Computational Models of
Complex Systems

Dept of Computer Science & Engineering
UNR, Spring 2005
Course information - Prerequisites - Organization - Grading - Description - Objectives
Schedule & slides - Homework assignments - Bibliography - Useful links - Topics
Course Information
  • Credits: 1.0 - 3.0
  • Class hours: Tuesday & Thursday, 4:00 - 5:15pm
  • Class room: FA 109 (Fleischmann Agriculture)
  • Call number: #32697
  • Maximum Enrollment: 20

  • Instructor: Dr. René Doursat
  • Web page: http://www.cse.unr.edu/~doursat
  • Office: ARF 120
  • Office hours: by appointment only

  • Course flyer


This advanced level interdisciplinary course welcomes graduate students in science and engineering, including: Computer Science & Engineering, Mathematics, Physics, Electrical Engineering, Chemistry, Biology, Biomedical Engineering, Earth Sciences and others.

Students should have good scientific programming skills, knowledge of calculus and linear algebra, a curious mind for exploring other sciences and a willingness to share their own field of expertise.

If you are interested in this seminar but do not feel you have the necessary computational and/or mathematical background, please contact me for possible arrangements (credit assignment follows a sliding scale; see below).


  1. Introductory & guest lectures   I will give an introduction to complex systems and an overview of the topics addressed in the seminar. I will open, moderate and conclude the paper sessions. There will also be a few invited talks from other faculty members.

  2. Paper presentations and discussions   Students will choose journal papers and book chapters from a reading list and prepare presentations for the class. There will be 1 or 2 required readings per session (possibly in combination with additional sources), to be read by everyone and presented by 1 or 2 students. Presentations must be prepared using Microsoft PowerPoint, contain figures and be emailed to the instructor. Speakers should also run a companion demo (ready-made or self-made) to illustrate the presented topic, including an exploration of the parameters and overview of the code. Total duration: 60 minutes, including the demo.

  3. Homework assignments  Students will carry out "convince-yourself" experiments in the form of programming exercises, generally derived from the models reviewed in class. Some exercises will be based on the NetLogo platform, others written in a programmation language such as C/C++, Java, Fortran, MATLAB, etc. There will be approximately one homework assignment every other week (every 4 sessions).

  4. Research project  Students will also complete a modeling & simulation project individually. This includes a program (written in the language of their choice), a technical report and a presentation to the class with a live demo. Topics chosen by the students must address complex systems and may be either related to the paper reviews, or overlapping with their current MSc or PhD work in progress, or fully original for this seminar. Important deadlines (see schedule below): 1 month after start = project proposals; 2 months after start = project status reports; end of the semester = final code, report and presentation.

Late policy: Late assignments of any kind (presentation, exercises, project) will not be accepted.

Academic integrity: All assignments must be prepared individually. Cheating and plagiarism will not be tolerated. Please refer to the UNR policy on Academic Standards.

Disability statement: If you have a disability for which you will need to request accommodations, please contact me or someone at the Disability Resource Center (Thompson Student Services - 107), as soon as possible.


Credits will be based on the involvement with assignments 2, 3 and 4 (see above) and attendance throughout the semester, according to the following sliding scale:

  • 1.0 credit for attendance + completion of assignment 2
  • 3.0 credits for attendance + completion of assignments 2, 3 and 4.

Grading from A to F will depend on the quality of the presentations and participation in the discussions (see 2) and, if elected, the successful completion of both programming exercises and research project (see 3 and 4).

Grading policy (tentative)

  1. Attendance and participation in discussions: 40% (1.0 credit), 20% (3.0 credits)
  2. Paper review presentation: 60% (1.0 credit), 20% (3.0 credits)
  3. Programming exercises: 20% (3.0 credits)
  4. Research project: 40% (3.0 credits)

Grading scale (tentative)

  • 90% - 100%: A-, A
  • 80% - 90%: B-, B, B+
  • 65% - 80%: C-, C, C+
  • 55% - 65%: D
  • 0% - 55%: F


This course explores the cross-disciplinary field of complex systems, or "complexity", through modeling and numerical simulation. Complex systems are characterized by a large number of elements interacting locally and combining their simple individual behaviors to produce an emergent behavior at a macroscopic scale. It is difficult or impossible to explain this emergence in analytical terms, whereas numerical models are often able to reproduce it and make valid predictions.

