The Beauty of Fractals: Images of Complex Dynamical Systems

Heinz-Otto Peitgen, Peter H. Richter

Springer Science & Business Media, 1986 - Mathematics - 199 pages

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.

Contents

• FRONTIERS OF CHAOS: 1
• SPECIAL SECTIONS: 23
• Julia Sets and Their Computergraphical Generation: 27
• Sullivans Classification and Critical Points: 53
• The Mandelbrot Set: 56
• External Angles and Hubbard Trees: 63
• Newtons Method for Complex Polynomials Cayleys Problem: 95
• Newtons Method for Real Equations: 105
• A Discrete VolterraLotka System: 129
• MAGNETISM AND COMPLEX BOUNDARIES: 133
• SPECIAL SECTIONS: 141
• Renormalization: 144
• REFERENCES: 149
• INVITED CONTRIBUTIONS: 153
• Julia Sets and the Mandelbrot Set: 163
• Freedom Science and Aesthetics: 177
• Refractions of Science into Art: 183
• DO IT YOURSELF: 191
• DOCUMENTATION: 195
• INDEX: 199

Bibliographic information

• Title: The Beauty of Fractals: Images of Complex Dynamical Systems; The Beauty of Fractals: Images of Complex Dynamical Systems, Heinz-Otto Peitgen
• Authors: Heinz-Otto Peitgen, Peter H. Richter
• Edition: illustrated
• Publisher: Springer Science & Business Media, 1986
• ISBN: 3540158510, 9783540158516
• Length: 199 pages
• Subjects: Mathematics / General; Mathematics / Geometry / General; Mathematics / History & Philosophy; Mathematics / Logic