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Index
Title Page Copyright Contents Why Do Fractals Matter? A Smooth World or a Rough One? The Texture of Reality The Origins of Fractals Classical Geometry The Calculus The Paradox of Infinitesimals Effects of Calculus The First Fractal Explaining Numbers Firm Foundations and Sets What Are Sets? Cantor and the Continuum The Cantor Set Peano’s Space-Filling Curve Topological and Fractal Dimension Self-Similarity The Koch Curve Similarity Dimension Similarity and Fractal Dimension Measuring Fractal Dimension Lewis Richardson How Long is a Coastline? The Sierpinski Gasket The Chaos Game Strange Attractor Pascal’s Triangle Basins of Attraction Poincaré and Non-Linearity Malthus and Population Growth Negative Feedback The Logistic Equation Iteration Video Feedback Robert May and the Verhulst Model Bifurcation Points The Period-Doubling Cascade The Fig Tree Chaos Theory and Fractals The Feigenbaum Constant Real Numbers, Other Numbers Complex Numbers The Complex Plane Gaston Julia and Pierre Fatou Benoît Mandelbrot Uncle Szolem A Practical Education The Shape of Things The Wiles of Bourbaki On the Run Again The More the Merrier Emerging Patterns Fractals in Practice Bad Noise Fractal Errors A General Principle Emerges The Simplest Possible Transformation Two Types of Julia Sets A Map of Julia Sets A Whole New World Simple Rules, Complex Behaviour Newton’s Law and Chaos Let’s Admit – It is Complicated … Phase Transitions Hazy Areas of Calculation The Mathematics of Wrinkles Natural Templates Forest Fires: the Fractal Boundary More Phase Transitions Electro-plated Fractals Viscous Fingering Growth by Aggregation Brownian Motion and the Quantum World Dimensional Magic The Three-Quarter Power Law The Mysterious Brain Knowing the Mind of God? Fractals and Medical Research Viruses and Bacteria AIDS Detecting Cancer Women at Risk Bubbly Bones and Breaks Fractal Beats Practical Solutions Striking Oil The Spring is Sprung Stress Loadings Detection Fractal Ecology Orchid Fractals and Crowds Olbers’ Paradox The Great Wall The Big Bang Cosmic Connections How Do We See? Fractal Image Compression Affine Transformations Morphogenesis Satellites The Money Markets What Are the Rules? Market Self-Affinity Generators Beyond Portfolio Theory Multifractals Fractals in Art: Mandalas Decorative Patterns: Self-Similarity Scaling and Repetition Cues in the Landscape Fractals in Music Dysfunction in Modern Architecture Organic Architecture Fractal Traditions Strength in the Details Fracology Quo Vadis? Not Everyone Agrees … The Special Talent of Mandelbrot The Order Is Out There Further Reading Acknowledgements Biographies Index
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