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© 1986

The Beauty of Fractals

Images of Complex Dynamical Systems

Book

Table of contents

  1. Front Matter
    Pages I-XII
  2. Frontiers of chaos

    1. Front Matter
      Pages 1-22
    2. Special Sections

      1. Heinz-Otto Peitgen, Peter H. Richter
        Pages 23-26
      2. Heinz-Otto Peitgen, Peter H. Richter
        Pages 27-52
      3. Heinz-Otto Peitgen, Peter H. Richter
        Pages 53-55
      4. Heinz-Otto Peitgen, Peter H. Richter
        Pages 56-62
      5. Heinz-Otto Peitgen, Peter H. Richter
        Pages 63-92
      6. Heinz-Otto Peitgen, Peter H. Richter
        Pages 93-102
      7. Heinz-Otto Peitgen, Peter H. Richter
        Pages 103-124
      8. Heinz-Otto Peitgen, Peter H. Richter
        Pages 125-138
  3. Magnetism and Complex Boundaries

    1. Front Matter
      Pages 129-138
    2. Special Sections

      1. Heinz-Otto Peitgen, Peter H. Richter
        Pages 139-141
      2. Heinz-Otto Peitgen, Peter H. Richter
        Pages 142-146
  4. References

    1. Heinz-Otto Peitgen, Peter H. Richter
      Pages 147-150
  5. Invited Contributions

    1. Benoit B. Mandelbrot
      Pages 151-160
    2. Adrien Douady
      Pages 161-174
    3. Gert Eilenberger
      Pages 175-180
    4. Herbert W. Franke
      Pages 181-188

About this book

Introduction

In 1953 I realized that the straight line leads to the downfall of mankind. But the straight line has become an absolute tyranny. The straight line is something cowardly drawn with a rule, without thought or feeling; it is the line which does not exist in nature. And that line is the rotten foundation of our doomed civilization. Even if there are places where it is recognized that this line is rapidly leading to perdition, its course continues to be plot­ ted . . . Any design undertaken with the straight line will be stillborn. Today we are witnessing the triumph of rationalist knowhow and yet, at the same time, we find ourselves confronted with emptiness. An esthetic void, des­ ert of uniformity, criminal sterility, loss of creative power. Even creativity is prefabricated. We have become impotent. We are no longer able to create. That is our real illiteracy. Friedensreich Hundertwasser Fractals are all around us, in the shape of a mountain range or in the windings of a coast line. Like cloud formations and flickering fires some fractals under­ go never-ending changes while others, like trees or our own vascular systems, retain the structure they acquired in their development. To non-scientists it may seem odd that such familiar things have recently become the focus of in­ tense research. But familiarity is not enough to ensure that scientists have the tools for an adequate understanding.

Keywords

chaos computer creativity design development dynamical systems field fractal iteration Mandelbrot set polynomial set sets time tool

Authors and affiliations

  1. 1.Fachbereich MathematikUniversität BremenBremen 33Germany
  2. 2.Department of MathematicsUniversity of California, Santa CruzSanta CruzUSA
  3. 3.Fachbereich PhysikUniversität BremenBremen 33Germany

Bibliographic information

  • Book Title The Beauty of Fractals
  • Book Subtitle Images of Complex Dynamical Systems
  • Authors Heinz-Otto Peitgen
    Peter H. Richter
  • DOI https://doi.org/10.1007/978-3-642-61717-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1986
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-15851-6
  • Softcover ISBN 978-3-642-61719-5
  • eBook ISBN 978-3-642-61717-1
  • Edition Number 1
  • Number of Pages XII, 202
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Mathematical Logic and Foundations
  • Buy this book on publisher's site

Reviews

"..a rare and extraordinary book...anyone who has ever explored the intricate folds of the Mandelbrot set will want this book and will be delighted by it...above all, a celebration of fractal forms and as such it works superbly...buy this book and enjoy it" Personal Computer World
"A literally wonder-ful book!" Physikalische Blätter