Think Complexity: Complexity Science and Computational Modeling

by Allen Downey

Overview

Complexity science uses computation to explore the physical and social sciences. In Think Complexity, you'll use graphs, cellular automata, and agent-based models to study topics in physics, biology, and economics.

Whether you're an intermediate-level Python programmer or a student of computational modeling, you'll delve into examples of complex systems through a series of worked examples, exercises, case studies, and easy-to-understand explanations.

In this updated second edition, you will:

• Work with NumPy arrays and SciPy methods, including basic signal processing and Fast Fourier Transform
• Study abstract models of complex physical systems, including power laws, fractals and pink noise, and Turing machines
• Get Jupyter notebooks filled with starter code and solutions to help you re-implement and extend original experiments in complexity; and models of computation like Turmites, Turing machines, and cellular automata
• Explore the philosophy of science, including the nature of scientific laws, theory choice, and realism and instrumentalism

Ideal as a text for a course on computational modeling in Python, Think Complexity also helps self-learners gain valuable experience with topics and ideas they might not encounter otherwise.

Product Details

ISBN-13:	9781492040200
Publisher:	O'Reilly Media, Incorporated
Publication date:	08/06/2018
Edition description:	2nd ed.
Pages:	198
Product dimensions:	5.90(w) x 9.40(h) x 1.30(d)

About the Author

Allen Downey is a professor of Computer Science at Olin College and the author of a series of free, open-source textbooks related to software and data science, including Think Python, Think Bayes, and Think Complexity, published by O’Reilly Media. His blog, Probably Overthinking It, features articles on Bayesian probability and statistics. He holds a Ph.D. in computer science from U.C. Berkeley, and M.S. and B.S. degrees from MIT. He lives near Boston, MA with his wife and two daughters.

Table of Contents

Preface vii

1 Complexity Science 1

The Changing Criteria of Science 3

The Axes of Scientific Models 4

Different Models for Different Purposes 5

Complexity Engineering 6

Complexity Thinking 7

2 Graphs 9

What Is a Graph? 9

NetworkX 11

Random Graphs 13

Generating Graphs 14

Connected Graphs 15

Generating ER Graphs 17

Probability of Connectivity 18

Analysis of Graph Algorithms 20

Exercises 21

3 Small World Graphs 23

Stanley Milgram 23

Watts and Strogatz 24

Ring Lattice 25

WS Graphs 27

Clustering 28

Shortest Path Lengths 29

The WS Experiment 30

What Kind of Explanation Is That? 32

Breadth-First Search 33

Dijkstra's Algorithm 34

Exercises 36

4 Scale-Free Networks 39

Social Network Data 39

WS Model 42

Degree 42

Heavy-Tailed Distributions 44

Barabási-Albert Model 45

Generating BA Graphs 48

Cumulative Distributions 49

Explanatory Models 51

Exercises 53

5 Cellular Automatons 55

A Simple CA 55

Wolfram's Experiment 56

Classifying CAs 57

Randomness 58

Determinism 60

Spaceships 61

Universality 62

Falsifiability 64

What Is This a Model Of? 64

Implementing CAs 66

Cross-Correlation 67

CA Tables 69

Exercises 70

6 Game of Life 73

Conway's GoL 73

Life Patterns 74

Conway's Conjecture 76

Realism 77

Instrumentalism 78

Implementing Life 79

Exercises 81

7 Physical Modeling 85

Diffusion 85

Reaction-Diffusion 87

Percolation 90

Phase Change 92

Fractals 93

Fractals and Percolation Models 95

Exercises 97

8 Self-Organized Criticality 99

Critical Systems 99

Sand Piles 100

Implementing the Sand Pile 101

Heavy-Tailed Distributions 103

Fractals 105

Pink Noise 109

The Sound of Sand 110

Reductionism and Holism 112

SOC, Causation, and Prediction 114

Exercises 115

9 Agent-Based Models 117

Schelling's Model 117

Implementation of Schelling's Model 118

Segregation 120

Sugarscape 122

Wealth Inequality 124

Implementing Sugarscape 125

Migration and Wave Behavior 127

Emergence 128

Exercises 130

10 Herds, Flocks, and Traffic Jams 133

Traffic Jams 133

Random Perturbation 136

Boids 137

The Boid Algorithm 138

Arbitration 140

Emergence and Free Will 141

Exercises 142

11 Evolution 145

Simulating Evolution 146

Fitness Landscape 147

Agents 148

Simulation 148

No Differentiation 149

Evidence of Evolution 150

Differential Survival 153

Mutation 154

Speciation 157

Summary 159

Exercises 160

12 Evolution of Cooperation 161

Prisoner's Dilemma 161

The Problem of Nice 163

Prisoner's Dilemma Tournaments 164

Simulating Evolution of Cooperation 165

The Tournament 167

The Simulation 168

Results 169

Conclusions 173

Exercises 174

A Reading List 177

Index 179