1. Recent updates
  2. Course description
  3. Schedule
  4. Problem sets
  5. Exams
  6. Links


1. Recent updates

This course is replaced by two courses starting spring 2017:  Intelligent agents and Autonomous robots. Intelligent agents home page: http://www.me.chalmers.se/~mwahde/courses/ia/2017/ia.html


2. Course description

Course specific prerequisites

Basic mathematical and programming skills are required. It is an advantage, but not absolutely necessary, to be familiar with Matlab. Some background concerning microcontrollers is advantageous, but not a requirement.


The course aims at giving the students an understanding of design principles for autonomous systems, both robots and software agens, and also gives students the opportunity to apply their knowledge in practice through the construction of a simple autonomous robot.

Learning outcome (after completion of this course, the student should be able to)

After successfully completing the course, the student will be able to:

- Understand and describe basic properties of robotic hardware, including sensors, actuators and microcontrollers.
- Describe the basics of animal behavior (ethology) and its connection to robotic behaviors.
- Understand the basics of behavior-based robotics and evolutionary robotics.
- Set up and use basic kinematic and dynamic equations for robot motion.
- Define and set up computer simulations of wheeled autonomous robots (using a simulator provided by the lecturer).
- Define and set up evolutionary simulations for the optimization of robotic control systems (using a simulator provided by the lecturer).
- Understand and apply basic methods for behavior generation and behavior selection in autonomous robots.
- Understand the basics of utility theory and its application in robotic behavior selection.
- Understand and describe the basics of swarm intelligence and agent-based economics.
- Construct and use a simple autonomous robot.


The contents of the course are as follows:

- Theory of autonomous robots: Kinematics and dynamics
- Behavior-based robotics
- Evolutionary robotics
- Utility theory, behavioral economics, theory of rational decision-making
- Behavior selection in autonomous robots
- Artificial life and swarm intelligence
- Software agents, particularly agent-based economics
- Learning in autonomous agents
- Robot construction


The course extends over two quarters. In the first part of the course, the theory is covered in 14 lectures. In the second part, a robot construction project is carried out (in groups of 5-6 students). In the final weeks of the course, the constructed robots are applied in a variety of simple tasks.


Lecture notes and handouts


The robot construction project is graded and corresponds to around 30% of the grade. 40% of the grade is determined based on the results of two home problems, and the remaining 30% are determined by the results on a written exam (at the end of the first half of the course).

3. Schedule

Please have a look on the external course webpage for more information.

4. Problem sets

Please have a look on the external course webpage for more information.

5. Exams

Please have a look on the external course webpage for more information.

6. Links

External course webpage: http://www.me.chalmers.se/~mwahde/courses/aa/2014/aa.html

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


  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.

S. Sigurdson, Robin This email address is being protected from spambots. You need JavaScript enabled to view it.
Srinivasan, Abhishek This email address is being protected from spambots. You need JavaScript enabled to view it.
Wallengren, Elona This email address is being protected from spambots. You need JavaScript enabled to view it.
Suarez Madrigal, Andres This email address is being protected from spambots. You need JavaScript enabled to view it.

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?

Watch slides

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.

Watch slides

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.

Watch slides

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.

Watch slides

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?

Watch slides

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.

Watch slides

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.

Watch slides

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.

Watch slides

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.

Watch slides

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.

Watch slides


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.

Watch slides


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.

Watch slides


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.

Watch slides

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 this course is to give an understanding of fundamental concepts used to describe complex systems. As examples, chaotic low-dimensional systems, self-organizing systems, and cellular automata are discussed.

The fact that systems composed of a large number of simple components can exhibit complex phenomena is exemplified in, for example, self-organising systems (in the form of chemical reaction-diffusion systems), the second law of thermodynamics (as a statistical result of large physical systems), neural networks, evolution of cooperation, cellular automata (as an example of an abstract computational class of systems), economic systems of interacting trading agents, urban growth and traffic systems.

There is no universal definition of a complex system, but there are several features that are usually brought up when a system is considered complex, typically involving order/disorder and correlations. An important scientific question is whether these and other characteristics of the systems can be quantified in a comprehensive way. This is one of the aims with this course -- to provide a set of tools that can be used to give a quantitative description of a complex system for a variety of different types of systems. All quantities derived can be interpreted in terms of information, referring to the information quantity introduced by Shannon and Weaver.

Information-theoretic concepts can be applied on the macro-level of a system, for example, in order to describe the spatial structure formed in a chemical self-organizing system. The connection between information theory and statistical mechanics makes it possible to relate such an analysis to the thermodynamic properties and limitations of the system. Other examples include complex phenomena in cellular automata, entropy in microscopic physical systems (spin systems), and chaotic behaviour in dynamical systems.

Student portal page: http://www.student.chalmers.se/sp/course?course_id=14967

Course page: 

Published in Courses
  1. News
  2. Course information (overview, literature, teachers)
  3. Schedule and lecture plan
  4. Problem sessions and solutions
  5. Homework
  6. Projects
  7. Exam, grading
  8. Exams with solutions


14 January 2020

The course starts with an introduction and a first lecture on Monday, 20 January, at 15.15 in MC.

The schedule is available in TimeEdit.

Before the course start, the new home page will be available in Canvas.

The information below is from previous year, but it contains the important information on course content and structure.


Old Information:

12 April 2019

Solution sketches for this year's exam 2019-03-22 are available here.

