Contents

• • Preface
• Contents
• Introduction
  • Overview
  • Examples
    • Schooling of Fish
    • Bacterial Colonies
    • Forest Fires
    • The Double Pendulum
    • The Leopard Spots
  • Summary
  • Exercises
  • References
• Fractals
  • Mathematical Fractals
    • The Koch Curve and Snowflake
  • Dimensions
  • Random Fractals
  • Dynamical generation of fractals: Diffusion Limited Aggregation
  • Occurrence and uses of Fractals
  • Summary
  • Exercises
  • References
• Chaos
  • Introduction
  • Dynamical Systems and Iterative Maps
  • A Simple Example of an Iterative Map
    • An Intuitive Analysis
    • A Graphical Analysis
    • The Analytical Approach
  • A Discrete Model of Population Growth
    • Varying the control parameter in the logistic map
    • Bifurcation Diagrams
    • The Feigenbaum Constant and Universality
  • Experimental Tests
  • The Rossler System
  • The Lorenz map
  • Noise versus Chaos
  • Summary
  • Exercises
  • References
• Equilibrium Systems
  • Thermodynamics and Kinetic Theory
    • State Variables
    • The Ideal Gas
  • Statistical Mechanics
  • The Second Law
  • The First Law
  • Entropy for Open Systems
  • Phase Transitions
    • Second Order Transitions
  • Correlation Function
  • The Scaling Hypothesis
  • The Ising Model
  • Critical Opalescence
  • Percolation
  • Summary
  • Exercises
  • References
• Systems Far From Equilibrium
  • Order in Nature
  • Vortices
  • Benard Cells
  • Non-Equilibrium Pattern Formation vs Equilibrium Phase Transitions
  • The Belousov-Zhabotinski Reaction
  • Turing Structures
  • Predator-Prey Systems
  • War and Love
  • Summary
  • Exercises
  • References
• Self-Organisation
  • Game of Life
  • Termites
  • Boids
  • Ants
  • Herd Behaviour in Humans
  • Evolving Complex Networks
  • Summary
  • Exercises
  • References
• Self-Organised Criticality
  • Power Laws in Nature
  • Models
  • Experiments
  • Life
  • Zipf's Law
  • War and Peace
  • Summary
  • Exercises
  • References
• Measures of Complexity
  • Exercises
  • References
• Conclusion
  • Summary
  • Exercises
  • References
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