Complex Adaptive Systems


Professor Robert Goldstone

338 Psychology Building

Percepts and Concepts Laboratory


Course Description

Psychology, computer science, economics, biology, and neuroscience depend upon a deeper understanding of the mechanisms that govern adaptive systems.  A common feature of these systems is that organized behavior emerges from the interactions of many simple parts.  Individual cells interact to form differentiated body parts, ants interact to form colonies, neurons interact to form intelligent systems, and people interact to form social networks.  The goals of the course are to: 1) give students an intuitive appreciation for the behavior of complex adaptive systems, 2) present the student with specific case studies of these systems, and 3) describe the formal underpinnings for the complex behavior of these systems.  Properties shared by many complex systems are emergent behavior, self-organization, adaptation, the development of specialized parts, patterns of cooperation and competition, and decentralized control.


To address the essential question of 襑hat are the properties of complex adaptive systems?, case studies of several systems will be explored: chaotic growth in animal populations, human learning, cooperation and competition within social groups, social networks,  cellular automata, the development of stable and globally coherent perceptual representations, and the evolution of artificial life.  A central thesis will be that apparently dissimilar systems (businesses, ant colonies, and brains) share fundamental commonalities.  These commonalities will be described in terms of mathematical and computational formalisms. Good algebra skills are required, and some experience with calculus and a computer programming language is recommended.  During the course, students will become familiar Netlogo, a high-level computer language for developing complex systems.


The topics will be explored by hands-on use of interactive computer simulations.  In the first half of the course, students will be evaluated by their performance on laboratory assignments (some of the laboratories will be based on the computer simulations accessible at  In the second half of the course, students will lead a class on a reading of their own choosing, and will execute and describe their own individual projects.  Projects could involve devising a complex adaptive system model of a natural phenomenon, fitting an existing model to data, conducting an experiment, or providing a novel critique or assessment of a complex adaptive system.  Relevant topics for individual projects include but are not limited to: dynamical systems, artificial life, chaotic systems, biological growth and development, group and collective behavior, bottom-up models of economies, swarm intelligence, game theory, learning, resource utilization in a population, pattern formation, pattern recognition, neural networks, genetic algorithms, emergent organization in social systems, and evolutionary theory.  Each student is expected to lead one class period, centered on a specific, well-contained literature (or even a single article), and another class period on their own project.


Click here for the course syllabus


Weekly Topics


Week 1: Overview on Complex Adaptive Systems

               Class Notes


        Properties of Complex Adaptive Systems

Emergent behavior



Dynamic Change

Competition and Cooperation


        What makes a good computer simulation?

        Orientation to Sub-topics

               Reading: Wilensky & Resnick (1999)

               Optional reading: Macy & Willer (2002). From factors to actors: Compuational                sociology and agent-based modeling.


Week 2: Starlogo & Netlogo

Class Notes


        Ontology: Agents and Patches

        Programming Constructs


Conway誷 Game of Life

Langton誷 Virtual Ants

Path Finder

Slime Mold


               Readings: Resnick (1994) Chapters 2 and 3 (Password: Agent)


        Starlogo This is the newest version of the Starlogo simulation environment developed at MIT by Mitchell Resnick and his collaborators.

        StarlogoT The version of Starlogo originally developed at Tufts University by Uri Wilensky誷 team.  It is a Macintosh-only version of Starlogo.  Version 2 runs native in OS X.  See StarlogoT誷 page of models to see many examples.  Check out the User誷 guide, and the comprehensive reference manual with all programming commands.

        Netlogo This is a cross-platform simulator very similar in its language to StarlogoT (and Starlogo).  It is developed by Uri Wilensky誷 group, and  includes a programming environment (Hubnet) for developing multi-user participatory simulations where the individual agents are operated by individual human users!  Check out Netlogo誷 page of models to see some of the simulations developed for it.  Here are the all-important user誷 guide and dictionary of all programming commands.

               Exercise: Programming in Starlogo


Week 3: Cellular Automata (CAs)

               Class Notes


        Properties of Cellular Automata

        Classification of Cellular Automata

        Substitution Systems

        Mobile automata

        CA Turing machines

        Plant Growth


        Applications in biology

Pine Cone Phyllotaxis

Oscillations in Firefly Populations

Spots and Stripes in biological development

        Bridges Explanations in the Chaos Game and Replicating Game of Life

Readings: Wolfram (2002), Chapters 3 and 8, Douady & Couder (1992), Ball (1999)


        Mathematica notebooks for code examples from the book

        A New Kind of Life Explorer: Interactive software for demonstrating many of the examples from Wolfram誷 book

        Fequently Asked Questions about Cellular Automata

        Java Applets demonstrating several species of Cellular Automata

        Life-lab: A Macintosh program for exploring cellular automata including variants of Conway誷 Game of Life.  This is recommended software for completing the exercise.

