1. News

3 November 2019

Welcome to the course! We will start with an introductory lecture on Monday, November 4, at 10.00 in FL51.


The schedule with lecture rooms is available in TimeEdit.

The new course page is available in Canvas.

Below follows the old page that is not valid any longer.


January 24, 2019

The exams from January 7 are now corrected. Please see below to find a zip file with scores for the anonymous codes. Emails with results will be sent out as soon as the exams have been deanonymized.

January 7, 2019

Solutions to today's exam are now posted below.

December 19, 2018

By popular demand, the slides from the seminar of group 9 are now available in the Dropbox folder.

December 17, 2018

The preliminary project presentations are on Wednesday December 19 at 13.15-15.00. We will divide the groups into two rooms and run the presentations in the following order:

  • FL51: Groups 9, 6, 2, 1
  • FL63: Groups 3, 4, 5, 10

Each group will be given 15 minutes to present and another 5 minutes for questions and discussion. Please think of the presentation as a work meeting to improve your project. We don't grade your presentations because the purpose is to help you develop the projects.

The session on Wednesday before lunch is canceled.

December 13, 2018

Materials for seminars 9 and 10 are now available in the Dropbox folder.

Update on obligatory attendance: We expect you to take part in at least 5 of 7 two-hour blocks of seminars and/or guest lectures. Anyone who is close to missing this requirement will be contacted by email. We apologize for the unclear information on this previously.

December 10, 2018

You should now have recieved an email with your score and anonymous code from the midterm exam. Please see below in Section 3 to find answers and scores in Excel and csv files.

December 9, 2018

Materials for seminars 5 and 6 are now available in the Dropbox folder.

December 6, 2018

On the re-exam: Anyone may take the re-exam (January 7th, 2019, at 08.30-10.30). We always count your best score, so there is no risk involved in taking the re-exam.

Seminars: Materials for Seminar 4 are now available in the Dropbox folder.

A few messages from Erik Sterner who gave the example seminar:

  • Erik's slides are now available in the Dropbox folder (in the directory Seminars).
  • "on mentimeter.com you can create a free account (allows for two questions if I'm not mistaken)."
  • "Suggestion for feedback question: Please give us feedback on how this seminar worked (Optional comment: you may want to use the model for efficient feedback presented in the course.)"

December 5, 2018

Materials for Seminar 3 are now available in the Dropbox folder.

November 30, 2018

About the exam:

  • The exam is now corrected. The exams have however not been deanonymized yet, so we can't connect the scores to students yet. But if you remember your anonymous code, feel free to send Rasmus an email to know your score.
  • There will be a re-exam on January 7th, 2019, at 08.30-10.30.

About the seminars:

  • Reading materials for Seminars 1 and 2 are now posted in the Dropbox. Thanks to groups 1 and 2 for being well on time.

About project groups:

  • The supervisors are now decided: Susanne has groups 1, 2, 6; Rasmus has groups 3, 4, 5; Kristian has groups 9, 10. Your supervisors will get in touch to schedule supervision meetings.

November 29, 2018

The preparation materials for Monday's example seminar are now posted in the Dropbox. Please make sure to read them in detail before the seminar on Monday.

November 28, 2018

Yesterday's exam and solutions are now posted below.

November 22, 2018

  • We have extended the exam time by 15 minutes. This means you will be given 120 minutes to complete the exam, from 10.00 to 12.00 in room SB-M500. Good luck!
  • The strategies you submitted for assignment 2 are now available in the Dropbox.

November 21, 2018

The models presented today on finitely and infinitely repeated Prisoner's Dilemma on a lattice are described in papers found in the DropBox (Lindgren, 1997; Lindgren & Nordahl, 1994). The Mathematica code for the simulations is also available, both for the finitely repeated PD and the infinitely repeated PD.

November 16, 2018

The old exams are now also posted without solutions. See below.

On Monday November 19, Rasmus will demonstrate solutions to the exam from 2018-01-26.

November 15, 2018

The overview slide of games you proposed for Assignment 1 is now available in the Dropbox folder. The paper describing the evolutionary model (Lindgren, 1991) presented yesterday is available under the recommended reading, and the Mathematica code for the simulation is also available.

November 14, 2018

The games you proposed for Assignment 1 are now available in the Dropbox folder.

Also, some instructions for the midterm exam:

  • The exam will be in room SBM500.
  • You do not need to register for the exam.
  • Make sure to bring a valid photo ID (e.g., passport or Swedish driver's license) and your student union membership card.

November 8, 2018

The deadline for forming project/seminar groups is postponed to Wednesday 21 November. This change is now reflected in the documents below.

November 6, 2018

Lectures 2 and 3 on Basic concepts will primarily be based on Chapters 1, 2, and 4 in the course book. Since the book is short and concise, we recommend a broader introduction to the area that is found in two texts by Roger Myerson, covering work by John Nash and Thomas Schelling. The texts are found in the Dropbox folder under "Recommended reading".

October 30, 2018

Welcome to the course! We will start with an introductory lecture on Monday, November 5, in FL51.

The schedule with lecture rooms is available in TimeEdit.

2. General course information


Other online resources:

3. Assignments, seminars, projects, etc

4. Other materials

Kristian's implementation of the Schelling segregation model: download (Mathematica notebook).

Published in Course page

The course responsible for this course has chosen not to move his or her course web page to Studycas yet.


Course page for 2013/2014 (link updated 2014-08-28):


Published in Course page

Simulation of Complex Systems Fall 2016

The course information this term will be published on pingpong.chalmers.se. If you have any requests regarding the course, please contact This email address is being protected from spambots. You need JavaScript enabled to view it..



  1. Recent updates
  2. Course description
  3. Schedule
  4. Problem sets
  5. Modeling and simulation project
  6. Project ideas

1. Recent updates

  • Dec 9: Added Mathematica files used in lectures 2 and 7 (see below under attachments).
  • Dec 1: Computer lab Dec 5 is cancelled. I will return with information on how we will deal with the last two sessions. 
  • Dec 1: Added compulsory and additional reading for Lecture 6 on cellular automata (see below).
  • Dec 1: Fourth and fifth home problems uploaded (see below).
  • Nov 26: Additional reading on the Barábasi-Albert preferential model added under Lecture 5.
  • Nov 21: Third home problem uploaded (see below).
  • Nov 21: Added lecture slides for Lecture 5 on networks.
  • Nov 21: Added link to compulsory reading for Lecture 5 on networks.
  • Nov 17: Added link to compulsory reading for Lecture 4 on modeling of complex systems.
  • Nov 17: Updated flawed link to reading on Schelling's model of segregation under Lecture 2 (spatial model of segregation).
  • Nov 11: Regarding homework: You are all meant to write your own code, in your preferred language. But you will work together as a group in discussing the homework and resolving algorithmic issues.
  • Nov 10: If you are taking this course, but have not yet received an email from me with your assigned group, please send me an email as soon as possible. 
  • Nov 10: Second home problem uploaded (see below).
  • Nov 10: First home problem uploaded (see below).
  • Nov 05: Slides for today's lecture added (see below).
  • Nov 05: Homepage updated for 2014. The course starts Wednesday Nov 05 and ends with project presentations Dec 19. This is the last date you have to be present at Chalmers for this course, as there is no exam. 

2. Course description

Much of modelling in the sciences focuses on simple models, highlighting key mechanisms using small sets of moving parts. However, in complex systems the interesting features are often a direct result of having large sets of particles or agents with different characteristics. This makes new tools a necessity. The course introduces simulation techniques frequently used in complex systems to handle models with many heterogeneous parts. Specifically, we will look at agent-based modelling, evolutionary game theory, cellular automata, and networks, with application to physics, biology and social science. We also learn how to validate the outcomes of simulation models in order to reach scientifically sound conclusions.


There is no single book that covers all the topics in the course so we have no required books. However, we aim to provide a set of compulsory (and additional) readings assigned to each lecture that covers and perhaps broadens the content of the lectures.  

If you still want something for your shelf, here are some recommendations:

Mark Newman's book on Networks is very good, both comprehensive and well-written. It covers much more than this course, but if you're the type that reads non-fiction and textbooks for fun, I can recommend it. If you want something shorter, the review article Statistical Mechanics of Complex Networks by Albert and Barabasi are available for free and covers most of the network topics we discuss.

