Natural Complexity

Preface xiii
1. Introduction: What Is Complexity? 1
1.1 Complexity Is Not Simple 1
1.2 Randomness Is Not Complexity 4
1.3 Chaos Is Not Complexity 10
1.4 Open Dissipative Systems 13
1.5 Natural Complexity 16
1.6 About the Computer Programs Listed in This Book 18
1.7 Suggested Further Reading 20
2 Iterated Growth 23
2.1 Cellular Automata in One Spatial Dimension 23
2.2 Cellular Automata in Two Spatial Dimensions 31
2.3 A Zoo of 2-D Structures from Simple Rules 38
2.4 Agents, Ants, and Highways 41
2.5 Emergent Structures and Behaviors 46
2.6 Exercises and Further Computational Explorations 47
2.7 Further Reading 50
3 Aggregation 53
3.1 Diffusion-Limited Aggregation 53
3.2 Numerical Implementation 54
3.3 A Representative Simulation 58
3.4 A Zoo of Aggregates 60
3.5 Fractal Geometry 63
3.6 Self-Similarity and Scale Invariance 73
3.7 Exercises and Further Computational Explorations 76
3.8 Further Reading 78
4 Percolation 80
4.1 Percolation in One Dimension 80
4.2 Percolation in Two Dimensions 83
4.3 Cluster Sizes 85
4.4 Fractal Clusters 98
4.5 Is It Really a Power Law? 98
4.6 Criticality 100
4.7 Exercises and Further Computational Explorations 102
4.8 Further Reading 104
5 Sandpiles 106
5.1 Model Definition 106
5.2 Numerical Implementation 110
5.3 A Representative Simulation 112
5.4 Measuring Avalanches 119
5.5 Self-Organized Criticality 123
5.6 Exercises and Further Computational Explorations 127
5.7 Further Reading 129
6 Forest Fires 130
6.1 Model Definition 130
6.2 Numerical Implementation 131
6.3 A Representative Simulation 134
6.4 Model Behavior 137
6.5 Back to Criticality 147
6.6 The Pros and Cons of Wildfire Management 148
6.7 Exercises and Further Computational Explorations 149
6.8 Further Reading 152
7 Traffic Jams 154
7.1 Model Definition 154
7.2 Numerical Implementation 157
7.3 A Representative Simulation 157
7.4 Model Behavior 161
7.5 Traffic Jams as Avalanches 164
7.6 Car Traffic as a SOC System? 168
7.7 Exercises and Further Computational Explorations 170
7.8 Further Reading 172
8 Earthquakes 174
8.1 The Burridge-Knopoff Model 175
8.2 Numerical Implementation 182
8.3 A Representative Simulation 184
8.4 Model Behavior 189
8.5 Predicting Real Earthquakes 193
8.6 Exercises and Further Computational Explorations 194
8.7 Further Reading 196
9 Epidemics 198
9.1 Model Definition 198
9.2 Numerical Implementation 199
9.3 A Representative Simulation 202
9.4 Model Behavior 205
9.5 Epidemic Self-Organization 213
9.6 Small-World Networks 215
9.7 Exercises and Further Computational Explorations 220
9.8 Further Reading 222
10 Flocking 224
10.1 Model Definition 225
10.2 Numerical Implementation 228
10.3 A Behavioral Zoo 235
10.4 Segregation of Active and Passive Flockers 240
10.5 Why You Should Never Panic 242
10.6 Exercises and Further Computational Explorations 245
10.7 Further Reading 247
11 Pattern Formation 249
11.1 Excitable Systems 249
11.2 The Hodgepodge Machine 253
11.3 Numerical Implementation 260
11.4 Waves, Spirals, Spaghettis, and Cells 262
11.5 Spiraling Out 266
11.6 Spontaneous Pattern Formation 270
11.7 Exercises and Further Computational Explorations 272
11.8 Further Reading 273
12 Epilogue 275
12.1 A Hike on Slickrock 275
12.2 Johannes Kepler and the Unity of Nature 279
12.3 From Lichens to Solar Flares 285
12.4 Emergence and Natural Order 288
12.5 Into the Abyss: Your Turn 290
12.6 Further Reading 291
A. Basic Elements of the Python Programming Language 293
A.1 Code Structure 294
A.2 Variables and Arrays 297
A.3 Operators 299
A.4 Loop Constructs 300
A.5 Conditional Constructs 304
A.6 Input/Output and Graphics 305
A.7 Further Reading 306
B. Probability Density Functions 308
B.1 A Simple Example 308
B.2 Continuous PDFs 312
B.3 Some Mathematical Properties of Power-Law PDFs 313
B.4 Cumulative PDFs 314
B.5 PDFs with Logarithmic Bin Sizes 315
B.6 Better Fits to Power-Law PDFs 318
B.7 Further Reading 320
C Random Numbers and Walks 321
C.1 Random and Pseudo-Random Numbers 321
C.2 Uniform Random Deviates 323
C.3 Using Random Numbers for Probability Tests 324
C.4 Nonuniform Random Deviates 325
C.5 The Classical Random Walk 328
C.6 Random Walk and Diffusion 335
D Lattice Computation 338
D.1 Nearest-Neighbor Templates 339
D.2 Periodic Boundary Conditions 342
D.3 Random Walks on Lattices 345
Index 351