Processes of self-organization far from equilibrium are pervasive in nature (inanimate systems and living organisms) and human-made structures. Yet, because they raise the problem of the "form" and its appearance, emergent systems have been dismissed as nonobjective phenomena for a long time. Only recently did they become legitimate objects of study per se and a renewed focus of inquiry. After a boom in the 1980's and 1990's, they now promise to be the leading scientific paradigm of this century.

Increasing needs for prediction and control of geophysical, biological or societal structures have triggered rapid advances in the understanding of complexity at the transition between order and chaos. These important insights were made possible by the dramatic progress of information technology and computing power. Consequently, new algorithmic disciplines and new ways to solve problems were founded. These make use of massively parallel, decentralized systems that store and process information as single entities ("emergent computation"). Striking similarities in the observation of various complex phenomena created a fruitful exchange of ideas and techniques among disciplines—such as the ecological perspective on economics (based on the evolution and extinction of species) or the behavior of ant colonies exported to optimization problems.


  1. become familiarized with some of the most prominent case studies and models of complex systems across a variety of topics

  2. understand the key concepts that unify these phenomena

  3. introduce some of the theoretical and computational fields dealing with complexity and their important potential for applications
(a) Cases of complex systems
in nature & human structures
(b) Unifying concepts
of complex systems
(c) Theoretical & computational
fields of complex systems
  • spin glasses, convection cells
  • excitable media & waves
  • genes & cell differentiation
  • animal patterns (coats, shells)
  • insect societies (ants, termites)
  • flocks, herds, schools
  • ecosystems & evolution
  • neurons, brain & cognition
  • cities, economy, Internet
  • etc.
  • emergence
  • self-organization
  • nonlinear dynamics
  • order, chaos, complexity
  • competition/cooperation
  • feedback & homeostasis
  • phase transitions
  • adaptation
  • edge of chaos, criticality
  • etc.
  • cellular automata
  • artificial life, virtual ants
  • swarm intelligence
  • pattern formation
  • oscillators, synchronization
  • Boolean networks
  • genetic algorithms
  • neural networks
  • small worlds
  • etc.
As it appears in this list, complex systems constitute an immensely vast interdisciplinary topic! Therefore, it cannot be the intention of this seminar to be exhaustive or systematic but rather to offer an exploration and discovery of complex systems through "sampling" of the literature and pragmatic experiments.

Schedule & Slides

See Bibliography below for references. The NetLogo demo scripts can be found in the /models folder of the NetLogo installation directory.

