Ebook: Chaos and Fractals: New Frontiers of Science

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Content:
Front Matter....Pages i-7
Introduction....Pages 9-14
The Backbone of Fractals: Feedback and the Iterator....Pages 15-62
Classical Fractals and Self-Similarity....Pages 63-134
Limits and Self-Similarity....Pages 135-181
Length, Area and Dimension: Measuring Complexity and Scaling Properties....Pages 183-228
Encoding Images by Simple Transformations....Pages 229-296
The Chaos Game: How Randomness Creates Deterministic Shapes....Pages 297-352
Recursive Structures: Growing of Fractals and Plants....Pages 353-405
Pascal’s Triangle: Cellular Automata and Attractors....Pages 407-456
Irregular Shapes: Randomness in Fractal Constructions....Pages 457-505
Deterministic Chaos: Sensitivity, Mixing, and Periodic Points....Pages 507-583
Order and Chaos: Period-Doubling and its Chaotic Mirror....Pages 585-653
Strange Attractors: The Locus of Chaos....Pages 655-768
Julia Sets: Fractal Basin Boundaries....Pages 769-840
The Mandelbrot Set: Ordering the Julia Sets....Pages 841-901
Back Matter....Pages 903-984

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Content:
Front Matter....Pages i-7
Introduction....Pages 9-14
The Backbone of Fractals: Feedback and the Iterator....Pages 15-62
Classical Fractals and Self-Similarity....Pages 63-134
Limits and Self-Similarity....Pages 135-181
Length, Area and Dimension: Measuring Complexity and Scaling Properties....Pages 183-228
Encoding Images by Simple Transformations....Pages 229-296
The Chaos Game: How Randomness Creates Deterministic Shapes....Pages 297-352
Recursive Structures: Growing of Fractals and Plants....Pages 353-405
Pascal’s Triangle: Cellular Automata and Attractors....Pages 407-456
Irregular Shapes: Randomness in Fractal Constructions....Pages 457-505
Deterministic Chaos: Sensitivity, Mixing, and Periodic Points....Pages 507-583
Order and Chaos: Period-Doubling and its Chaotic Mirror....Pages 585-653
Strange Attractors: The Locus of Chaos....Pages 655-768
Julia Sets: Fractal Basin Boundaries....Pages 769-840
The Mandelbrot Set: Ordering the Julia Sets....Pages 841-901
Back Matter....Pages 903-984
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