The exams have been corrected, but there will be a delay until they show up in Ladok. Sorry for that!


3 April 2019

Two open PhD student positions in Complex systems are announced (as part of a broader call for applications), see:

Two PhD student positions in Energy, Environment & Complex Systems


13 March 2019

Solutions to exam 2016-03-18 are now included in the zip file with old exams below.

20 February 2019

The following course representatives have accepted: Fanny, Gabriella, Henrik, and Wilhelm. We had a short meeting, and a request that was brought up is that I post PDFs of slides that I use in the lectures. So, as a start, I provide the slides of today's lecture in the following summary.   

In the lecture today, we discussed an Ising dynamics model (microscopically reversible and energy conserving) and how the approach to equilibrium can be understood. The slides are available here, and for further reading you may download the paper "The approach towards equilibrium in an Ising dynamics model".

18 February 2019

The solution to problem 5.8 in the PDF below is updated with a minor addition regarding the criterion for the parameter α.

11 February 2019

Note that the exam is on Friday, March 22, in the afternoon. (Previously, the last year's date was posted.)

2 February 2019

In the third week we will bring up the 100 Floors Egg Dropping Puzzle. Thinking about coding may guide you to a solution of this problem.

1 February 2019

We have posted a preliminary list of problems to be solved in the problem sessions below.

27 January 2019

The second week we will introduce information theory for symbol sequences, which will serve as a key theoretical basis for several applications throughout the course.

An interesting problem will be discussed on Wednesday: The Monks Spots Puzzle. Try to solve that. Consider also the situation in an information perspective (which is indeed very tricky).

21 January 2019

The course starts with an introductory lecture on Monday 21 January at 15.15 in MC.

All necessary information about the course is available below, including link to TimeEdit that contains the schedule, the lecture plan, the lecture nores in pdf, etc.

You may think about the balance problem puzzle that will be discussed in the first week.


General course information (overview, literature, teachers)


The course provides an understanding of fundamental concepts used to describe complex systems, in particular dynamical systems such as chaotic low-dimensional systems, self-organizing systems, and simple spatially extended systems such as cellular automata. Many of the concepts are based in information theory.

  • Basic concepts of information theory: Shannon entropy, complexity measures.
  • Information theory and statistical mechanics.
  • Geometric information theory -- randomness and complexity in spatially extended systems.
  • Information flow. The relation between microscopic and macroscopic levels.
  • Statistical models, in particular hidden Markov models.
  • Cellular automata.
  • Applications in nonlinear dynamics, computational biology, chemical self-organizing systems, and statistical mechanics.


The lectures will follow the presentation in:
K. Lindgren, Information theory for complex systems — An information perspective on complexity in dynamical systems, physics, and chemistry. (Chalmers, 2014.)

If you want to learn more: T. M. Cover and J. A. Thomas, Elements of information theory (Wiley, 1991).

See also: David MacKay, Information theory, Inference, and Learning (2003).


Kristian Lindgren (lecturer, examiner). Email: kristian.lindgren [at] chalmers.se

Susanne Pettersson (examples classes, projects) Email: susannep [at] chalmers.se

Rasmus Einarsson (examples classes, projects) Email: rasmus.einarsson [at] chalmers.se

Schedule and lecture plan

The schedule is in TimeEdit.

Further details are given the lecture plan (pdf).

Problem sessions and solutions

Preliminary list of problems to be solved in the problem sessions

  • 25 January: 2.2, 2.4, 2.6, 2.8, 2.9, 2.16
  • 1 February: 3.2, 3.3, 3.5, 3.7, 3.8 (possibly leaving one or two for the next session)
  • 13 and 15 February: 4.1, 4.2, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9
  • 22 February: 5.1, 5.2, 5.3, 5.4, 5.6, 5.8
  • 6 March: 8.1, 8.2, 8.7
  • 13 March: solving an old exam (which one to be determined)



Five optional homework problems are given below. Each one gives up to two (2) extra points for the exam. Late submissions will normally not be graded. Hand-written solutions are fine, but please take care to make them legible.

Hand in your solutions in one of these ways:

  • on paper at the lecture
  • by email as a PDF file named yourcid.pdf (e.g., rasmuse.pdf) to Rasmus (address: rasmus.einarsson [at] chalmers.se)

The deadlines are:

  • Homework 1: Friday 1 February 2019, 13.15
  • Homework 2: Friday 15 February 2019, 13.15
  • Homework 3: Friday 22 February 2019, 13.15
  • Homework 4: Wednesday 6 March 2019 10.00
  • Homework 5: Wednesday 13 March 2019 10.00



Optional project work can be done in groups of 1-3 students. The project work is awarded up to 10 extra points for the exam. Further instructions are given in this file:

Project ideas and instructions for projects (pdf)

Exam, grading

The exam is given on March 22, afternoon. A sheet with relevant equations etc is attached to the exam problems.

The course is graded based on the exam score including extra points from homework (max 10 points) and projects (max 10 points). The exam gives up to 50p. Grade limits (Chalmers/ECTS): 25p for 3/E, 28p for 3/D, 34p for 4/C, 38p for 4/B, 42p for 5/A. To pass, a minimum of 20p on the written exam is required, regardless of additional points.

Exams and solutions

Old exams, some of them with solutions (zip file with pdfs, about 19 MB) [updated 13 March 2010]

Exam 2018-03-16 problems (pdf) and solutions (pdf)

Published in Course page
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