# Dynamical systems and fractals

 Автор(ы): Becker Karl-Heinz 06.10.2007 Год изд.: 1989 Описание: This book is about chaos, fractals and complex dynamics, and is addressed to all people who have some familiarity with computers and enjoy using them. The mathematics has been kept simple, with few formulae, yet the reader is introduced to and can learn about an area of current scientific research which was scarcely possible before the availability of computers. The introduction is achieved through the extensive use of computer graphics. The book is divided into two main parts: in the first the most interesting problems are described, with, in each case, a solution in the form of a computer program. A large number of exercises enable the reader to undertake his or her own experimental work. In the second part, example programs are given for specific machines and operating systems; details refer to MS-DOC and Turbo-Pascal, UNIX 4.2 BSD with Berkley Pascal and C. Other implementations of the graphics routines are given for Apple Macintosh, Apple IIE and IIGS and Atari ST. Оглавление: Обложка книги. Foreword New Directions in Computer Graphics : Experimental Mathematics [vii] Preface to the German Edition [xi] 1 Researchers Discover Chaos   1.1 Chaos and Dynamical Systems - What Are They? [3]   1.2 Computer Graphics Experiments and Art [6] 2 Between Order and Chaos: Feigenbaum Diagrams [17]   2.1 First Experiments [18]   2.1.1 It's Prettier with Graphics [27]   2.1.2 Graphicallteration [34]   2.2 Fig-trees Forever [37]   2.2.1 Bifurcation Scenario - the Magic Number Delta [46]   2.2.2 Attractors and Frontiers [48]   2.2.3 FeigenbaumLandscapes [51]   2.3 Chaos - Two Sides to the Same Coin [53] 3 Strange Attractors [55]   3.1 The Strange Attractor [56]   3.2 The Henon Attractor [62]   3.3 The Lorenz Attractor [64] 4 Greetings from Sir Isaac [71]   4.1 Newton's Method [72]   4.2 Complex Is Not Complicated [81]   4.3 Carl Friedrich Gauss meets Isaac Newton [86] 5 Complex Frontiers [91]   5.1 Julia and His Boundaries [92]   5.2 Simple Formulas give Interesting Boundaries [108] 6 Encounter with the Gingerbread Man [127]   6.1 A Superstar with Frills [128]   6.2 Tomogram of the Gingerbread Man [145]   6.3 Fig-tree and Gingerbread Man [159]   6.4 Metamorphoses [167] 7 New Sights - new Insights [179]   7.1 Up Hill and Down Dale [186]   7.2 Invert It - It's Worth It! [186]   7.3 The World is Round [192]   7.4 Inside Story [199] 8 Fractal Computer Graphics [203]   8.1 All Kinds of Fractal Curves [204]   8.2 Landscapes: Trees, Grass, Clouds, Mountains, and Lakes [211]   8.3 Graftals [216]   8.4 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]   11.1 The Fundamental Algorithms [258]   11.2 Fractals Revisited [267]   11.3 Ready, Steady, Go! [281]   11.4 The Loneliness of the Long-distance Reckoner [288]   11.5 What You See Is What You Get [303]   11.6 A Picture Takes a Trip [319] 12 Pascal and the Rg-trees [327]   12.1 Some Are More Equal Than Others Graphics on Other Systems [328]   12.2 MS-DOS and PS/2 Systems [328]   12.3 UNIX Systems [337]   12.4 Macintosh Systems [347]   12.5 Atari Systems [361]   12.6 Apple П Systems [366]   12.7 'Kermit Here' - Communications [374] 13 Appendices [379]   13.1 Data for Selected Computer Graphics [380]   13.2 Figure Index [383]   13.3 Program Index [388]   13.4 Bibliography [391]   13.5 Acknowledgements [393] Index [395] Формат: djvu Размер: 4145083 байт Язык: ENG Рейтинг: 38
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