Dynamical Systems and Fractals (Computer Graphics Experiments with Pascal)

This 1989 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. Karl-heinz Becker, Michael Dörfler ; Translated By I. Stewart. Title From Publisher's Bibliographic System (viewed On 01 Jun 2016). Mode Of Access: World Wide Web. Contents......Page 5 Foreword......Page 7 Preface to the German Edition......Page 11 1 Researchers Discover Chaos I......Page 13 1.1 Chaos and Dynamical Systems - What Are They?......Page 15 1.2 Computer Graphics Experiments and Art.......Page 18 2 Between Order and Chaos: Feigenbaum Diagrams......Page 29 2.1 First Experiments......Page 30 2.1.1 It's Prettier with Graphics......Page 39 2.1.2 Graphicallteration......Page 46 2.2 Fig-trees Forever......Page 49 2.2.1 Bifurcation Scenario - the Magic Number'Delta......Page 58 2.2.2 Attractors and Frontiers......Page 60 2.2.3 FeigenbaumLandscapes......Page 63 2.3 Chaos - Two Sides to the Same Coin......Page 65 3 Strange Attractors......Page 67 3.1 The Strange Attractor......Page 68 3.2 The H6non Attractor......Page 74 3.3 The Lorenz Attractor......Page 76 4 Greetings from Sir Isaac......Page 83 4.1 Newton's Method......Page 84 4.2 Complex Is Not Complicated......Page 93 4.3 Carl Friedrich Gauss meets Isaac Newton......Page 98 5 Complex Frontiers......Page 103 5.1 Julia and His Boundaries......Page 104 5.2 Simple Formulas give Interesting Boundaries......Page 120 6 Encounter with the Gingerbread Man......Page 139 6.1 A Superstar with Frills......Page 140 6.2 Tomogram of the Gingerbread Man......Page 157 6.3 Fig-tree and Gingerbread Man......Page 171 6.4 Metamorphoses......Page 179 7 New Sights - new Insights......Page 191 7.2 Invert It - It's Worth It!......Page 198 7.3 The World is Round......Page 204 7.4 Inside Story......Page 211 8 Fractal Computer Graphics......Page 215 8.1 All Kinds of Fractal Curves......Page 216 8.2 Landscapes: Trees, Grass, Clouds, Mountains, and Lakes......Page 223 8.3 Graftals......Page 228 8.4 Repetitive Designs......Page 236 9 Step by Step into Chaos......Page 243 10 Journey to the Land of Infinite Structures......Page 259 11 Building Blocks for Graphics Experiments......Page 269 11.1 The Fundamental Algorithms......Page 270 11.2 Fractals Revisited......Page 279 11.3 Ready, Steady, Go!......Page 293 11.4 The Loneliness of the Long-distance Reckoner......Page 300 11.5 What You See Is What You Get......Page 315 11.6 A Picture Takes a Trip......Page 331 12 Pascal and the Fig-trees......Page 339 12.2 MS-DOS and PS/2 Systems......Page 340 12.3 UNIX Systems......Page 349 12.4 Macintosh Systems......Page 359 12.5 Atari Systems......Page 373 12.6 Apple II Systems......Page 378 12.7 'Kermit Here' - Communications......Page 386 13 Appendices......Page 391 13.1 Data for Selected Computer Graphics......Page 392 13.2 Figure Index......Page 395 13.3 Program Index......Page 400 13.4 Bibliography......Page 403 13.5 Acknowledgements......Page 405 Index......Page 407 This study of chaos, fractals and complex dynamics is intended for anyone familiar with computers. While keeping the mathematics to a simple level with few formulas, the reader is introduced to an area of current scientific research that was scarcely possible until the availability of computers. The book is divided into two main parts; the first provides the most interesting problems, each with a solution in a computer program format. Numerous exercises enable the reader to conduct his or her own experimental work. The second part provides sample programs for specific machine and operating systems; details refer to IBM-PC with MS-DOS and Turbo-Pascal, UNIX 42BSD with Berkeley Pascal and C. Other implementations of the graphics routines are given for the Apple Macintosh, Apple IIE and IIGS and Atari ST. This study of chaos, fractals and complex dynamics is intended for anyone familiar with computers. It shows how to create fractals with the reader's computer. Sample programs are provided for IBM-PC with MS-DOS and Turbo Pascal, UNIX 42BSD with Berkeley Pascal and C. Other routines are given for Apple Macintosh, Apple IIE and IIGS and Atari ST.