Fractals and Chaos

1. Front Matter

   Pages i-ix

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2. Introduction Fractals and Chaos

   1. Introduction Fractals and Chaos

      • A. J. Crilly, R. A. Eamshaw, H. Jones

      Pages 1-4

3. Fractals

   1. Front Matter

      Pages 5-5

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   2. Fractals Before Mandelbrot A Selective History

      • Huw Jones

      Pages 7-33

   3. Mandelbrot, Julia Sets and Nonlinear Mappings

      • Dominic E. Reeve

      Pages 35-42

   4. Cities as Fractals: Simulating Growth and Form

      • Michael Batty

      Pages 43-69

   5. Modelling Growth Forms of Sponges with Fractal Techniques

      • J. A. Kaandorp

      Pages 71-88

   6. Random Fractals in Image Synthesis

      • Dietmar Saupe

      Pages 89-118

   7. IFSs and the Interactive Design of Tiling Structures

      • Alastair N. Horn

      Pages 119-144

   8. Neural Networks, Learning Automata and Iterated Function Systems

      • P. C. Bressloff, J. Stark

      Pages 145-190

4. Chaos

   1. Front Matter

      Pages 191-191

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   2. The Roots of Chaos—A Brief Guide

      • Tony Crilly

      Pages 193-209

   3. Chaos, Design and Creativity

      • John Lansdown

      Pages 211-224

   4. Relativistic Particles in a Magnetic Field

      • Miroslav M. Novak

      Pages 225-236

   5. Chaos in Physical Systems

      • Tom Miillin

      Pages 237-245

   6. Phase Portraits from Chaotic Time Series

      • A. G. Darbyshire, T. J. Price

      Pages 247-257

   7. Data Visualisation Techniques for Nonlinear Systems

      • David Pottinger

      Pages 259-268

5. Back Matter

   Pages 269-277

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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.

• Dynamisches System
• Komplexität
• Mandelbrot
• Potential
• chaos
• complexity
• dynamical system
• dynamical systems
• fractal
• function
• magnetic field
• modeling
• nonlinear system
• visualization

• Middlesex Polytechnic, Barnet, UK

  A. J. Crilly

• University of Leeds, UK

  R. A. Earnshow

• Middlesex Polytechnic, UK

  H. Jones

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