For agent-based models we have used Epstein's Generative Social Science for a reading project earlier years. It gives a good overview of what kind of questions agent-based models can be used to handle in the social sciences and also discusses a range of fairly deep issues regarding e.g. what it means to explain a social phenomenon. Epstein's and Axtell's Growing Artificial Societies is shorter and focuses more on a single type of model, but can also serve as an introductory text.

For cellular automata, Ilachinski's Cellular Automata - A Discrete Universe is very comprehensive and covers almost everything even remotedly related to CA. I'm not very impressed with its quality though, and would only recommend it to someone who only need the coverage and can afford to read it with a skeptical mind. You can also take a look at Wolfram's A New Kind of Science (full book available online), though even stronger caveats apply here (see e.g. this review). Wolfram's papers are much more measured, though a bit dated by now. You could for example take a look at his review Statistical Mechanics of Cellular Automata.


Main lecturer: Kolbjørn Tunstrøm (This email address is being protected from spambots. You need JavaScript enabled to view it.)

Tutors: Erik Edlund, Vilhelm Verendel, Clas Andersson, Jonas Einarsson, Martin Nilsson Jacobi

Examiner: Martin Nilsson Jacobi (This email address is being protected from spambots. You need JavaScript enabled to view it.)

You can find us in our offices at the division of Physical Resource Theory, in the EDIT-building.

3. Schedule

Ordinary lectures are 8.00-10.00 in MC on Wednesdays and Fridays. Computerlabs replace Friday lectures some weeks and take place in F-T7204 (in Forskarhuset Fysik, street address Fysikgränd 3).

Variations can occur, please check the lecture plan below.

Lecture plan

Lecture 1: Wednesday Nov 05 The role of simulations in the study of complex systems; Course information; Introduction to agent based modeling; Collective motion.

Compulsory reading:

Additonal reading:

Lecture slides:

Lecture 2: Friday Nov 07 Agent based models continued; SIR model of disease spreading; Schelling's model of segregation.

Compulsory reading:

Additonal reading:

Lecture 3: Wednesday Nov 12 Evolutionary game theory (guest lecture by Kristian Lindgren).

Compulsory reading:

Lecture 4: Wednesday Nov 19 Modeling of complex systems (guest lecture by Philip Gerlee).

Compulsory reading:

Lecture 5: Friday Nov 21 Networks Part 1; Preferential growth and scale free networks; The small world model.

Compulsory reading:

Additonal reading:

Lecture slides:

Lecture 6: Wednesday Nov 26 Introduction to cellular automata (CA); CA as modeling technique (guest lecture by Martin Nilsson Jacobi).

Compulsory reading:

Additonal reading:

Lecture 7: Wednesday Dec 03 Networks part 2; Community structure and modularity; Percolation and disease spreading on networks.

Lecture 8: Wednesday Dec 10 Stability of complex systems.

See also TimeEdit. But note the change we have made in presentation date from Jan 09 2015 to Dec 19 2014.

4. Problem sets

The purpose of the problem sets is to provide you with hands on experience of the different methods presented in the course. You will work in groups of 3 and have your work assessed in a series of scheduled computer labs. The problem sets account for 50% of your total course grade.


There are five problem sets available, each accounting for 25 points. The homework deadlines are set with the assumption that you choose one of Homework 1 and Homework 2, followed by doing the other three. A perfect score is therefore 100.

Note 1: A necessary (but not sufficient) requirement for passing grade is that 10 points are achieved in each homework 1 or 2, 3, 4, and 5.
Note 2: You can build your score anyway you want, attaining a maximum of 125 points (that's right; 25 points more than a perfect score).

The grade limits will be 45 points for grade 3, 65 points for grade 4, and 85 points for grade 5. For GU the limits will be 45 points for G and 75 for VG.

Computer labs

The computer lab sessions serve two purposes: 1) To get help if you are stuck in a problem set (and have not managed to get unstuck by consulting some of your classmates); and 2) To have your homework graded. Previous terms, we have experienced queues during lab hours. Therefore, we emphasise the “home” in homework; being prepared before you enter the lab is crucial for these sessions to run smoothly.


You will be randomly divided into groups of three (possibly two). The reason for this is to allow for efficient execution of the computer labs; we only have two people available this year assisting in the lab sessions. But: Everyone is meant to program their own code, or at least contribute significantly to each problem set. That is, while you can split up the work in each problem set, you are not allowed to split the problem sets between you. Honor code: If you have not contributed to solving the problems, you should say so during assessment.

The topics of the homework are given below. Instructions for the specific homework's will follow throughout the term.

  • Homework 1: Disease spreading Implementing the agent-based SIR-model from the lecture on Nov 7. Deadline is Nov 28 (but first possibility of assessment is Nov 14). For instructions, download H1_DiseaseSpreading.pdf.
  • Homework 2: Evolutionary game theory A cellular automaton demonstrating the spatial prisoners dilemma, related to Kristian's lecture Nov 12. Deadline is Nov 28 (but first possibility of assessment is Nov 14). For instructions, download H2_EvoGamesCA.pdf.
  • Homework 3: Network models: Implementation and investigations of different random network models.  For instructions, download H3_NetworkModels.pdf. This pdf also contains links to files you need for the homework.
  • Homework 4: Cellular automaton model of forest fires. For instructions, download H4_ForestFires.pdf.
  • Homework 5: Communities and disease spreading on networks. For instructions, download H5_NetworkCommunitiesDynamics. This pdf also contains links to files you need for the homework.

Lab schedule

All computer labs take place in F-T7204.

  • Lab 1: Friday         Nov 14 08:00-09:45    Homework 1 & 2
  • Lab 2: Friday         Nov 28 08:00-09:45    Homework 3
  • Lab 3: Friday         Dec 05 08:00-09:45    Homework 4
  • Lab 4: Friday         Dec 12 08:00-09:45    Homework 4 & 5
  • Lab 5: Wednesday Dec 17 08:00-09:45    Extra lab

Each lab is intended to focus on the specified homework, but there will be an extra lab in the end where you can have assessed any of the homeworks.

5. Modeling and simulation project

The purpose of the project work is to provide you with training in

  • Defining your own research question. 
  • Executing a collaborative project.
  • Presenting your independent work in writing and as a summary talk.

The project accounts for 50% of your total course grade.

General information

You will be randomly divided into groups of three (possibly four). The reason for this is twofold; it will assure a broad distribution of skills and interest; it is a realistic scenario for later work in academia or industry.

Each group gets a tutor assigned and has ~3 meetings with this tutor during the course. Should it be so that you experience problems with the group assembly, you need to take this up with your tutor as soon as possible.

The project should be presented to the class on Friday December 19, and in a written report, to be handed in (by email) to your tutor within January 16. The effort spent on the project and the report/presentation should be around 50% of the total effort spent on the course.

On topics and questions

Your project needs two things to get started: a topic and a question (or problem formulation). A topic explains what you are going to do, a question explains why. A typical topic description could be "we want to do a agent-based simulation of a predator-prey system." A corresponding question could be "to see whether space changes the stability as compared to the behaviour in the standard ODE models.”

General advice

If I had an hour to solve a problem and my life depended on it, I would use the first 55 minutes to formulate the right question because as soon as I have identified the right question I can solve the problem in less than five minutes.

—Albert Einstein

Everything takes longer time than you expect, so getting started with your model implementation is essential for a successful project. Do not interpret the time ratio in the quote too literally; the moral is that you need to have a question you want to answer with your model. This provides the project with direction and makes navigating it much easier. But research (as much else) is a highly iterative process, so don’t expect a perfect question from the start. If you realize your question didn't make sense half-way through your project, take the time to try and formulate a new one. In a lot of real research the question in the paper ends up being quite different from the one that started the project (similarly among start-ups, many end up with a completely different product that their initial idea).

Start simple. It is fine to have a grand, pie-in-the-sky idea, but make sure the steps to the goal has some value in themselves. Not only does this prevent you from being stuck with nothing to show at the end of the course, it also gives you feedback on your big idea as early as possible. Start with a small question and iterate it towards greatness.

If there is a simpler model of what you are trying to do that shows some part of the interesting features, at the very least think about how they compare. Ideally, implement both and do a careful comparison. You can often get great project ideas out of thinking about what you lose when you remove features.

It's OK to fail. Research has a large portion of luck involved. If you have a good idea that don't work out, analyze why and we're happy.


Each project group gets assigned a tutor. The tutor’s job is to give you general advice on anything you need as best as he or she can. The tutor’s job is not to formulate your project for you, nor to debug your code. The general guideline is to have three meetings in total: one in the beginning when you have a problem formulation and maybe have started implementing something; one in the middle when you have gotten your first results and thought about whether you need to reformulate your problem; and one at the end, to decide what more should be done and to get advice on the report and the oral presentation.