        StarlogoT example of a one-dimensional cellular automata

        StarlogoT version of the Conway誷 game of Life

        There are hundreds of cellular automata simulators of different stripe (and spot).  Check out Zooland for a mere sampling.

        Pine Cone Simulator A Macintosh simulation of the development of pine cone and other plant leaves.

        Firefly A StarlogoT simulation of the emergence of flash synchrony in fireflies

               Exercise: Bridging Explanations


Week 4: Applications of Cellular Automata in the Social Sciences

               Class Notes


        Propagation of beliefs in a spatially distributed community

        Attitude formation

        Schelling誷 segregation  model


        Distribution of wealth

        Cultural transmission

Readings:        Nowak, Szamrej, & Latane (1990), Nowak & Lewenstein (1996), Epstein & Axtell (1996) Chapters 2 and 3


        Segregation A StarlogoT simulation of Schelling誷 segregation model

        Sitsim A simple Netlogo simulation of Latane誷 work on social influence

        Rauch, Jonathan, 襍eeing Around Corners,  Atlantic, April 2001.

        Poletta & Jasper (2001).  Collective identity and social movements

        Wealth ditribution A StarlogoT version of the Epstein and Axtell model of wealth distribution

        The home for Sugarscape, at the Brookings Institute

        Movies of Sugarscape simulations


Week 5 Adaptation in communities

               Class Notes


        Predator-prey dynamics the Lotka-Volterra model

        Chaotic growth in a population with the logistic function

        Prisoner誷 dilemma: simple, iterated, spatial

        Diffusion limited aggregation

        Frequency-dependent selection

               Reading: Ball (1999) Communities chapter, Flake (1998) Chapter 10


        Predators & Prey a Macintosh simulation of population dynamics

        Background information on the Prisoner誷 Dilemma

        A spatial Prisoner誷 Dilemma and other links

        Useful Prisoner誷 Dilemma links

        A Netlogo version of Diffusion limited aggregation


Week 6: Student-led Discussions (see potential topics below)

Information Diffusion  (led by Winter Masson)

A Dynamic Field Model of the A-Not-B Error (led by Joseph Anderson)


Week 7: Student-led Discussions

Reinforcement Learning (led by Michael Roberts)

The Evolution of Language (led by Brianna Conrey)


Week 8: Student-led Discussions

Conceptual Role Semantics(led by Ellie Hua Wang)

The Ultimatum Game (led by Shakila Shayan)


Week 9: Student-led Discussions

The Baldwin Effect(led by Georg Theiner)

Small World Phenomena(led by Abhijit Mahabal)


Week 10 Genetic Algorithms

               Class Notes


        Search algorithms for rough landscapes

        Fundamental schema theorem

        K-armed bandit problems

        Tradeoffs between Exploitation and Exploration

        Genetic programming

               Readings:  Goldberg (1989), Holland (1992)


        An interactive overview of Genetic algorithms

        Genetic algorithm and artificial life resources

        The genetic algorithms archives

Week 11 Swarm Intelligence (Guest visit by Russ Eberhart on April 1)

               Class Notes


        Axelrod誷 Adaptive Culture Model

        Particle Swarms, compared to Genetic Algorithms


        Memetic algorithms

               Reading:  Kennedy & Eberhart (2001), Chapters 6 and 7

               Optional readings

                   A comparison of genetic algorithms and particle swarms (Eberhart & Shi)

                   A concise overview of particle swarms (Eberhart & Shi)


        The official site for the book Swarm Intelligence

        Xiaohui Hu誷 Particle Swarm site

        Maurice Clerc誷 Particle Swarm site


Week 12 Emergent organization in perception and cognition

               Class Notes


        Constraint satisfaction networks for the perception of ambiguous objects

        Apparent motion

        Stereo vision and depth perception

        The dynamics of perceptual organization

        Neural networks for constraint satisfaction

        Semantic networks

               Readings:  Dawson (1991), Ramachadran & Anstis (1986)


        Apparent motion experiment and model.  This Macintosh software will allow you to run yourself in apparent motion perception experiments.  It will also let you compare your perceptions to a neural network model誷 襭erceptions.

        Computational stereo vision.  This site evaluates models that take as input two side-by-side pictures of the same scene, and outputs a 3D representation of the scene.

