Dynamical Systems and Fractals ：Computer Graphics Experiments with Pascal

Publication subTitle ：Computer Graphics Experiments with Pascal

Author： Karl-Heinz Becker; Michael Dörfler; I. Stewart  

Publisher： Cambridge University Press‎

Publication year： 1989

E-ISBN: 9780511874628

P-ISBN(Paperback): 9780521360258

Subject： O415.5 Chaos theory

Keyword： 混沌理论

Language： ENG

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Dynamical Systems and Fractals

Description

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.

Chapter

Cover

Half-title

Title

Copyright

Contents

Foreword

New Directions in Computer Graphics: Experimental Mathematics v

Preface to the German Edition

1 Researchers Discover Chaos

1.1 Chaos and Dynamical Systems - What Are They?

1.2 Computer Graphics Experiments and Art.

2 Between Order and Chaos: Feigenbaum Diagrams

2.1 First Experiments

2.1.1 It's Prettier with Graphics

2.1.2 Graphicallteration

2.2 Fig-trees Forever

2.2.1 Bifurcation Scenario - the Magic Number 'Delta

2.2.2 Attractors and Frontiers

2.2.3 FeigenbaumLandscapes

2.3 Chaos - Two Sides to the Same Coin

3 Strange Attractors

3.1 The Strange Attractor

3.2 The H6non Attractor

3.3 The Lorenz Attractor

4 Greetings from Sir Isaac

4.1 Newton's Method

4.2 Complex Is Not Complicated

4.3 Carl Friedrich Gauss meets Isaac Newton

5 Complex Frontiers

5.1 Julia and His Boundaries

5.2 Simple Formulas give Interesting Boundaries

6 Encounter with the Gingerbread Man

6.1 A Superstar with Frills

6.2 Tomogram of the Gingerbread Man

6.3 Fig-tree and Gingerbread Man

6.4 Metamorphoses

7 New Sights - new Insights

7.1 Up Hill and Down Dale

7.2 Invert It - It's Worth It!

7.3 The World is Round

7.4 Inside Story

8 Fractal Computer Graphics

8.1 All Kinds of Fractal Curves

8.2 Landscapes: Trees, Grass, Clouds, Mountains, and Lakes

8.3 Graftals

8.4 Repetitive Designs

9 Step by Step into Chaos

10 Journey to the Land of Infinite Structures

11 Building Blocks for Graphics Experiments

11.1 The Fundamental Algorithms

11.2 Fractals Revisited

11.3 Ready, Steady, Go!

11.4 The Loneliness of the Long-distance Reckoner

11.5 What You See Is What You Get

11.6 A Picture Takes a Trip

12 Pascal and the Fig-trees

12.1 Some Are More Equal Than Others - Graphics on Other Systems

12.2 MS-DOS and PS/2 Systems

12.3 UNIX Systems

12.4 Macintosh Systems

12.5 Atari Systems

12.6 Apple II Systems

12.7 'Kermit Here' - Communications

13 Appendices

13.1 Data for Selected Computer Graphics

13.2 Figure Index

13.3 Program Index

13.4 Bibliography

13.5 Acknowledgements

Index

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