To get the most out of the meetings, make sure to prepare yourselves. Have specific questions written down. Have a demonstration of your code ready to run.


The presentation of the project should take maximum 10 minutes, with an additional 5 minutes for questions and discussion. The timing will be enforced, so make sure you go through the presentation beforehand and check its duration. You decide whether and how to divide the material between yourselves.

Put the emphasis on what your problem formulation is, a general discussion about how you tackled it, what problems you had, and what your conclusions are. 


Structure your report like a scientific article, with an abstract summarizing the rationale and results of the project; an introduction shortly explaining background and motivating why the question is interesting; methods and/or results section(s) describing your model and what you do with it; a discussion section; and ending with a short summary. Put some work into the discussion section. This is where you demonstrate that you truly understand the implications of your work, including shortcomings and uncertainties. It is important that the discussion does not fall out as a simple summary of what the figures show.

Write enough to say what you need to say. Don't think "the report feels short, better throw in some extra figures." If you can say the same thing in fewer words, do so. Short reports make for happy graders. Do not exceed 10 pages.

Be sure to reference any source you use. The report should be readable and understandable on its own, but there is no need to reproduce for example derivations of equations from your sources; a citation is enough.

Figures are an important part of the report, but only those that substantially contribute to your analysis should be included. Make sure that each figure is well designed with informative captions (not just "Fig. X shows how quantity A depends on quantity B"). If you find it hard to do this, you probably are not clear on why you include an figure, so cut it out.

Most importantly, use your own judgement and try to write a report you would like to read.

Evaluation criteria

The project grade will be based on your report, but the presentation might be used as input for deciding on whether to tip a grade upwards or downwards. Criteria that will be considered are:
  • Is the project report well structured (see above)?
  • Does the project have a clear research question?
  • Does the project answer the initial or iterated research question?
  • Are the methods and analysis appropriate for convincingly answering the research question?
  • Is there a clear coupling between the model, the research question, and conclusions?
  • Are the figures included informative with descriptive captions?
  • Is the length of the report appropriate for the story it tells?
Note that the research question does not have to be answered in the affirmative. A negative result is equally valid as long as an analysis is carried out that properly explains the negative result and what eventually would work better.

After you get your grades, it will be possible to make a revised submission to raise your grades. The feedback from your tutor should provide you with the necessary input for achieving a higher grade.

6. Project ideas

Here are a few project titles from Simulation of Complex Systems 2013:

  • Predator avoidance in schools of fish
  • Cartel formation in Bertrand’s model of oligopoly
  • Simulation of escape panic behaviour
  • Public services and segregation
  • Disease dynamics in the informative society
  • The size-rank law and urban growth
  • Optimal resource allocation using genetic algorithms
  • Traffic light and roundabout performance evaluation with IDM/MOBIL

There are lots of interesting papers to be found under publications (and working papers) at the Santa Fe Institute (SFI). Many ideas that have been brought up and discussed at the Complex Systems seminar can be developed into projects in this course. Also, projects that some of you have done in earlier courses, like Stochastic optimization algorithms, can be continued and developed into new projects here. I also recommend that you search the web; there are so many good papers and ideas to be found out there.

Many of the links below point to papers describing the investigation of a certain model. You may use such a model a starting point for the project, which usually means that you have to do your own implementation. Then you may critically test the limits of the model. What are critical assumptions and parameter values? To what extent are the conclusions drawn by the authors general, etc?

Social systems

Societal structure - hierarchies, norms, institutions. The online Journal of Artificial Societies and Social Simulation provides some ideas and papers.

Voting models

The results of a democratic voting process may heavily depend on the voting system. Explore this by modelling a population of people voting. Read "The complexity of voting" by David A. Meyer.

Modelling segregation in urban areas

See, for example, relevant chapters in Schelling's book on micromotives and macrobehaviour (at Kristian Lindgren's office).

Evolution of strategies in game-theoretic models

There are several possible ideas that could be developed into projects here. Kristian Lindgren and Anders Eriksson have a set of papers, most of them dealing with the Prisoner's Dilemma game, that could serve as a starting point or for inspiration. There are several examples of games in Herbert Gintis' book "Game Theory Evolving" that can be developed into interesting multi-agent models. There are several models (some with source code) presented at Axelrod's "Complexity of Cooperation" web site.

a) The ultimatum game. Make a critical analysis or a modification of the model presented in Science: M. A. Nowak, K. M. Page, and K. Sigmund: "Fairness versus reason in the Ultimatum Game", Science 289, 1773-1775 (2000).
b) Evolution of Cooperation through Indirect Reciprocity, see Leimar, O. and Hammerstein, P. (2001), Proc.Royal.Soc.Lond.B, 745–753. (online text version). This is a reply and critisism of a paper by Nowak and Sigmund i Nature.

Panic and other types of basic group behaviour

How to model the group behaviour in panic situations. See link related to Nature paper Simulating dynamical features of escape panic by Helbing et. al.

Networks and infrastructure systems

Traffic simulation
Make a realistic model of a small part of Göteborg's traffic system. Model a highway with some exits, include tunnel, etc... Very nice Java simulations are available on Helbing's page (two-lane version). A quantitative analysis of how traffic flow is affected by road characteristics, could be a suitable goal for one project.

City growth simulation
How will Göteborg develop in the future? Or, from the map of 1809, how could Göteborg have developed to today? See Project Gigalopolis for an example on how such models can be constructed. We also have a number of papers in the Complex Systems Group, see our project description. One project may involve exploring how different local rules can give rise to different types of growth.

Small world networks
See book and papers by Duncan J. Watts (Small Worlds: The dynamics of networks between order and randomness, Princeton Univ. Press, 1999). A very good review by Mark Newman is available here. There are a lot of new papers published on these ideas.

Economic systems

Artificial markets, software agents, etc.
Lots of information to be found under Leigh Tesfatsion's web page on Agent-Based Computational Economics. She also offers a number of links to software useful for multi-agent modelling, and she offers a long list of suitable student projects (covering a lot of complex systems), see at the bottom of the syllabus page for her course).

a) A simple stock market with a stock (or two).
b) Cournot duopoly, or a simple oligopoly model; see, for example, Fudenberg & Tirole p.14.
c) A Sugarscape inspired model, see Epstein's and Axtell's book.

If you are interested in working on software agents, check the online tutorial by Patty Maes from Software Agents Group at MIT Media Laboratory.

Natural systems, ecosystems

Pattern formation in chemical, biological, and ecological systems.

a) Make a PDE model of a simple chemical system that exhibits pattern formation (2X -> 3X model, see Science paper).
b) Host-parasitoid interactions may lead to complicated space-time patterns; Hassell has done a lot in this area, see, e.g., Hassell, M.P., H.N. Comins, and R.M. May. 1991. Spatial structure and chaos in insect populationd dynamics. Nature 353: 255-258 and Pacala, S., M.P. Hassell, and R.M. May. 1990. Host-parasitoid associations in patchy environments. Nature 344: 150-153.
c) Spatial dynamics in a host-pathogen system, see, for example, paper by G.M. Hood with model description.

Modelling population dynamics - comparing agent-based models with ODEs

Make an agent-based model of a few variations of simple one and two species population dynamics and compare the behaviour with simpler models in terms of ordinary differential equations. When does an ODE work as a good approximation to the more complicated agent-based model?

Ecosystems in fragmented environments

Build an individual based model of a species that lives in a fragmented environment.

Decentralized dynamics of animal flocks

Construct a model in which various types of flocking behaviour may evolve.

Global issues, resources, and the environment

See, for example, the link to Beyond the Limits (incl Mac program and hints on how to get the model for PC)

How many will there be 2050? Try to make a projection of the world population growth to year 2050. There are several approaches possible, see for example paper in Nature by Lutz et al. (For fun, see web page on "world population since creation" with figure that shows a 9 billion population before the flood...)

Modelling resource use in multi-agent systems; tragedy of the commons

Fishery models: Make a model of fishermen harvesting a population that follows a simple dynamics model. Model the fishermen as adaptive agents. Think on how to model their behaviour. How do they adapt their strategies to each other and to the resource?

