TAILIEUCHUNG - Dynamical systems and fractals Computer graphics experiments in ascal

Experimental mathematics, a child of our ‘Computer Age’, allows us glimpses into the world of numbers that are breathtaking, not just to mathematicians. Abstract concepts, until recently known only to specialists - for example Feigenbaum diagrams or Julia sets - are becoming vivid objects, which even renew the motivation of students. Beauty and mathematics: they belong together visibly, and not just in the eyes of mathematicians | Dynamical systems and fractals Computer graphics experiments in Pascal Published by the Press Syndicate of the University of Cambridge The Pitt Building, Trumpington Street, Cambridge CB2 1RP 40 West 20th Street, New York, NY lOOllL4211, USA 10 Stamford Road, Oakleigh, Melbourne 3166, Australia Originally published in German as Computergrafische Experimente mit Pascal: Chaos und Ordnung in Dynamischen Systemen by Friedr. Vieweg & Sohn, Braunschweig 1986, second edition 1988, and 0 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig 1986, 1988 First published in English 1989 Reprinted 1990 (three times) English translation 0 Cambridge University Press 1989 Printed in Great Britain at the University Press, Cambridge Library of Congress cataloguing in publication data available British Library cataloguing in publication data Becker, Karl-Heinze Dynamical systems and fractals 1. Mathematics. Applications of computer graphics I. Title II. Doffler, Michael III. Computergrafische Experimente mit Pascal. English 5 lo’.28566 ISBN 0 521 36025 0 hardback ISBN 0 521 36910 X paperback Dynamical systems and fractals Computer graphics experiments in Pascal Karl-Heinz Becker Michael Diirfler Translated by Ian Stewart CAMBRIDGE UNIVERSITY PRESS Cambridge New York Port Chester Melbourne Sydney vi Dynamical Systems and Fractals 7 New Sights - new Insights 179 Up Hill and Down Dale 186 Invert It - It’s Worth It! 186 The World is Round 192 Inside Story 199 8 Fractal Computer Graphics 203 All Kinds of Fractal Curves 204 Landscapes: Trees, Grass, Clouds, Mountains, and Lakes 211 Graftals 216 RepetitiveDesigns 224 9 Step by Step into Chaos 231 10 Journey to the Land of Infinite Structures 247 11 Building Blocks for Graphics Experiments 257 The Fundamental Algorithms 258 FractalsRevisited 267 Ready, Steady, Go! 281 The Loneliness of the Long-distance Reckoner 288 What You See Is What You Get 303 A Picture Takes a Trip .

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