Chaos and Fractals

New frontiers of science

Dietmar Saupe, Heinz-Otto Peitgen, Hartmut Jürgens

984 pages, parution le 15/10/1992

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Résumé

For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.

Contents

Preface
Authors
Foreword 1

Introduction: Causality Principle, Deterministic Laws and Chaos 9

1 The Backbone of Fractals: Feedback and the Iterator 15
2 Classical Fractals and Self-Similarity 63
3 Limits and Self-Similarity 135
4 Length, Area and Dimension: Measuring Complexity and Scaling Properties 183
5 Encoding Images by Simple Transformations 229
6 The Chaos Game: How Randomness Creates Deterministic Shapes 297
7 Recursive Structures: Growing of Fractals and Plants 353
8 Pascal's Triangle: Cellular Automata and Attractors 407
9 Irregular Shapes: Randomness in Fractal Constructions 457
10 Deterministic Chaos: Sensitivity, Mixing, and Periodic Points 507
11 Order and Chaos: Period-Doubling and its Chaotic Mirror 585
12 Strange Attractors: The Locus of Chaos 655
13 Julia Sets: Fractal Basin Boundaries 769
14 The Mandelbrot Set: Ordering the Julia Sets 841

A A Discussion of Fractal Image Compression 903
B Multifractal Measures 921

Bibliography 955
Index 971

L'auteur - Heinz-Otto Peitgen

Peitgen, H.-O., University of Bremen

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Dietmar Saupe, Heinz-Otto Peitgen, Hartmut Jürgens
Parution	15/10/1992
Nb. de pages	984
Format	20 x 24
Couverture	Relié
Poids	2300g
Intérieur	Quadri
EAN13	9780387979038
ISBN13	978-0-387-97903-8