Artifical worlds and virtual reality

"Physical" simulations in artificial worlds. Here one may use the software package, breve, that Jon Klein has developed in his Master's thesis (runs under MacOSX).

a) Make models of and simulate flock behaviour in 2D or 3D worlds. Follow links from breve; see also Craig Reynolds web page on Boids.
b) Simm's evolving creatures, see, e.g., "Evolving 3D Morphology and behaviour by competition", Artificial Life 1, 353-372 (1995).

Complex system games

Use complex systems ideas in order to design simple but tricky games (either computer-human or human-human). The first versions of the game Blobity of Catchy Software was a project of this course in 2000.


Published in Course page


  1. Recent updates
  2. Course description
  3. Groups and Schedule
  4. Instructions
  5. Grades
  6. Teachers and student representatives
  7. Topic inspiration
  8. Student seminars
  9. Guest lectures
  10. Student seminars from 2015-2016
  11. Student seminars from 2014-2015

1. Recent updates (Back to top)

[08.29.2016] Update for 2016-2017 class

[01.05.2017] Schedule completed through LP3 and LP4

2. Course description (Back to top)

This course runs through the entire first year of the CAS program. The course consists of two components:

1) Quarter 1 - An introduction to complexity science: concepts and history.

2) Quarter 2-4 - Student presentations

The first part is intended to provide concepts and opportunities for some reflection on complexity that goes beneath the level of learning about specific tools and theories.

The second part of the course gives the Master's students practice in oral presentation of scientific topics, practice in searching for scientific information, and opportunities to discuss ongoing projects with faculty and other students.

3. Groups and Schedule (Back to top)

Download group subdivision of the class as PDF

See timeedit for room information, and note that rooms are subject to rapid change.

(Note that this preliminary and subject to change. If timeedit and the schedule are contradictory, trust timeedit.)

Introduction Classes LP 1

Date Time Topic Resources
Wednesday August 31 10:00-11:45 Intro to course; introduction to LP 1 lectures.
Wednesday September 7 10:00-11:45 Complex and Complicated systems
Wednesday September 14 13:15-15:00 From early primates to higher primates: from complexity to trans-complexity
Wednesday September 21 13:15-15:00 From Great Apes to Early Homo: sub-wicked and new complicatedness
Wednesday September 28 13:15-15:00 From the Palaeolithic to the Anthropocene: from sub-wicked to trans-complicated and wicked.
Wednesday October 5 13:15-15:00 The history of complexity
Wednesday October 12 13:15-15:00 Giving oral presentation (hand-out)

Presentation Schedule LP 2 - LP 4

Download schedule as PDF

Please be on time since it is highly distracting for both the audience and the presenter to have people showing up late.

4. Instructions (Back to top)

Download instructions as PDF

Please download the present feedback form here!

5. Grades (Back to top)

The course only has a pass and fail grade. It is not a difficult course, in the sense that if you do your best you should pass. Not doing your best includes:

  • Attending less than 80% of the sessions.
  • Not contributing in an acceptable way to the work of your Presentation Group.
  • Not following instructions, such as to submit abstract and title, arrange a dry run, and so on.
  • Not performing your Review Group duties.

Either of these will lead to a fail grade. The rules are not overly burdensome or many, but they are there and they are strict.

6. Teachers and student representatives (Back to top)

Claes works at the department for Physical Resource Theory (Energy and Environment) in the Electro (EDIT) building, floor 3V. If you have questions or comments that are not covered here, please feel free to send me an email, call or to stop by the office (best to make an appointment).

Student representatives

Please contact the student representatives if you wish to convey any feedback to the teachers regarding the course, if you do not wish to communicate with the teachers directly.The course representatives are selected randomly and automatically by a large clunky robot at the central administration.

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7. Topic Inspiration (Back to top)

Due to popular demand, I've assembled a list of examples of possible topics. If you can, please don't be lazy and just pick a topic from the list, but use it as inspiration and pick something new and innovative!

See also the list of presentations from the previous year below (15/16 and 14/15). While, obviously, you are not allowed to just pick one, the students are new every year, and many of the topics can be well worth considering.

  • Game of Life - The Game of Life is a cellular automaton developed by John Conway in 1970. The cellular automaton plays out on an infinite two-dimensional grid of square cells, each in one of two possible states: "alive" or "dead". At each time step, any live cell with fewer than two live neighbors die ("underpopulation"); any live cell with two or three live neighbors lives on; any live cell with three or more neighbors die ("overcrowding"), and any dead cell with exactly three neighbors becomes alive ("reproduction"). These simple rules result in the generation of highly complex spatiotemporal patterns, such as "gliders", "pulsars" and "blinkers", in a system so simple that it permits mathematical analysis.
  • Scaling Laws - Certain patterns can be found throughout nature, and seem to depend only on size. For example, metabolic rate, time scales (such as life span and heart rate), and size of component parts (such as length of the aorta or height of a tree) can be expressed as power-law relationships with body-mass exponents that are multiplies of 1/4 (e.g. 1/4, 3/4, 3/8). Others are independent of scale: an elephant can't jump higher than a cockroach. This seems to be valid for almost all forms of life, from mice to bulls. Some scaling laws seem to apply also human systems, such as cities (for example the number of patents seem to follow a power-law as a function of city size).
  • Percolation Models -If a liquid is poured on top of some porous material - will it be able to make its way from hole to hole and reach the bottom? This can be modeled as the behavior of connected clusters in a random graph. It turns out that at a certain level of connectivity in the graph, a phase transition occurs. Due to their simplicity, percolation models can also be used as models to understand the dynamics of other systems.
  • Fractals and Chaos - Fractals are infinitely complex patterns that are self-similar across different scales, generally created through an the iteration of a simple process. Fractals can in a way be seen as pictures of chaos. Geometrically, they exist in between the integer dimensions. While seemingly strange, most of what we see in nature is in fact fractal: trees, lungs, rivers, cities, etc. Abstract fractals (such as the Mandelbrot Set) can be generated by a computer calculating a simple equation over and over, and thus serve as illustration of how something extremely simple can lead to the emergence of something infinitely complex. Some researchers have spent their lives analyzing the many hidden secrets of the Mandelbrot set (for example, the number pi can be found in surprising places).
  • Evolutionary Art -Using certain stochastic professes, beautiful patterns can be generated by a computer. These algorithms can often be based on evolutionary ideas: the most esthetically pleasing patterns are chosen to reproduce. This is not only fun, but can also be useful in certain models.
  • (Game Theory) Tragedy of the Commons? - In a classic paper from 1968, Garrett Hardin theorized that groups of people using a public resource (such as the water from a well or the fish from a lake), will inevitably overuse it until depletion. This essay has had huge policy impact, resulting primarily in wide-spread privatization (even though Hardin is negative to privatization in the essay). Later work, for which she was given the so-called "Nobel prize" in economics, by Elinor Ostrom shows that Hardin in many cases were wrong: people can under certain condition self-organize to manage a common pool resource. This is highly relevant for a large number of political and environmental issues.
  • Eco-systems - Eco-systems consist of numerous species interacting in a complex network. They eat each other, they affect each others habitats, etc. Introduction of new species, the extinction of old species or changing environmental factors (such as global warming) can affect the stability of such systems, possibly causing an unexpected collapse. But as even the interaction between only two species can be complex and have unexpected dynamics (as the famous Lotka-Volterra model shows), the interaction between hundreds or thousands of species in a complex web is highly difficult to analyze.

Other examples:

  • Complexity perspectives on cities
  • The human brain
  • The immune system
  • Cultural evolution
  • Development and regulatory networks
  • EvoDevo/DevoEvo, Niche Construction
  • Consciousness as an emergent phenomenon
  • The climate as a complex system
  • Complexity economics
  • Threshold effects in complex systems
  • Practical uses of cellular automata (e.g. encryption)
  • Complexity perspective on stock market dynamics


8. Student seminars from the 2016-2017 class (Back to top)

November 2, 2016 "Strong Artificial Intelligence"

PG A: Husam Abdulwahhab, Armin Azhirnian and Philipp Arndt


It has taken life on earth about 3.8 billion years to produce humans -- an intelligent species able to consciously solve complex tasks. Many researchers believe that this intelligence can be explained solely by the immense computational abilities of the human brain. With computational power of supercomputers having grown at rates of about 100% every two years throughout the last few decades, recent developments beg the question: will machines ever outsmart humans -- and what happens then?