Date Speaker Topic Presentation Papers Background References Presentation Demo
Jan 18 Dr. René
Lecture 1: Examples of complex systems (part I) and course organization
Jan 20 Dr. René
Lecture 2: Examples (part II) and concepts of complex systems
Jan 25 Christine
Topic review:
Cellular Automata 1
Gardner (1970)
Wolfram (2002), Ch. 1, 2 & 3
-- Life
CA 1D Elementary
Jan 27 Richard
Topic review:
Slime Mold
Camazine et al. (2003), Ch. 8 Höfer et al. (1995)
Pálsson & Cox (1996)
B-Z Reaction
Feb 1 Rich
Topic review:
Animal Patterns
Wolfram (2002), pp422-429
Bar-Yam (1997), 7.1, 7.2.1-7.2.5
Young (1984) Fur
Feb 3 Kai Xu Topic review:
Ant Trails
Camazine et al. (2003), Ch. 13 -- Ants
Feb 8 Jeff
Topic review:
Iterated Prisoner's
Flake (1998), Ch. 17
Lindgren & Nordahl (1994)
Axelrod & Hamilton (1981)
Nowak & May (1992)
PD Evolutionary
Feb 10 Janet
Topic review:
Attractor Neural
Flake (1998), Ch. 18
Bar-Yam (1997), 2.1 & 2.2
Hopfield (1982) Hopfield Java applet
Feb 15 Dr. René
Lecture 3 (Review):
Complex Networks
Strogatz (2001)
Barabási & Bonabeau (2003)
Wang, X. F. (2002)
Barabási & Albert (1999)
Watts & Strogatz (1998)
Feb 17 R. Drewes Project proposal: Self-emergence of spatial structure of genetically distinct subpopulations
J. Snape Project proposal: Music networks as complex systems
J. Wallace Project proposal: Optimizing the game of Pente with a genetic algorithm
K. Xu Project proposal: Modeling collective insect behavior in a maze
Feb 22 Dr. René
Lecture 4 (Tutorial): Introduction to NetLogo Termites Tutorial
Feb 24 Richard
Topic review:
Cellular Automata 2
Wolfram (2002), Ch. 6 & 8 -- CA 1D Elementary
Tree Simple
Mar 1 Dr. Allen
Lecture 5 (Guest):
Computability and
Wolfram (2002), Ch. 11 & 12
Brady (1988)
-- --
Mar 3 Christine
Topic review:
Flocking and
Camazine et al. (2003), Ch. 11
Huth & Wissel (1992)
Reynolds (1987)
-- Flocking
Mar 8 Kai Xu Topic review:
Bonabeau et al. (1999), Ch. 1 & 6
Camazine et al. (2003), Ch. 19
Theraulaz & Bonabeau (1995a)
Theraulaz & Bonabeau (1995b)
Wasp Nest
Building Simulator
Mar 10 Rich
Topic review:
Spatial Ecology
Solé & Goodwin (2000), Ch. 7
Solé et al. (1992)
Bascompte, J. & Solé (1996)
May (1972)
Solé & Manrubia (1995)
-- --
Mar 15 Jeff
Topic review:
Solé & Goodwin (2000), Ch. 9
Kauffman (1993), Ch. 2 & 6
Kauffman & Weinberger (1989)
Kauffman & Johnsen (1991)
Mar 17 Janet
Topic review:
Autocatalytic and
Genetic Nets
Kauffman (1995), Ch. 2-5
Kauffman (1969)
Kauffman (1986)
-- --
Mar 22 Dr. Thomas
Lecture 6 (Guest):
Selection Theory vs.
Complexity Theory?
Campbell (1974)
Goodwin (1994), Ch. 5
-- --
Mar 24 R. Drewes Project status: Self-emergence of spatial structure of genetically distinct subpopulations
J. Snape Project status: Music networks as complex systems
J. Wallace Project status: Optimizing the game of Pente with a genetic algorithm
K. Xu Project status: Modeling collective insect behavior in a maze
Mar 29 Spring break - no class
Mar 31 Spring break - no class
Apr 5 R. Tillett Paper review:
and Adaptation
Cole (2002) • (see Homework 2) --
R. Drewes Paper review:
Evolution of Complex
Features (Avida)
Lenski et al. (2003) -- --
Apr 7 J. Wallace Paper review:
Cohort Genetic
Holland (2000) -- --
K. Xu Paper review:
Food Webs
Williams & Martinez (2000) -- --
Apr 12 J. Snape Paper review:
in Synfire Chains
Abeles et al. (2004) -- --
C. Wilson Paper review:
Complex Biological
Weng et al. (1999) -- --
Apr 14 Sam
Guest talk:
Tuning CA
with GA
Goldberg (1989), Ch. 1
Louis & Raines (2003)
-- --
Apr 19 Dr. Guy
Lecture 7 (Guest):
Natural Selection
& Self-Organization
Hoelzer et al. (2005)
Schneider & Kay (1994)
-- --
Apr 21 Project preparation - no class
Apr 26 Project preparation - no class
Apr 28 Dr. René
Lecture 8:
Synchronization in
Neural Networks
Wang, D. L. (2000)
Bienenstock & Geman (1995)
Abeles et al. (2004)
-- --
May 3 J. Snape Final project presentation: Music networks as complex systems
J. Wallace Final project presentation: Optimizing the game of Pente with a genetic algorithm
May 5 K. Chu Final project presentation: Modeling collective insect behavior in a maze
R. Drewes Final project presentation: Self-emergence of spatial structure of genetically distinct subpopulations
Dr. Guy
Lecture 7 (part II): Natural Selection & Self-Organization
Dr. René

Homework Assignments

See Bibliography below for references.

