Chaos and Fractals New Frontiers of Science

ISBN-10: 0387979034

ISBN-13: 9780387979038

Edition: 1993

List price: $69.95
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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 captures the attention and enthusiasm of a worldwide audience. The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot Set, Julia Sets, Cellulair Automata, L- systems, Percolation and Strange Attractors. Each chapter is closed by a "Program of the Chapter" which provides computer code for a central experiment. Two appendices complement the book. The first, by Yuval Fisher, discusses the details and ideas of fractal images and compression; the second, by Carl J.G. Evertsz and Benoit Mandelbrot, introduces the foundations and implications of multifractals.
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Book details

List price: $69.95
Copyright year: 1993
Publisher: Springer
Publication date: 2/12/1993
Binding: Hardcover
Pages: 984
Size: 7.89" wide x 9.53" long x 2.25" tall
Weight: 5.346
Language: English

Introduction: Causality Principle, Deterministic Laws and Chaos
The Backbone of Fractals: Feedback and the Iterator
The Principle of Feedback
The Multiple Reduction Copy Machine
Basic Types of Feedback Processes
The Parable of the Parabola--Or: Don't Trust Your Computer
Chaos Wipes Out Every Computer
Classical Fractals and Self-Similarity
The Cantor Set
The Sierpinski Gasket and Carpet
The Pascal Triangle
The Koch Curve
Space-Filling Curves
Fractals and the Problem of Dimension
The Universality of the Sierpinski Carpet
Julia Sets
Pythagorean Trees
Limits and Self-Similarity
Similarity and Scaling
Geometric Series and the Koch Curve
Corner the New from Several Sides: Pi and the Square Root of Two
Fractals as Solutions of Equations
Length, Area and Dimension: Measuring Complexity and Scaling Properties
Finite and Infinite Length of Spirals
Measuring Fractal Curves and Power Laws
Fractal Dimension
The Box-Counting Dimension
Borderline Fractals: Devil's Staircase and Peano Curve
Encoding Images by Simple Transformations
The Multiple Reduction Copy Machine Metaphor
Composing Simple Transformations
Relatives of the Sierpinski Gasket
Classical Fractals by IFSs
Image Encoding by IFSs
Foundation of IFS: The Contraction Mapping Principle
Choosing the Right Metric
Composing Self-Similar Images
Breaking Self-Similarity and Self-Affinity: Networking with MRCMs
The Chaos Game: How Randomness Creates Deterministic Shapes
The Fortune Wheel Reduction Copy Machine
Addresses: Analysis of the Chaos Game
Tuning the Fortune Wheel
Random Number Generator Pitfall
Adaptive Cut Methods
Recursive Structures: Growing Fractals and Plants
L-Systems: A Language for Modeling Growth
Growing Classical Fractals with MRCMs
Turtle Graphics: Graphical Interpretation of L-Systems
Growing Classical Fractals with L-Systems
Growing Fractals with Networked MRCMs
L-System Trees and Bushes
Pascal's Triangle: Cellular Automata and Attractors
Cellular Automata
Binomial Coefficients and Divisibility
IFS: From Local Divisibility to Global Geometry
HIFS and Divisibility by Prime Powers
Catalytic Converters, or How Many Cells Are Black?
Irregular Shapes: Randomness in Fractal Constructions
Randomizing Deterministic Fractals
Percolation: Fractals and Fires in Random Forests
Random Fractals in a Laboratory Experiment
Simulation of Brownian Motion
Scaling Laws and Fractional Brownian Motion
Fractal Landscapes
Deterministic Chaos: Sensitivity, Mixing, and Periodic Points
The Signs of Chaos: Sensitivity
The Signs of Chaos: Mixing and Periodic Points
Ergodic Orbits and Histograms
Metaphor of Chaos: The Kneading of Dough
Analysis of Chaos: Sensitivity, Mixing, and Periodic Points
Chaos for the Quadratic Iterator
Mixing and Dense Periodic Points Imply Sensitivity
Numerics of Chaos: Worth the Trouble or Not?
Order and Chaos: Period-Doubling and Its Chaotic Mirror
The First Step from Order to Chaos: Stable Fixed Points
The Next Step from Order to Chaos: The Period-Doubling Scenario
The Feigenbaum Point: Entrance to Chaos
From Chaos to Order: A Mirror Image
Intermittency and Crises: The Backdoors to Chaos
Strange Attractors: The Locus of Chaos
A Discrete Dynamical System in Two Dimensions: Henon's Attractor
Continuous Dynamical Systems: Differential Equations
The Rossler Attractor
The Lorenz Attractor
Quantitative Characterization of Strange Chaotic Attractors: Ljapunov Exponents
Quantitative Characterization of Strange Chaotic Attractors: Dimensions
The Reconstruction of Strange Attractors
Fractal Basin Boundaries
Julia Sets: Fractal Basin Boundaries
Julia Sets as Basin Boundaries
Complex Numbers--A Short Introduction
Complex Square Roots and Quadratic Equations
Prisoners versus Escapees
Equipotentials and Field Lines for Julia Sets
Binary Decomposition, Field Lines and Dynamics
Chaos Game and Self-Similarity for Julia Sets
The Critical Point and Julia Sets as Cantor Sets
Quaternion Julia Sets
The Mandelbrot Set: Ordering the Julia Sets
From the Structural Dichotomy to the Binary Decomposition
The Mandelbrot Set--A Road Map for Julia Sets
The Mandelbrot Set as a Table of Content
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