The topic becomes a quite philosophical one, and gives rise to a multi-facetted discussion of what our future might look like. Could machines develop such things as a conscience, sentient or free will? If so, how could we test it, and which moral standards should apply when dealing with machines? Which threats may arise in the short and long term? How will the labor market cope with machines that become better workers than any human? Can we control AI agents that may ultimately become smarter than us? Does strong AI pose an existential threat to humanity? If so, how can we responsibly research AI in the future?

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November 9, 2016 "Creativity"

PG B: Jonathan Kammerland and Alexander Reinthal


Creativity is an important part of human intelligence. Novel acts can improve a situation or completely backfire like a joke falling flat. What qualifies as a creative act? How is it different from random behavior?

In our presentation we look at what constitutes a creative act and how it can be achieved by artificial intelligence.

We then look at some AIs that use creative elements. Can the decisions made by such AIs be called creative?

We invite you to discussion of how to evaluate creativity and the implications of automating this process.

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November 16, 2016 "Complexity in Financial Markets"

PG C: Mattias Patricks and Oskar Rödholm


Effective and well functioning financial markets is a cornerstone in every capitalist society. Since the early 1980s increased market integration and product innovation has made things ever more complex. In this presentation we take a look at complexity in financial markets and how to model it.

The presentation begins with a quick historical review of how simple bartering in pre-agricultural society grew into the world’s first stock market with opening of the Amsterdam Stock Exchange in 1602. What characterizes a financial market as a complex adaptive system? Three areas of complexity can be identified and a modern case study of a specific financial instrument is presented. Different approaches to model each level of complexity is suggested and demonstrated in an easy to follow non-technical way. We also provide many real life example of successful and less successful attempts to apply them. The presentation is ended with a open ended discussion with questions about today’s challenges and dilemmas with financial markets.

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November 23, 2016 "Applications of Deep Learning"

PG D: Henrik Arnelid, Yvonne Krumbeck and Robin S. Sigurdson


Research in artificial neural networks has improved a lot the past few years. Big companies like Google utilize deep learning algorithms for their services.

In the course of this presentation we would like to show some examples of applications where deep learning has been used to solve and improve existing system performance. We are going to cover three examples where deep learning algorithms have reached or even surpassed the human ability to solve certain tasks, like playing complex board games, language translating and optimizing dynamical systems with many parameters such as data-center cooling.

This will give a brief insight in different fields where deep learning networks are used and might inspire the research of utilization in other applications.

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November 30, 2016 "Self-organized criticality"

PG E: Marios Aspris, Michael Lagerstrand and Pierre Seez


Twenty five years ago, self organized criticality was a concept put forward by Per Bak and other scientists for describing complexity in systems. The basic model revolves around the avalanches occurring in the growing sand-pile, the distribution of which follow a power law. Since then, the model has been used in applications in other complex systems, such as biological evolution, forest fires, traffic networks etc. The interesting thing about these systems is that they can be said to be at the edge of chaos.

During our presentation, we will start by defining some important aspects of systems that demonstrate self organized criticality, such as the fact that they are dissipative and out of equilibrium. Then we will show how this applies to earthquakes, and finally, in neural systems in the brain. Can the concept be used to model earthquakes and give us useful information? Is self organized criticality a fundamental property of biological neural systems?

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December 7, 2016 "Fall of civilizations"

PG F: Björn Mattson, Arash Shahsavari and Ivar Josefsson


Since the first larger complex civilization was erected by mankind some thousands of years ago we have seen them come and go through history. We have all heard tales of how they fell. In this seminar we will discuss two different perspectives on what makes civilizations fall. Joseph Tainter argues that civilizations fall due rising complexity and cost of solving problems. Jared Diamonds view on the other hand is that they fall due to an inability to cooperate with nature. Historical examples of societal collapses are analysed from the two perspectives.

This analysis naturally raises the question of whether our current civilization is doomed to fall or if it stands a chance of surviving for a long time? Will our inability to live in harmony with our nature make long term survival on the earth impossible, or is the ever rising complexity of our society in itself an impossibility in the long run? We will analyze these types of questions from the viewpoint of both Joseph Tainter and Jared Diamond.

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December 14, 2016 "Evolutionary Computation"

PG G: Martin Baerveldt, Maximilian Leyman and Abhishek Srinivasan


In the last few decades there have been great developments within the field of Evolutionary Computation, where the algorithms used are based on the processes governing natural selection.

Not only can these algorithms be used to solve engineering problems. Research shows that they can also be used in areas which were long thought to be outside the domain of mathematics and science: subjectivity and personal preference. This is achieved by using human evaluators to evaluate the different solutions generated by the algorithm. The field dealing with these types of algorithms is known as Interactive Evolutionary Computation.

We will explore the benefits and drawbacks of this method. We will also look at how these methods have been applied to optimize systems according to one's own aesthetic tastes as well as help construct personalized products.

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January 19, 2017 "AI in healthcare"

PG H: Oscar Beronius, Lars Liberg and Jacob Steffenburg


Healthcare today is in heavy need of improvement. A larger global population together with longer life spans has lead to a personnel deficit within medicine, increasing treatment costs and decreasing individualized care.

Due to the large amounts of research and clinical data in medicine it is an area which is perfect for applications of AI-powered systems. An example of this is IBM’s Watson, which is able to diagnose cancer patients and provide treatment plans.

We will talk about recent progress of AI in healthcare by exploring different applications, as well as look at some challenges and future prospects of the subject, hoping to give a larger insight into the wide array of application areas of AIs and machine learning.

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January 26, 2017 "Machine learning and chronic diseases"

PG I: Alexander Bükk, Edvard Lindelöf and André Stén


As we all know, the field of applied data analysis and machine learning is on the rise. While typical applications so far has been in online retail and other interned-based services, greater availability to data from all sorts of sources paves the way for many new and exciting uses.

In this presentation, we discover some of the huge potential of machine learning as a tool in medicine. Specifically, we focus on three chronic conditions, namely Parkinson's Disease, Diabetes and Hashimoto's Disease, and see how emerging data analysis-tools can improve the life of sufferers in more than one way.

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February 2, 2017: "The Fermi Paradox"

PG J: Mathias Carlson, Magnus Lindström and Andres Suarez Madrigal


The Fermi Paradox is an apparent contradiction between the expectation of the existence of many highly advanced civilizations in the Universe and the lack of observation/contact with any of them. Many theories have been put forward as attempts to explain the discrepancy. In this presentation we will explain estimates for finding intelligent civilizations in the Galaxy and the main possible explanations to the paradox.

Are we alone in the Universe?

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February 9, 2017 "Weather forecasting"

PG K: Christoffer Dahlen, Axel Löf and Richard Sundqvist


For over a millennia mankind have tried to predict the weather. There is evidence that weather forecasting dates as far back as the babylonians which predicted weather from cloud patterns as well as astrology. In today's weather forecasting some of the world's most powerful supercomputers are used to solve partial differential equations that describes the time evolution of the atmosphere. Even with the increasing power of these supercomputers, the accuracy of the forecasts are limited to approximately 6 days. The main problem with producing accurate forecasts are due to the chaotic behaviour of the atmosphere.

In our presentation we introduce the most basic partial differential equations used to describe the atmosphere as well as the basic conceptual numerical approach used to solve the equations. We proceed by discussing how to reduce the inherent uncertainty remaining in numerical predictions by the use of statistical methods to gauge confidence in the forecasts. Lastly, we discuss the challenges and possible future developments in the field.

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February 23, 2017 "Complexity and modelling in botany"

PG L: Johan Ek, Kevin Larsson and Joakim Thorén


Botany is an often forgotten field of research, often thought of as something quite isolated from other science fields. In this presentation we will talk about why this isn’t true and how plants and other vegetation has a complex underlying structure that proves difficult to simulate.

We present the basic theory of Lindenmayer systems (L-systems) that was developed in the late 60’s by means to describe how the development in cells of plants works. An L-system is a type of formal grammar, or string-rewriting system, that goes well in hand with many features of plants such as branching structures, repeating patterns and self-similarity.

Because of this, L-systems and what is called turtle graphics can be combined to generate 3D models of plants for applications in for example computer games and animated movies. Lastly we will discuss other uses for L-systems and how botany in this sense can be the inspiration for work in other scientific fields.

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March 2, 2017 "Artificial intelligence in games"

PG M: Jonas Eriksson, Fredrik Mäkeläinen and Hampus Torén


We begin with a brief history of artificial intelligence in video games to see how it has evolved over the years.

Then we take a deeper dive into the fascinating world of RTS games to see how artificial intelligence is utilized in this genre. What problems are there for the AI to solve, and how does the best human players measure against their computer controlled counterpart.