Start Date Due Date Assignment References
Feb 22 Mar 1, 4pm Sandpile Automaton Solé & Goodwin (2000), pp53-57
Bak (1996)
Mar 1 Mar 22, 4pm Fluid Neural Network
Model of Ant Colony
Solé & Goodwin (2000), pp157-164
Solé et al. (1993)
Solé & Miramontes (1995)


References will be continuously added as the seminar unfolds. Please check again regularly.

Books with full online text are indicated in boldface. Other links refer either to a review of the book or to a presentation Web site that may include useful information and material such as table of contents, illustrations, selected chapters, companion software, etc.

Articles with online text are indicated with a direct link to the text or a link to the journal via the UNR Library subscription (you will need your library code outside of the university network). Individual third-party Web sites that host journal articles online are not considered course material as a whole, only the specific links that lead to the papers.

  • Abeles, M., Hayon, G. and Lehmann, D. (2004) Modeling compositionality by dynamic binding of synfire chains. Journal of Computational Neuroscience, 17(2): 179-201.

  • Axelrod, R. and Hamilton, W. D. (1981) The evolution of cooperation. Science, 211(4489): 1390-1396.

  • Bak, P. (1996) How Nature Works: The Science of Self-Organized Criticality. Springer, New York.

  • Barabási, A.-L. (2002) Linked: The New Science of Networks. Perseus Books.

  • Barabási, A.-L. and Albert, R. (1999) Emergence of scaling in random networks. Science, 286(5439): 509-512.

  • Barabási, A.-L. and Bonabeau, E. (2003) Scale-free networks [9.3MB]. Scientific American, 288: 60-69.

  • Bascompte, J. and Solé, R. V. (1996) Habitat fragmentation and extinction thresholds in spatially explicit models. Journal of Animal Ecology, 65: 465-473.

  • Bar-Yam, Y. (1997) Dynamics of Complex Systems. Perseus Books. (Note: If the page does not appear, copy and paste the following URL in your browser: http://necsi.org/publications/dcs The problem seems to be caused by a server-side redirection to a nonconventional port, which your firewall might be blocking.)

  • Bienenstock, E. and Geman, S. (1995) Compositionality in neural systems. In The Handbook of Brain Theory and Neural Networks, M. Arbib, ed., pp. 223-226. Bradford Books/MIT Press.

  • Brady, A. H. (1988) The Busy Beaver game and the meaning of life. In The Universal Turing Machine: A Half-Century Survey, R. Herken, ed., pp. 259-277. Oxford University Press.

  • Bonabeau, E., Dorigo, M. and Theraulaz, G. (1999) Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press.

  • Camazine, S., Deneubourg, J.-L., Franks, N. R., Sneyd, J., Theraulaz, G. and Bonabeau, E. (2003) Self-Organization in Biological Systems. Princeton University Press.

  • Campbell, D. T. (1974) Unjustified variation and selective retention in scientific discovery. In Studies in the Philosophy of Biology, F. J. Ayala and T. Dobzhansky, eds., pp. 139-161. University of California Press.

  • Cocho, G., Perez-Pascual, R. and Rius, J. L. (1987) Discrete systems, cell-cell interactions and color pattern of animals. Journal of Theoretical Biology, 125(4): 419-435.

  • Cole, B. J. (2002) Evolution of self-organized systems. Biol. Bull., 202(3): 256-261.

  • Flake, G. (1998) The Computational Beauty of Nature. MIT Press.

  • Gardner, M. (1970) Mathematical Games: The fantastic combinations of John Conway's new solitaire game "life". Scientific American, 223(4): 120-123.

  • Goldberg, D. E. (1989) Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley.

  • Goodwin, B. (1994) How the Leopard Changed Its Spots: The Evolution of Complexity. Princeton University Press.

  • Hoelzer, G. A., Pepper, J. and Smith, E. (2005) On the logical relationship between natural selection and self-organization. (Submitted to Evolution.)

