....Pages 193-209
Chaos, Design and Creativity....Pages 211-224
Relativistic Particles in a Magnetic Field....Pages 225-236
Chaos in Physical Systems....Pages 237-245
Phase Portraits from Chaotic Time Series....Pages 247-257
Data Visualisation Techniques for Nonlinear Systems....Pages 259-268
Back Matter....Pages 269-277

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This volume brings together a number of distinctive 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 modeling 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 which we are part. It is anticipated that the investigations of fractal structure associated with phase portraits will be an exciting area for future work.
Content:
Front Matter....Pages i-ix
Introduction Fractals and Chaos....Pages 1-4
Front Matter....Pages 5-5
Fractals Before Mandelbrot A Selective History....Pages 7-33
Mandelbrot, Julia Sets and Nonlinear Mappings....Pages 35-42
Cities as Fractals: Simulating Growth and Form....Pages 43-69
Modelling Growth Forms of Sponges with Fractal Techniques....Pages 71-88
Random Fractals in Image Synthesis....Pages 89-118
IFSs and the Interactive Design of Tiling Structures....Pages 119-144
Neural Networks, Learning Automata and Iterated Function Systems....Pages 145-190
Front Matter....Pages 191-191
The Roots of Chaos—A Brief Guide....Pages 193-209
Chaos, Design and Creativity....Pages 211-224
Relativistic Particles in a Magnetic Field....Pages 225-236
Chaos in Physical Systems....Pages 237-245
Phase Portraits from Chaotic Time Series....Pages 247-257
Data Visualisation Techniques for Nonlinear Systems....Pages 259-268
Back Matter....Pages 269-277
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