If the AI can learn complex game concepts, can it later utilize this knowledge for something else? We present some thoughts and ongoing projects that investigate the possibilities of training AI in games to prepare it for real world tasks.

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March 9, 2017 "History of Machine Learning"

PG N: Eleftherios Filippakis, Tarun Nandakumar and Gabriel Wagner


For many of us machine Learning has become a very familiar term. Possibly the biggest buzzword of recent years in the compute world. To some it is the start of A.I. others just see it as the hot new tool. It's a broad term and encompasses quite a few methods, and no matter what you think machine learning is changing the IT landscape

We want to stop looking forward for a second and instead look at the origins of what we call machine learning. Travel back to 1950 when the computer was in its infancy and machine learning was just an idea. Then we jump forward in time, stopping at some of the major events that had an impact on the development of machine learning. Eventually coming back to the present and look at some of the implementations that are being used today.

There are often lessons to be learned from history, to know what is in store for the future of Machine learning there may be something to be learned from its past.

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March 22, 2017 "Complexity in social interactions"

PG O: Carl Fredriksson, Per Nilsson Lundberg and Elona Wallengren


Social complexity is defined by the number and types of interactions within a society. Understanding this concept can give us a better understanding of topics ranging from trends to causes of instability in society.

In this presentation, we take a look at the concept of social complexity and how it leads to other benefits. Starting from parrots and simple human societies, we discuss the role of social complexity in advancing a species and its connection to advanced cognitive skills. We then look at how social complexity has helped shape our society today and how recent technological advancements have affected the stability of this theory.

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March 29, 2017 "Natural Language Understanding "

PG P: Martin Fägerlind, Erik Nilsson and Dorian Valverde Baspineiro


Natural Language Understanding is one of the most important topics of research in the attempts to create a general AI. Early attempts to implement Natural Language Understanding in computers dates back more than 50 years and the research has come far, and many of us have some program using limited Natural Language Understanding in our phones.

In this presentation we will give a short overview of how it works, both in the human brain and in computers, as well as give a brief introduction to in what ways a computer can generate text with some actual meaning.

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April 5, 2017 "Autonomous vehicles"

PG Q: Siddhartha Kasaraneni, Linus Norström and Jeanette Warnborg


Autonomous vehicles are on the rise, with manufacturers like Tesla, Volvo and even Google working on autonomous cars and developments being made in an increasing ammount of fields.

In order to understand were we're coming from, this seminar will start with a history lesson and a short look on autonomous vehicles outside of cars. We'll then present some of the technology behind todays autonomous cars, and have a look at some current examples. Finally we'll take a look into what the future might bring for autonomous vehicles, and what dilemmas and consequences this future might bring with it.

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April 20, 2017 "Mating Systems"

PG R: Anders Hansson, Freddie Ogemark and Simon Westlund


One of most important building blocks for biological evolution is selection for reproduction for many species. The actual selection of mating partners is a complex system which depends on many variables including mating systems. There are many types of reproduction and mating systems, but this seminar will focus on sexual selection and the most common mating systems for species who undergo male-female reproduction. Can we understand why the selection strategies and mating systems used by humans and animals have emerged? Throughout the presentation we will explain important concepts of mating systems as well as provide relevant examples of where different mating systems and mating strategies occur in the world. We will then combine the different parts of the presentation to show how the selection of mates is a complex system.

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April 26, 2017 "What AIs Can't Do — Criticism Throughout History and Present Issues "

PG T: Jose Perez Hidalgo and Anton Älgmyr


Since the conception of AI and machine learning the field has been subject of critisism. Today it's still unclear what the main goal is: to create an intelligence on par with human intelligence or to create powerful tools that acts like a brain to perform difficult tasks and improve well-being in society.

We will discuss past criticism of humanlike intelligence and bring it into the light of current developments to see what is still applicable and what is deprecated.

We will also do a case study of current issues in AI and machine learning by considering two recent papers in which differences in perception between human vision and computer vision are highlighted.

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May 3, 2017 "Adaptation and Intelligence"

PG S: Daniel Hansson, Tirtha Rahaman and Rasmus Åkerlund


Evolution is the mechanism that has given rise to the diverse ecosystem that surrounds us, and over time, this process has resulted in a multitude of intelligent species. In this seminar we will discuss how the pressure to adapt has driven this development, and some of the shapes intelligence can take in different animals, and their limitations.

Next, we will see that intelligence is not restricted to being an individual property, but can also emerge as a collective property in a complex system comprised of many relatively simple individuals. This is exemplified in social insects, such as ants, and we will see a few examples of this in coordination, task partitioning and self-organizing building schemes. We subsequently discuss some models from literature, and how these models have inspired implementations of artificial swarm intelligence.

We finish the presentation with an outlook on how natural intelligence and the human created artificial intelligence evolve at different timescales, and what that might mean in the future.

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May 10, 2017 "Classifying music using quantitative measures on musical content "

PG U: Erik Kratz, Andreas Perme and Daniel Ödman


Today there is an abundance of music easily available thanks to services like Spotify, etc. One problem that arises for the user is to browse through this material to find the music that suits him/her best. In this presentation, we will describe proposed methods to solve this using the acoustic information in audio files. Music is built up by very simple parts but give rise to advanced patterns such as emotions in listeners. Can these patterns be predicted by analysing the basic features of a given song?

During the presentation we will:

  1. Define the basic framework of music: which components build up a music piece and which rules do they abide to?
  2. Introduce some ways of finding different quantitative measures of the musical content.
  3. Present some ideas on how to use these measures in applications to perform various tasks, such as automatic song suggestion based on user preferences.

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9. Guest lecures (Back to top)

November 29, 2016 "Resilience of Social-Ecological Systems"

Steven Lade, Stockholm Resilience Centre and Stockholm University

Time and Place:

10:00-11:45, Room VasaC


How do we solve the grand social and environmental challenges that face humanity today? `Resilience' is emerging as an approach that researchers and organisations (as large as the United Nations) use to understand and deal with these problems. Resilience thinking is based on a fundamentally complex adaptive system view of the world, together with an understanding that social and ecological systems are fundamentally intertwined.

In this lecture I provide a brief introduction to the resilience of social-ecological systems, and the cross-fertilisation between resilience and complex adaptive systems. First, local stability concepts of nonlinear dynamics are closely linked to the original, resistance to shock conception of resilience. Concepts such as the 'planetary boundaries' recognise that there exist basins of attraction beyond which sustainable human development may be difficult. Second, it is increasingly being recognised that appropriately modeling human behaviour is crucial to dealing with contemporary environmental challenges. Human behaviour needs to be appropriately modelled in settings where social and ecological relationships are contested and uncertain is highly challenging. Third, the understanding of resilience has expanded to include the ability of a system to adapt and transform in response to threats and challenges, which demands new modeling approaches such as adaptive networks. We will work through together some case studies from local to global scales.

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10. Student seminars from the 2015-2016 class (for your inspriation) (Back to top)

May 4, 2016 "The Complex Challenge of Traffic"



Simulation of traffic has been done for over 50 years, and has long been a crucial part of any new roading project. Recent increases in the amount of data we are able to collect and process have renewed interest in the field, improved the accuracy of our models, and facilitated modelling traffic as a complex system of individual agents.

We will talk about the importance to society of understanding traffic, and how it relates to complexity. Then we will outline some of the techniques used to simulate traffic flows. We will also give some examples of emergent behaviour in traffic networks, and finish up with an example of how complexity theory can solve some of the problems we have with traffic.

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April 27, 2016 "Artificial Creativity: The difference between man and machine"

PG U: Martin Henoch and Nils Carlsson


Creativity is something so fundamental for humans we seldom reflect on what it actually means. Even the actual definition of creativity is not set in stone, and has been the subject of a philosophical debate that's been going on since the Renaissance, and maybe earlier. And as AI and machines continue to develop, the ability or non-ability to be creative is possibly the last divider between humans and "true" AI. Ada Lovelace famously declared that no "analytical machine" would ever be able to create anything new, and "Lady Lovelace's objection" was included in Alan Turings paper Computing Machinery and intelligence.

In this seminar we'll discuss what creativity means, along with common objections to the idea of that an AI could be truly creative. And since pilosophical objections never stopped anyone from trying, the discussion nowadays isn't only purely theoretical. There have been several projects trying to achieve a creative AI, in fields varying from visual arts, poetry, music and even mathematics, which we will showcase and try to give a picture of their "creative" process.

