Author | Peitgen, Heinz-Otto. author |
---|---|
Title | Fractals for the Classroom [electronic resource] : Part Two: Complex Systems and Mandelbrot Set / by Heinz-Otto Peitgen, Hartmut Jรผrgens, Dietmar Saupe |
Imprint | New York, NY : Springer New York, 1992 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4406-6 |
Descript | XII, 500 p. online resource |
Introduction: Causality Principle, Deterministic Laws and Chaos -- 8 Recursive Structures: Growing of Fractals and Plants -- 8.1 L-Systems: A Language For Modeling Growth -- 8.2 Growing Classical Fractals with MRCMs -- 8.3 Turtle Graphics: Graphical Interpretation of L-Systems -- 8.4 Growing Classical Fractals with L-Systems -- 8.5 Growing Fractals with Networked MRCMs -- 8.6 L-System Trees and Bushes -- 8.7 Program of the Chapter: L-systems -- 9 Pascalโs Triangle: Cellular Automata and Attractors -- 9.1 Cellular Automata -- 9.2 Binomial Coefficients and Divisibility -- 9.3 IFS: From Local Divisibility to Global Geometry -- 9.4 Catalytic Converters or how many Cells are Black? -- 9.5 Program of the Chapter: Cellular Automata -- 10 Deterministic Chaos: Sensitivity, Mixing, and Periodic Points -- 10.1 The Signs of Chaos: Sensitivity -- 10.2 The Signs of Chaos: Mixing and Periodic Points -- 10.3 Ergodic Orbits and Histograms -- 10.4 Paradigm of Chaos: The Kneading of Dough -- 10.5 Analysis of Chaos: Sensitivity, Mixing, and Periodic Points -- 10.6 Chaos for the Quadratic Iterator -- 10.7 Numerics of Chaos: Worth the Trouble or Not? -- 10.8 Program of the Chapter: Time Series and Error Development -- 11 Order and Chaos: Period-Doubling and its Chaotic Mirror -- 11.1 The First Step From Order to Chaos: Stable Fixed Points -- 11.2 The Next Step From Order to Chaos: The Period Doubling Scenario -- 11.3 The Feigenbaum Point: Entrance to Chaos -- 11.4 From Chaos to Order: a Mirror Image -- 11.5 Intermittency and Crises: The Backdoors to Chaos -- 11.6 Program of the Chapter: Final State Diagram -- 12 Strange Attractors: The Locus of Chaos -- 12.1 A Discrete Dynamical System in Two Dimensions: Hรฉnonโs Attractor -- 12.2 Continuous Dynamical Systems: Differential Equations -- 12.3 The Rรถssler Attractor -- 12.4 The Lorenz Attractor -- 12.5 The Reconstruction of Strange Attractors -- 12.6 Fractal Basin Boundaries -- 12.7 Program of the Chapter: Rรถssler Attractor -- 13 Julia Sets: Fractal Basin Boundaries -- 13.1 Julia Sets as Basin Boundaries -- 13.2 Complex Numbers โ A Short Introduction -- 13.3 Complex Square Roots and Quadratic Equations -- 13.4 Prisoners versus Escapees -- 13.5 Equipotentials and Field Lines for Julia Sets -- 13.6 Chaos Game and Self-Similarity for Julia Sets -- 13.7 The Critical Point and Julia Sets as Cantor Sets -- 13.8 Quaternion Julia Sets -- 13.9 Program of the Chapter: Julia Sets -- 14 The Mandelbrot Set: Ordering the Julia Sets -- 14.1 From the Structural Dichotomy to the Potential Function -- 14.2 The Mandelbrot Set โ A Road Map for Julia Sets -- 14.3 The Mandelbrot Set as a Table of Content -- 14.4 Program of the Chapter: The Mandelbrot Set