The Beauty of Fractals: Images of Complex Dynamical Systems

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

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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
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

A Discrete VolterraLotka System
129
MAGNETISM AND COMPLEX BOUNDARIES
133
SPECIAL SECTIONS
141

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