Think Complexity: Exploring Complexity Science in Python
Think Complexity
Version 2.6.3
Think Complexity
Version 2.6.3
Allen B. Downey Green Tea Press
Needham, Massachusetts
Copyright ? 2016 Allen B. Downey.
Green Tea Press 9 Washburn Ave Needham MA 02492
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iv
Contents
Preface
xi
0.1 Who is this book for? . . . . . . . . . . . . . . . . . . . . . . xii
0.2 Changes from the first edition . . . . . . . . . . . . . . . . . xiii
0.3 Using the code . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1 Complexity Science
1
1.1 The changing criteria of science . . . . . . . . . . . . . . . . 3
1.2 The axes of scientific models . . . . . . . . . . . . . . . . . . 4
1.3 Different models for different purposes . . . . . . . . . . . . 6
1.4 Complexity engineering . . . . . . . . . . . . . . . . . . . . . 7
1.5 Complexity thinking . . . . . . . . . . . . . . . . . . . . . . 8
2 Graphs
11
2.1 What is a graph? . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 NetworkX . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Random graphs . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Generating graphs . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Connected graphs . . . . . . . . . . . . . . . . . . . . . . . . 18
2.6 Generating ER graphs . . . . . . . . . . . . . . . . . . . . . 20
2.7 Probability of connectivity . . . . . . . . . . . . . . . . . . . 22
vi
CONTENTS
2.8 Analysis of graph algorithms . . . . . . . . . . . . . . . . . . 24 2.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Small World Graphs
27
3.1 Stanley Milgram . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Watts and Strogatz . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Ring lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 WS graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.6 Shortest path lengths . . . . . . . . . . . . . . . . . . . . . . 35
3.7 The WS experiment . . . . . . . . . . . . . . . . . . . . . . . 36
3.8 What kind of explanation is that? . . . . . . . . . . . . . . . 38
3.9 Breadth-First Search . . . . . . . . . . . . . . . . . . . . . . 39
3.10 Dijkstra's algorithm . . . . . . . . . . . . . . . . . . . . . . . 41
3.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 Scale-free networks
47
4.1 Social network data . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 WS Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 Degree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4 Heavy-tailed distributions . . . . . . . . . . . . . . . . . . . 53
4.5 Barab?asi-Albert model . . . . . . . . . . . . . . . . . . . . . 55
4.6 Generating BA graphs . . . . . . . . . . . . . . . . . . . . . 57
4.7 Cumulative distributions . . . . . . . . . . . . . . . . . . . . 59
4.8 Explanatory models . . . . . . . . . . . . . . . . . . . . . . . 62
4.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
CONTENTS
vii
5 Cellular Automatons
67
5.1 A simple CA . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2 Wolfram's experiment . . . . . . . . . . . . . . . . . . . . . . 68
5.3 Classifying CAs . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.4 Randomness . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.5 Determinism . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.6 Spaceships . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.7 Universality . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.8 Falsifiability . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.9 What is this a model of? . . . . . . . . . . . . . . . . . . . . 78
5.10 Implementing CAs . . . . . . . . . . . . . . . . . . . . . . . 80
5.11 Cross-correlation . . . . . . . . . . . . . . . . . . . . . . . . 82
5.12 CA tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.13 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6 Game of Life
89
6.1 Conway's GoL . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2 Life patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.3 Conway's conjecture . . . . . . . . . . . . . . . . . . . . . . 92
6.4 Realism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.5 Instrumentalism . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.6 Implementing Life . . . . . . . . . . . . . . . . . . . . . . . . 97
6.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7 Physical modeling
103
7.1 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.2 Reaction-diffusion . . . . . . . . . . . . . . . . . . . . . . . . 105
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