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April 20, 2016 "The Brain as a Complex System"

PG T: Eduardo Sesma and Mahmod Nazari


It is no overstatement to voice that the human brain is a spectacular organ and a complex system yet to bring to light. It governs our thinking, problem solving and our behaviors. Continuously, it helps modulating critical aspects of our physiology, such as heart rate and breathing. This most complex structure in the known universe is the ultimate aim of neuroscientific enquiry to be understood further.

Not long ago, the studies of the brain relied either on looking at aggregation changes resulting from head injuries or on plotting oxygen and glucose consumption in the brain. Needless to say that, the results of such approaches had been too little that the new techniques such as network sciences have emerged and become more fashionable. But how to take advantage the most from the network science in the aim of the discovery of such a complex system?

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April 13, 2016 "Meteorology and Neural Networks"

PG S: Donal Scanlan, Victor Tengnäs and Richard Lan


From the dawn of civilization, humans have attempted to both control and predict the weather. While early people believed this could be achieved by rituals and mysticism, the limits of our capabilities were recognized by Lorentz and the birth of chaos theory in the 60’s. Since then, we have relied almost solely on computers to overcome the implications of a chaotic climate. Up to this point, numerical weather prediction (NWP) has been the staple of forecasting. With its evolution however, we have still been unable to fully encapsulate climatic complexities and the past few decades have not been without costly, and deadly, forecasting errors.

Currently, there has been significant scientific interest in employing neural networks, and hybrid NN and NWP models, as a possible way of providing more accurate forecasts. Furthermore, the importance of accurate forecasts is growing with the extremity and variability of weather events associated with climate change. In our presentation, we hope to trace the evolution of these methods and give a brief forecast of forecasting.

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March 23, 2016 "Group Dynamics"

PG Q: David Hansson, Konstantina Elmpasidou and Radenko Ristic


Understanding how groups develop and evolve has been the subject of studies by organizational behaviorists and researchers since early in the 20th century.

From early research, many models have been developed to explain what we can expect in typical group development. The application of CAS theory to Group Dynamics is relatively new. In the last decades, CAS theory has been suggested as a constructive way to view groups by researchers.

In our presentation we will cover the fundamentals of Group Dynamics and give some examples of social applications that have to do with the Group Dynamics theory and sub-theories.

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March 10, 2016 "Tragedy of the Commons"

PG R: Dennis Sångberg, Ludvig Vikström and Victor Nilsson


History shows us many examples of when independent agents acting rationally in their own interest while exploiting a shared resource has been able to deplete that shared resource in contrary to the common good.

In 1968 the ecologist Garret Hardin wrote an article on this subject naming the system collapse transition as the ‘tragedy of the commons’ and this is in our days the the most widespread name of systems exhibiting a phase transition that depletes a common resource.

There are many examples of systems where such events has occurred throughout history including ecological systems involving air, water or forests. But also in completely different topics such as information technology where email spam or subjective wikipedia article editing can be seen as a ’tragedy of the commons’. In our presentation we will cover some of these topics in depth and talk about the subjects history in science.

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March 3, 2016 "Complexity Economics"

PG P: Daniel Viknander, Karl Bäckström and Ulf Hjolman


For centuries, the global economy has generally been considered a static system in equilibrium. In recent years, the idea that it is more accurately modelled as a constantly evolving complex system, has gained more traction. These controversial ideas have become known as Complexity economics.

This new field generally consists of models based on individual profit-seeking agents, which can develop personal strategies, through e.g. evolutionary algorithms, and on occasion even make mistakes.

During the presentation, we will discuss features of this approach to economic modelling, as well as examples of some models that are commonly used. We will also discuss critique that has been raised towards this approach by prominent Economists.

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February 25, 2016 "Biologically Inspired Computing: Artificial Immune Systems"

PG N: Andreas Magnusson, Eirik Seljelid and Benjamin Waubert


For many years we have gained knowledge and inspiration from natural phenomena and mechanisms, and learned to adapt these into different areas to improve and optimize the outcome. One commonly known biological system of this sort is our immune system. It is a robust and very complex system which protects us from foreign pathogens. It does so through self-organization, without any central control, in a highly distributed fashion and is able to quickly adapt to never before encountered pathogens.

In addition it exhibits a distributed form of memory which enables it to identify previously encountered pathogens and react appropriately. All of these features have attracted the attention of engineers and computer scientist, who’re looking to mimic the underlying mechanisms and create new approaches to complex problems.

In artificial immune systems (AIS) the immune system is used as a metaphor due to its properties as self-organized, adaptive, highly distributed and most importantly: it has no central point of control. The idea of studying using artificial immune systems is not to model the immune system itself, but rather to make use of mechanisms that can be used to develop computational tools.

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February 11, 2016 "Consciousness & Integrated Information Theory"

PG L: Joel Thorstensson, Julia Reibring and Simon Nilsson


Throughout recorded history, consciousness has been one of the largest unanswered mysteries. Countless ancient philosophers and mystics have struggled with questions like “What is existence? “ and “How did we get here?”. In the 17th century philosopher René Descartes expressed the famous words “Cogito ergo sum” (I think therefore I am) and in the same century John Locke laid the foundations to the modern concept of consciousness. Most people today have an an intuitive understanding of what consciousness is. However, even if we conceptually understand what consciousness is, we still haven’t been able to pin down its essential properties. In recent times interest in consciousness has grown in the natural sciences. One framework intended to understand and explain consciousness which has gained traction is Integrated Information Theory (IIT). IIT is an attempt to characterize consciousness mathematically both in quantity and quality. By studying the complexity of mechanisms in systems formed out of phenomenological axioms, IIT is able to derive a measurement of consciousness. IIT is far from a fully developed theory though, and one of the major limits is that it takes a huge amount of modeling and computational power to calculate the level of consciousness for larger systems as our brain.

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February 4, 2016 "A New Kind of Science, is cellular automata the future of science?"

PG K: August von Hacht, Joakim Johansson and Simon Andersson


In the 17th century science went trough a revolution when a mathematical approach was introduced in multiple scientific areas. New ideas were formed of how rules based on mathematical equations could describe the natural world. Until today this has been a well-recognized truth in science, but will it last forever? A person who is critical to this idea is Stephen Wolfram. In his book A New Kind of Science he reveals the flaws of this approach and proposes a new kind of science based on more general rules that can be used by simple computer programs forming complex systems.

In our presentation we are going to bring up some of the ideas presented in A New Kind of Science. We are going to explain Wolframs criticism to traditional mathematical approach and compare it to his new ideas. Cellular Automata is a significant part of his ideas and we will describe this in general and Wolfram ideas in particular. We will also give example of areas where the new kind of science could be applied including fundamental physics and biology. The book and ideas of Wolfram has also been criticized among other scientist and we will try to describe and discuss this in the presentation.

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January 28, 2016 "Climate change as a complex system"

PG J: Barbara Schnitzer, Joakim Andersson and Viktor Wänerlöv


'Men argue, nature acts', Voltaire.

This sums up what we are facing today. Political leaders discuss a lot about the climate and what to do while the nature keeps on changing. In order to react we have to understand the mechanisms involved and develop and analyse models to come up with measures to prevent the negative consequences of these changes.

In this seminar we will give an introduction to climate change and the complexities involved with modelling it, as well as a short discussion of ethical problems that arise.

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January 21, 2016 "Machine Learning - An introduction"

PG I: Benjamin Lindberg, Jacob Nolkrantz and Rickard Johansson


Machine learning was defined in 1959 by Arthur Mitchel as a "Field of study that gives computers the ability to learn without being explicitly programmed". The field has exploded in the last years, mostly thanks to more computing power and more data that can be analyzed. Machine learning has now caught up with its' parent subject artificial intelligence and papers in the two subjects are now published at about the same rate. The interest in getting valuable information from large amount of data is bigger. An example of this is the big internet companies that want to categorize most of the internet users, to be able to personalize commercials. So now machine learning contains studies such as big data, also medical diagnosis, self-driving cars and hopefully, in the future, a path to general AI. This seminar hopes to mainly give a good introduction to Machine Learning and also dive into some specific examples..

