Author | Peitgen, Heinz-Otto. author |
---|---|
Title | Chaos and Fractals [electronic resource] : New Frontiers of Science / by Heinz-Otto Peitgen, Hartmut Jรผrgens, Dietmar Saupe |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1992 |
Connect to | http://dx.doi.org/10.1007/978-1-4757-4740-9 |
Descript | XXXII, 999 p. online resource |
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 Pascalโs 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