The Beauty of Fractals

1. Front Matter

   Pages I-XII

   PDF

2. Frontiers of chaos

   1. Front Matter

      Pages 1-22

      PDF

   2. Special Sections

      1. Verhulst Dynamics

         • Heinz-Otto Peitgen, Peter H. Richter

         Pages 23-26

      2. Julia Sets and their Computergraphical Generation

         • Heinz-Otto Peitgen, Peter H. Richter

         Pages 27-52

      3. Sullivan’s Classification and Critical Points

         • Heinz-Otto Peitgen, Peter H. Richter

         Pages 53-55

      4. The Mandelbrot Set

         • Heinz-Otto Peitgen, Peter H. Richter

         Pages 56-62

      5. External Angles and Hubbard Trees

         • Heinz-Otto Peitgen, Peter H. Richter

         Pages 63-92

      6. Newton’s Method for Complex Polynomials: Cayley’s Problem

         • Heinz-Otto Peitgen, Peter H. Richter

         Pages 93-102

      7. Newton’s Method for Real Equations

         • Heinz-Otto Peitgen, Peter H. Richter

         Pages 103-124

      8. A Discrete Volterra-Lotka System

         • Heinz-Otto Peitgen, Peter H. Richter

         Pages 125-138

3. Magnetism and Complex Boundaries

   1. Front Matter

      Pages 129-138

      PDF

   2. Special Sections

      1. Yang-Lee Zeros

         • Heinz-Otto Peitgen, Peter H. Richter

         Pages 139-141

      2. Renormalization

         • Heinz-Otto Peitgen, Peter H. Richter

         Pages 142-146

4. References

   1. References

      • Heinz-Otto Peitgen, Peter H. Richter

      Pages 147-150

5. Invited Contributions

   1. Fractals and the Rebirth of Iteration Theory

      • Benoit B. Mandelbrot

      Pages 151-160

   2. Julia Sets and the Mandelbrot Set

      • Adrien Douady

      Pages 161-174

   3. Freedom, Science, and Aesthetics

      • Gert Eilenberger

      Pages 175-180

   4. Refractions of Science into Art

      • Herbert W. Franke

      Pages 181-188

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.

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

"..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

• Fachbereich Mathematik, Universität Bremen, Bremen 33, Germany

  Heinz-Otto Peitgen

• Department of Mathematics, University of California, Santa Cruz, Santa Cruz, USA

  Heinz-Otto Peitgen

• Fachbereich Physik, Universität Bremen, Bremen 33, Germany

  Peter H. Richter

Policies and ethics