        Research from Bremen University on human and computer stereo perception


Week 13 Social Networks

               Class Notes


        Small world graphs

        The strength of weak ties

        Scale free networks

        Hubs and authorities

        Preferential attachment models

               Readings: Watts & Strogatz (1998), Barabasi & Albert (1999)


        Articles by Mark Newman on graph structures and dynamics

        The Erdos number project

        The Oracle of Bacon

        Albert-Laszlo Barabasi誷 Networks Laboratory



Week 14 Student project descriptions


Week 15 Student project descriptions




Non-exhaustive List of Topics for Student-led Discussions

Evolution of cooperation

Altruism in communities

Prisoner誷 Dilemma

The Minority Game (Here is Savitt誷 work on this)

The Ultimatum Game

The diffusion of beliefs (see, Wejnert (2002))

The Baldwin effect (and Hinton & Nowlan誷 [1987] computer simulation of it)

Waddington canalization of acquired characteristics

Information propagation in a community

Chaotic population change

Wilson and Sober誷 view on group selection models

Per Bak誷 work on Self-organized criticality

Computation at the edge of chaos

Speciation and niche creation

Models of invention and innovation

Stuart Kauffman誷 NK systems the Origins of Order

James Crutchfield誷 Finite State Automata for pattern discovery

Kirby and Hurford誷 model of the evolution of language in a community

1/f noise in cognition

Goldstone & Rogosky誷 work on cross-system translation using within-system relations

Latent Semantic Analysis for using word co-occurrences to determine meaning

Social clustering and clique formation (Here's a Physica A by Plewczyinksi)

Coalition formation

Bikhchandani et al誷 work on fads and cultural change

Valente誷 work on the diffusion of innovations in a community

Tuevo Kohonen誷 work on Self-organized Maps

Auto-encoder networks

Hopfield誷 work on attractors in neural networks

Internal representations in neural networks

Simulated annealing

Scott Camazines work on self-organization in biological systems

Bernd Fritske誷 work on growing self-organizing networks

L-systems for modeling growth

Langton誷 Lambda parameter for characterizing cellular automata

Flocking, herding, and schooling behavior

Other papers by Albert-Laszlo Barabasi誷 lab on network structure

Percolation theory (see an introduction here)

Reinforcement learning

Minimum description length

Lyapunov stability

Sparse distributed memory

Support vector machines

Competitive learning


Course Readings

Ball, P. (1999).  The self-made tapestry.  Oxford, England: Oxford University Press.

Barab噑i, A., & Albert, R. (1999).  Emergence of scaling in random networks, Science, 286, 509-512

Dawson, M. R. W. (1991).  The how and why of what went where in apparent motion: Modeling solutions to the motion correspondence problem.  Psychological Review, 98, 569-603.

Douady, S., & Couder, Y. (1992).  Phyllotaxis as a physical self-organized growth process.  Physical Review Letters, 68, 2098-2101.

Epstein, J. M., & Axtell, R. (1996).  Growing artificial societies: Social science from the bottom up.  Washington, D.C.: Brookings Institute Press.

Flake, G. W. (1998).  The computational beauty of nature.  Cambridge, MA: MIT Press.

Goldberg, D. E. (1989).  Genetic Algorithms.  Reading, MA: Addison-Wesley.  (Chapter 1.  pp.  1-23).

Holland, J. H. (1992).  Genetic algorithms.  Scientific American, July, 66-72.

Kennedy, J., & Eberhart, R. C. (2001).  Swarm intelligence.  San Francisco, CA: Morgan Kaufmann.

Nowak, Andrzej and Lewenstein, Maciej. (1996).  Modeling Social Change with Cellular Automata.

Pp 249-285 in Modeling & Simulation in the Soc. Sciences from a Philosophical Point of View.

Hegselmann et al., eds. Kluwer, Boston.

Nowak, A., Szamrej, J., & Latane, B. (1990).  From private attitude to public opinion: A dynamic theory of social impact.  Psychological Review, 97, 362-376.

Resnick, M. R. (1994).  Turtles, Termites, and Traffic Jams.  Cambridge, MA: MIT Press.

Ramachandran, V. S., & Anstis, S. M. (1986).  The perception of apparent motion.  Scientific American, June, 102-109.

Watts D. J. and Strogatz S. H. Collective dynamics of 'small-world' networks. Nature 393, 440-442 (1998).

Wilensky, U., and Resnick, M. (1999). Thinking in Levels: A Dynamic Systems Approach to Making Sense of the World. Journal of Science Education and Technology, vol. 8, no. 1, pp. 3-19.

Wolfram, S. (2002).  A new kind of Science.  Champaign, IL.: Wolfram Media.


Related Courses Around the World


Additional Web Resources on Complex Adaptive Systems