  • Höfer, T., Sherratt, J. A. and Maini, P. K. (1995) Dictyostelium discoideum: cellular self-organisation in an excitable biological medium. Proc. R. Soc. Lond. B, 259: 249-257.

  • Holland, J. H. (2000) Building blocks, cohort genetic algorithms, and hyperplane-defined functions. Evolutionary Computation, 8(4): 373-391.

  • Hopfield, J. J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA, 79(8): 2554-2558.

  • Huth, A. and Wissel, C. (1992) The simulation of the movement of fish schools. Journal of Theoretical Biology, 156: 365-385.

  • Kauffman, S. A. (1969) Metabolic stability and epigenesis in randomly constructed genetic nets. Journal of Theoretical Biology, 22: 437-467.

  • Kauffman, S. A. (1986) Autocatalytic sets of proteins. Journal of Theoretical Biology, 119: 1-24.

  • Kauffman, S. A. (1993) The Origins of Order. Oxford University Press.

  • Kauffman, S. A. (1995) At Home in the Universe: The Search for the Laws of Self-Organization and Complexity. Oxford University Press.

  • Kauffman, S. A. and Johnsen, S. (1991) Coevolution to the edge of chaos: Coupled fitness landscapes, poised states, and coevolutionary avalanches. Journal of Theoretical Biology, 149: 467-505.

  • Kauffman, S. A. and Weinberger, E. D. (1989) The NK model of rugged fitness landscapes and its application to maturation of the immune response. Journal of Theoretical Biology, 141: 211-245.

  • Lenski, R. E., Ofria, C., Pennock, R. T. and Adami, C. (2003) The evolutionary origin of complex features. Nature, 423: 139-144.

  • Lindgren, K. and Nordahl, M. G. (1994) Evolutionary dynamics of spatial games. Physica D, 75: 292-309.

  • Louis, S. J. and Raines, G. L. (2003) Genetic algorithm calibration of probabilistic cellular automata for modeling mining permit activity. In Proceedings of the International Conference on Tools for AI (ICTAI) 2003, Sacramento, CA. IEEE Press.

  • May, R. M. (1972) Will a large complex system be stable? Nature, 238: 413-414.

  • Nowak, M. A. and May, R. M. (1992) Evolutionary games and spatial chaos. Nature, 359(6398): 826-829.

  • Pálsson, E. and Cox, E. C. (1996) Origin and evolution of circular waves and spiral in Dictyostelium discoideum territories. Proc. Natl. Acad. Sci. USA, 93(3): 1151-1155.

  • Reynolds, C. W. (1987) Flocks, herds and schools: a distributed behavioral model. Computer Graphics, 21(4): 25-34.

  • Schneider, E. D. and Kay, J. J. (1994) Life as a manifestation of the second law of thermodynamics. Mathematical and Computer Modelling, 19(6-8): 25-48.

  • Solé, R. V., Bascompte, J. and Valls, J. (1992) Stability and complexity of spatially extended two-species competition. Journal of Theoretical Biology, 159: 469-480.

  • Solé, R. V. and Goodwin, B. C. (2000) Signs of Life: How Complexity Pervades Biology. Perseus Books.

  • Solé, R. V. and Manrubia, S. C. (1995) Are rainforests self-organized in a critical state? Journal of Theoretical Biology, 173: 31-40.

  • Solé, R. V. and Miramontes, O. (1995) Information at the edge of chaos in fluid neural networks. Physica D, 80: 171-180.

  • Solé, R. V., Miramontes, O. and Goodwin, B. C. (1993) Oscillations and chaos in ant societies. Journal of Theoretical Biology, 161(3): 343-357. (Note: Despite the start date of 1/7/1995 mentioned in the UNR Library catalog, the full text of this article is available online.)

  • Strogatz, S. H. (2001) Exploring complex networks. Nature, 410(6825): 268-276.

  • Theraulaz, G. and Bonabeau, E. (1995a) Coordination in distributed building. Science, 269(5224): 686-688.

  • Theraulaz, G. and Bonabeau, E. (1995b) Modelling the collective building of complex architectures in social insects with lattice swarms. Journal of Theoretical Biology, 177: 381-400.

