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Tables of Contents for Fractals for the Classroom
Chapter/Section Title
Page #
Page Count
Introduction: Causality Principle, Deterministic Laws and Chaos
1
8
Recursive Structures: Growing of Fractals and Plants
9
58
L-Systems: A Language For Modeling Growth
13
8
Growing Classical Fractals with MRCMs
21
13
Turtle Graphics: Graphical Interpretation of L-Systems
34
4
Growing Classical Fractals with L-Systems
38
13
Growing Fractals with Networked MRCMs
51
6
L-System Trees and Bushes
57
5
Program of the Chapter: L-systems
62
5
Pascal's Triangle: Cellular Automata and Attractors
67
50
Cellular Automata
72
13
Binomial Coefficients and Divisibility
85
12
IFS: From Local Divisibility to Global Geometry
97
13
Catalytic Converters or how many Cells are Black?
110
3
Program of the Chapter: Cellular Automata
113
4
Deterministic Chaos: Sensitivity, Mixing, and Periodic Points
117
78
The Signs of Chaos: Sensitivity
119
13
The Signs of Chaos: Mixing and Periodic Points
132
6
Ergodic Orbits and Histograms
138
10
Paradigm of Chaos: The Kneading of Dough
148
16
Analysis of Chaos: Sensitivity, Mixing, and Periodic Points
164
11
Chaos for the Quadratic Iterator
175
9
Numerics of Chaos: Worth the Trouble or Not?
184
7
Program of the Chapter: Time Series and Error Development
191
4
Order and Chaos: Period-Doubling and its Chaotic Mirror
195
74
The First Step From Order to Chaos: Stable Fixed Points
202
12
The Next Step From Order to Chaos: The Period Doubling Scenario
214
17
The Feigenbaum Point: Entrance to Chaos
231
9
From Chaos to Order: a Mirror Image
240
13
Intermittency and Crises: The Backdoors to Chaos
253
12
Program of the Chapter: Final State Diagram
265
4
Strange Attractors: The Locus of Chaos
269
82
A Discrete Dynamical System in Two Dimensions: Henon's Attractor
274
21
Continuous Dynamical Systems: Differential Equations
295
9
The Rossler Attractor
304
11
The Lorenz Attractor
315
13
The Reconstruction of Strange Attractors
328
10
Fractal Basin Boundaries
338
10
Program of the Chapter: Rossler Attractor
348
3
Julia Sets: Fractal Basin Boundaries
351
64
Julia Sets as Basin Boundaries
353
6
Complex Numbers --- A Short Introduction
359
8
Complex Square Roots and Quadratic Equations
367
5
Prisoners versus Escapees
372
12
Equipotentials and Field Lines for Julia Sets
384
13
Chaos Game and Self-Similarity for Julia Sets
397
6
The Critical Point and Julia Sets as Cantor Sets
403
8
Quaternion Julia Sets
411
2
Program of the Chapter: Julia Sets
413
2
The Mandelbrot Set: Ordering the Julia Sets
415
60
From the Structural Dichotomy to the Potential Function
417
10
The Mandelbrot Set --- A Road Map for Julia Sets
427
22
The Mandelbrot Set as a Table of Content
449
18
Program of the Chapter: The Mandelbrot Set
467
8
Bibliography
475
14
Index
489