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AuthorPeitgen, Heinz-Otto. author
TitleThe Beauty of Fractals [electronic resource] : Images of Complex Dynamical Systems / by Heinz-Otto Peitgen, Peter H. Richter
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1986
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Descript XII, 202 p. online resource


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 plotยญ 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, desยญ 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 underยญ 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 inยญ tense research. But familiarity is not enough to ensure that scientists have the tools for an adequate understanding


Frontiers of Chaos -- Special Sections -- 1 Verhulst Dynamics -- 2 Julia Sets and Their Computergraphical Generation -- 3 Sullivanโ{128}{153}s Classification of Critical Points -- 4 The Mandelbrot Set -- 5 External Angles and Hubbard Trees -- 6 Newtonโ{128}{153}s Method for Complex Polynomials: Cayleyโ{128}{153}s Problem -- 7 Newtonโ{128}{153}s Method for Real Equations -- 8 A Discrete Volterra-Lotka System -- Magnetism and Complex Boundaries -- Special Sections -- 9 Yang-Lee Zeros -- 10 Renormalization -- References -- Invited Contributions -- Fractals and the Rebirth of Iteration Theory -- Julia Sets and the Mandelbrot Set -- Freedom, Science, and Aesthetics -- Refractions of Science into Art -- Do it Yourself -- Documentation

Mathematics Mathematical logic Mathematics Mathematical Logic and Foundations


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