  • Wang, D. L. (2000) On connectedness: a solution based on oscillatory correlation. Neural Computation, 12: 131-139.

  • Wang, X. F. (2002) Complex networks: topology, dynamics and synchronization. International Journal of Bifurcation and Chaos, 12(5): 885-916.

  • Watts, D. J. and Strogatz, S. H. (1998) Collective dynamics of "small-world" networks. Nature, 393(6684): 440-442.

  • Weaver, W. (1948) Science and Complexity. American Scientist, 36: 536.

  • Weng, G., Bhalla, U. S. and Iyengar, R. (1999) Complexity in biological signaling systems. Science, 284(5411): 92-96.

  • Williams, R. J. and Martinez, N. D. (2000) Simple rules yield complex food webs. Nature, 404(6774): 180-183.

  • Wolfram, S. (2002) A New Kind of Science. Wolfram Media. (Note: After browsing a few pages, you will be asked to register your email for further reading. Refer to the FAQs about NKS|Online for help.)

  • Young, D. (1984) A local activator-inhibitor model of vertebrate skin patterns. Mathematical Biosciences, 72: 51-58.

Useful Links

Topics Covered (Tentative)

This is an illustrative list of topics. It does not necessarily follow the chronological order of the sessions and is subject to modification and reorganization, depending on the number of participants. Not all authors or works are cited here, while some items cited here might not be addressed in class.

  1. Introductory lectures

  2. Physics & phase transitions
    • spin glasses, Ising model
    • Rayleigh-Bénard convection

  3. Cellular automata
    • Conway's "Game of Life"
    • Wolfram's four classes of cellular automata
    • Langton's "lambda" parameter

  4. Excitable media: chemical and cellular traveling waves
    • processes of reaction-diffusion
    • chemical oscillations and the Belousov-Zhabotinsky reaction
    • slime mold aggregation
    • pacemaker heart waves
    • wave dynamics in cortical neural networks

  5. Developmental biology
    • Kauffman's gene networks (cellular differentiation)
    • pattern formation in organism development
    • Turing's morphogenesis paper (1952)
    • animal coats (spots & stripes)
    • butterfly wings
    • sea shells (cellular automata)
    • plant growth & phyllotaxis

  6. Social insects and swarm intelligence
    • adaptive trail formation in ants
    • swarm raids in army ants
    • division of labor in ants
    • Dorigo's "Ant Colony Optimization" (ACO)
    • nest building by termites (continuous stigmergy)
    • nest building by wasps (discrete stigmergy)
    • comb patterns in honey bees

  7. Coordinated population behavior
    • synchronized flashing in fireflies
    • fish schooling, bird flocking, cattle herding (Reynold's "boids")
    • Kennedy & Eberhardt's "Particle Swarm Optimization"
    • traffic jams

  8. Ecosystems & economics
    • elements of Game Theory
    • spatially extended ecological systems
    • Robert Axelrod's "Iterated Prisoner's Dilemma"
    • competition & cooperation
    • Kaneko & Solé's "Coupled Map Lattices"
    • Jim Lovelock's "Daisy World" (homeostasis)
    • multi-population dynamics, community ecology, complex webs

  9. Evolution & adaptation
    • Kauffman's random autocatalytic networks (origins of life)
    • Holland's "Genetic Algorithms"
    • variants: Evolutionary Programming, Evolutionary Strategies, Genetic Programming
    • Kauffman's NK models
    • rugged fitness landscapes
    • coevolution
    • explosions and extinctions
    • Langton's "Artificial Life"
    • Ray's "Tierra"

  10. Neural networks & cognitive science
    • Hopfield's associative memory
    • perceptrons
    • spiking neuron models
    • synchronized oscillators
    • pulse coupled networks
    • synfire chains
    • chaotic EEG's

  11. Complex networks
    • random networks
    • "small-world" networks
    • scale-free networks
    • network dynamics
    • spread of diseases
    • food webs
    • Internet & the Web
Course information - Prerequisites - Organization - Grading - Description - Objectives
Schedule & slides - Homework assignments - Bibliography - Useful links - Topics
Created and maintained by
René Doursat
Last update: 5/1/2005