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December 16, 2015 "Natural Language Processing"

PG G: Rebecka Jacobsson, Britta Thörnblom and Isac Boström


In the age of smart phones and deep neural networks, the field of natural language processing is developing faster than ever. Its relevance is continuously increasing as we rely more and more on machines to help us perform everyday tasks such as asking our phone to provide us with driving instructions or speaking with automated customer service to resolve issues with our tax returns. But how do we get machines to actually understand what we mean when we ask for the nearest pharmacy or tomorrow's weather? This seminar will discuss how an algorithm based on representing words as points in a high-dimensional vector space can lead to everything from improved translation services to automatic generation of clickbait headlines.

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December 9, 2015 "The Complex World of Fractals and their Place in Nature"

PG F: Calle Ekdahl, Rafal Piwowarczyk and Jonas Meinel


In the last decades fractals have gone from being something that was previously only used in abstract mathematics to having important real-world applications. Starting with Leibniz in 17th century we will trace the history of fractals up to today, through some of the canonical forms and familiar names. We will also explain where the name ”fractal” comes from. Then we will show how fractals appear in nature in the form of trees, broccoli and lightning as well as in other phenomenas. Finally we will show that fractals can be used to generate computer graphics for trees and mountains, among other applications of fractals in modern technology.

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December 2, 2015 "Deep Learning"

PG E: Carl Asplund, Victor Bäckman and Henrik Adolfsson


A reincarnation and re-branding of Artificial Neural Networks in to the field of Machine Learning. Why is it that the interest in these learning algorithms has risen again? What could big companies, like Google, achieve by using them?

Whatever the future holds for this field, its popularity has exploded and companies are trying their best to get on top of the wave. New applications are popping up at a fast pace, and these deep learning algorithms that were once considered science fiction are now becoming a part of our daily life.

In the next seminar, we will talk about how Google has implemented a large scale deep learning network and how deep learning is used in their applications.

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November 25, 2015 "Liguistics and Complex Systems"

PG D: Andreas Johansson, Gustavo Stolf Jeuken and Philip Rasko Nguyen



A topic as dull to us physicists, mathematicians and engineers as complex variable analysis is to a fiveyearold.

A subject as pointless as sitting on chair and watching sourdough rise. Blindfolded.

Or, is it?

We’ll introduce you to the Complex Adaptive Systems approach to linguistics and also present some other approaches that have been used to study languages throughout history. What similarities do languages share with other complex systems? How does language change how we perceive reality? How can the evolution of languages be understood from a CAS perspective?

These are some of the questions we’re going explore during our presentation “ Complex Systems and Linguistics ” this Wednesday! We hope to see you there!

Blindfolds are not provided.

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November 18, 2015 "Network Theory"

PG C: Andreas Falkovén, Evangelia Soultani and Oskar Lilja


How are social norms created? How can global outbreaks be triggered by very few adopters and why do people sometimes overestimate risky behaviours of their friends? Many real systems such as social systems, can be represented as networks where the elements of the system are nodes and interactions between elements are represented by links. Networks have become a crucial component of many complex systems and theoretical and computational network analysis allows us to gain valuable insights into numerous applications and make intelligent decisions.

The presentation aims to introduce you to the most important aspects of the theory of networks, show you how to model a real world system and discuss interesting effects and applications.

Ready to hear about networks? We would be happy to see you in our presentation "Network theory" this Wednesday!

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November 11, 2015 "Search and Rescue Robotics"

PG B: Amanda Nilsson, Erik Roos and Kristian Onsjö.


With the world growing smaller each day, the reports of natural disasters and terrorist attacks from around the world never seem to end. In each of these occasions there are people going through the rubble to try to find survivors and save them. With the development of robots the goal of search and rescue robotics is to develop robots that can assist in these kinds of situations. Being quite a new science, there are many problems that need to be dealt with.

The presentation means to discuss the problems faced today and how search and rescue robotics may work in the future. Challenges addressed in the presentation will be the task of navigating through complex environments, human-robot interaction at the operator side and efficient exploration.

If you’re interested in knowing how robots may one day save victims in disasters all around the world, come to our presentation “Search and Rescue Robotics” this Wednesday!

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November 4, 2015 "Chaos Theory and some of its applications"

PG: A: Albin Lorentszon, Timmy Forsberg


Mathematics and physics have for a long time analyzed systems with linear equations. Some models have worked perfectly for their purpose and some haven’t. For example, in cases like the weather and sea currents scientists found that their models couldn’t predict what would happen as time went on. In the middle of the 20th century a man named Edward Lorenz studied equations for vorticity and discovered a small change in the initial conditions made a huge change in the outcome of his model, and so chaos theory was born.

The presentation ”CHAOS THEORY AND SOME OF ITS APPLICATIONS” will introduce Chaos Theory and present two different applications of the field. By introducing chaotic maps like the Logistic map and the Lorenz map some key elements in the theory will be explained.

The two applications displays a wide range of what chaos theory can be used for. The first one is cryptography, where the aim is to find algorithms to encrypt messages that only can be read by the receiver. The second application is Neural Networks, relevant to the Complex Adaptive Systems master program.

Would you like to learn about cryptography, or perhaps what four-dimensional chaos sounds like, welcome to the lecture next Wednesday.

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11. Student seminars from the 2014-2015 class, for your inspiration (Back to top)


Shamit Bagchi

"Consciousness as Integrated Information"

Ivo Batkovic

"Unsupervised Evolutionary Art"

Milica Bijelovic

"Chaos - Making a new science"

Jens Carlsson

"Micro-simulation of disease spread"

Siamak Esmi Erkani


Oskar Fridell

"Matching Social and Ecological Systems in Complex Ocean Fisheries"

Johan Frisch

"Anticipating Critical Transitions"

Pontus Granström

"The Fractal Geometry of Nature"

Amrit Krishnan

"Rethinking Economics Using Complexity Theory"

Marcus Hägerstrand

"Predicting the Stock Market Using Twitter"

Mats Uddgård

"Watson - WatsonPaths"

Selvin Cephus Jayakumar

"Self-Programming Matter and Artificial Life"

Hjalmar Karlsson

"Cellular Automata Approaches to Biological Modeling"

Jared Karr

"Turing Tested"

Mattias Kjelltoft

"Fractal Terrain"

Fredrik Hoxell

"On the Role of Self-Organization in the Development of Individual and Collective Behaviour - How to Implement Advanced Behaviour in Robots"

Paul Lange

"Climate and Weather Simulation - Using Ensemble Methods to Predict Chaos"

Jonathan Larsson

"Models for simulating pedestrian behaviour and escape panic"

Olof Gustavsson


Laura Masaracchia

"Human Dynamics, From Small Group Interactions to Anthropology"

Björn Persson Mattson

"Honeybee Democracy - Consensus mechanisms in social insect societies"

Björnborg Nguyen

"Modeling vehicular traffic as a complex system"

Elin Romare

"Immunizing well-connected networks - why random immunization doesn't work"

Vitalii Iarko

"How I could be a millionaire - or - a bit about BitCoin"

Marcus Schmidt Birgersson

"Prediction and classification of cancer using artificial neural networks"

Niclas Ståhl

"Protein folding"

Alireza Tashivir

"Artificial Immune System inspired by Human Immune Systems"

Sebastian Hörl

"Modeling the dynamics of belief systems"

Nils Wireklint

"Fooling Neural Networks and adversarial examples"

Kristín Ólafsdóttir

"Rumor Spreading Model with Trust Mechanism in Complex Social Networks"

Peter Svensson

"Modeling Chemical Exposures"

Toby St. Clere Smithe

"Methods for a complex system: The neuroscience of visual object recognition"

Tomas Jacobsson


Kirill Blazhko


Kalle Hansson


Gustav Olsson



Published in Course page

The aim of the course is to give an introduction to fundamental concepts of game  theory and to explore the concept of rationality and a series of applications and extensions of game theory. We focus on the effects of individual rationality and also the aggregate behaviour between agents in a large population. What are general principles for rational action? How well does this describe human behavior in practice? 


The final content of the course can and will be influenced by the students attending it (i.e. other topics may be added to this list). Topics that were covered in last year’s version of the course include: 

Basic game-theoretic concepts, theory and principles of rational decision-making, backward induction and the rationality paradox, analysis of repeated interaction, tragedy of the commons, evolutionary game theory, public good games, agent-based models in economics, behavioural economics and the environment, bargaining theory and dynamic games. 

The course was developed by Kristian Lindgren and Erik Sterner following a request (from Erik and a few of his classmates) to Kristian, asking him if he could give a course in game theory. It was first given in 2010 and 2011. After a break and work on the course format the formal criteria for becomming an electable masters course was reached during 2013 and the course will be given starting autumn 2014 (Quarter 2).  

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