Chaos and fractals : new frontiers of science

Chaos and fractals : new frontiers of science / Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe.

For almost 15 years chaos and fractals have been riding a wave that has enveloped many areas of mathematics and the natural sciences in its power, creativity and expanse. Traveling far beyond the traditional bounds of mathematics and science to the distant shores of popular culture, this wave captur...

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Bibliographic Details
Main Author: Peitgen, Heinz-Otto, 1945-
Other Authors: Jürgens, H. (Hartmut), Saupe, Dietmar, 1954-
Format: eBook
Language:English
Published: New York : Springer-Verlag, ©1992.
Subjects:
Fractals.
Chaotic behavior in systems.
fractals.
Fractales
Comportamiento caótico en sistemas
Chaotic behavior in systems
Fractals
Chaos.
Fractales.
Chaos (Théorie des systèmes)
Online Access:Click for online access
Table of Contents:
  • Introduction: Causality Principle, Deterministic Laws and Chaos
  • 1 The Backbone of Fractals: Feedback and the Iterator
  • 2 Classical Fractals and Self-Similarity
  • 3 Limits and Self-Similarity
  • 4 Length, Area and Dimension: Measuring Complexity and Scaling Properties
  • 5 Encoding Images by Simple Transformations
  • 6 The Chaos Game: How Randomness Creates Deterministic Shapes
  • 7 Recursive Structures: Growing of Fractals and Plants
  • 8 Pascal's Triangle: Cellular Automata and Attractors
  • 9 Irregular Shapes: Randomness in Fractal Constructions
  • 10 Deterministic Chaos: Sensitivity, Mixing, and Periodic Points
  • 11 Order and Chaos: Period-Doubling and its Chaotic Mirror
  • 12 Strange Attractors: The Locus of Chaos
  • 13 Julia Sets: Fractal Basin Boundaries
  • 14 The Mandelbrot Set: Ordering the Julia Sets
  • A A Discussion of Fractal Image Compression
  • A.1 Self-Similarity in Images
  • A.2 A Special MRCM
  • A.3 Encoding Images
  • A.4 Ways to Partition Images
  • A.5 Implementation Notes
  • B Multifractal Measures
  • B.1 Introduction
  • B.2 The Binomial and Multinomial Measures
  • B.5 Some Applications, and Advanced Multifractals.

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