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