Ten evening sessions on the mechanisms of pattern formation in Nature, running from January to March 2013 as part of the open studies programme at Edinburgh University.

Course Information

Why do trees look like trees and snowflakes like snowflakes? How do termites build elaborate structures without supervision? What can boiling porridge tell us about clouds? This fully illustrated course explains how patterns in nature can form through self-organisation, using examples and methods from a variety of scientific disciplines. Suitable for anyone who’s ever wondered about the astonishing complexity of nature, you’ll never look at the world in quite the same way again.


  • Tutor: Stephan Matthiesen
  • Mondays from 14 January 2013 (10 Classes) 18:30 - 20:30
  • Turing Room, 15 Buccleuch Place, at the Office for Lifelong Learning, The University of Edinburgh
  • Course fee: £85.00/£56.00 conc. - please register at the Office for Lifelong Learning or online through the Course Information Page
  • Course code: S217 - Course details

Course contents

14 Jan 2013: Introduction

A tour through patterns in nature, outlining and structuring the topic, and brainstorming: which patterns have students observed in nature?

Presentation: PDF (low resolution, 2.5MB) or PDF (high resolution, 10.9MB)

21 Jan. 2013: Waves and oscillations

We look at waves in the ocean, the atmosphere (cloud patterns!) etc., and why our heart beats.

Presentation: PDF (low resolution, 1.1MB) or PDF (high resolution, 12.2MB)


Additional reading:

  • Cartwright, J. H. E., Nakamura, H. (2009). What kind of a wave is Hokusai's Great wave off Kanagawa? Notes and Records of the Royal Society 63 (2), 119-135. URL http://dx.doi.org/10.1098/rsnr.2007.0039


The Creeping Garden: A documentary about slime moulds and slime mould research is currently in production. The trailer was released on 29. January and is available online: Taster for Creeping Garden (Vimeo).

28 Jan. 2013: Regularity and chaos

Using examples like population cycles or climate fluctuations, we introduce concepts like the logistic equation, bifurcations and attractors.

Presentation: PDF (low resolution, 437kB) or PDF (high resolution, 2.7MB)

Modelling chaos in a spreadsheet:

  • Download the Logistic map spreadsheet (you need a spreadsheet programme like MS Excel, OpenOffice or LibreOffice to open it on your computer)
  • Vary the parameters in the yellow boxes (r and initial value), see presentation for details

Additional Reading:

4 Feb. 2013: Animal swarming and collective behaviour

How fish swarms communicate and how social insects cooperate.

Presentation: PDF (low resolution, 576kB) or PDF (high resolution, 3.7MB)


Additional Reading:

  • Krause, J., Ruxton, G. D., Krause, S., (2010). Swarm intelligence in animals and humans. Trends in Ecology & Evolution 25 (1), 28-34. URL http://dx.doi.org/10.1016/j.tree.2009.06.016 (behind paywall)
  • Katsikopoulos, K. V., King, A. J. (2010). Swarm Intelligence in Animal Groups: When Can a Collective Out-Perform an Expert? PLoS ONE 5 (11), e15505+. URL http://dx.doi.org/10.1371/journal.pone.0015505
  • Kastberger, G., Schmelzer, E., & Kranner, I. (2008). Social waves in giant honeybees repel hornets. PLoS ONE, 3(9), e3141. URL http://dx.doi.org/10.1371/journal.pone.0003141
  • Ballerini, M., Cabibbo, N., Candelier, R., Cavagna, A., Cisbani, E., & Giardina, I., et al. (2008). Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proceedings of the National Academy of Sciences, 105(4), 1232–1237. URL http://dx.doi.org/10.1073/pnas.0711437105

11 Feb. 2013: Spatial patterns

Cracks in mud, paint, soil patterns in Arctic soils, and similar topics.

Presentation: PDF (low resolution, 1.7MB) or PDF (high resolution, 17.3MB)

Videos and material:

Additional literature: 

  • Rietkerk, Max; van de Koppel, Johan (2008): Regular pattern formation in real ecosystems. Trends in Ecology & Evolution, 23(3), 169–175. DOI: 10.1016/j.tree.2007.10.013
  • Economou, Andrew D; Ohazama, Atsushi; Porntaveetus, Thantrira; Sharpe, Paul T; Kondo, Shigeru; Basson, M Albert; Gritli-Linde, Amel; Cobourne, Martyn T; Green, Jeremy B A (2012): Periodic stripe formation by a Turing mechanism operating at growth zones in the mammalian palate. Nature Genetics, 44(3), 348–351. DOI: 10.1038/ng.1090. (Note that this paper is quite incomprehensible if you're not a developmental biologist; I added it here mainly to show some recent research which indicates the importance of the Turing mechanism).

18 Feb. 2013: Aggregation and growth processes

Crystals, snowflakes, lichen, sunflowers: Find the Fibonacci sequence and the Golden Number in a plastic pineapple!

Presentation: PDF (low resolution, 1.3MB) or PDF (high resolution, 12.8MB)

25 Feb. 2013: Cellular automata and some other topics

How some patterns can be modelled/described by simple discrete models, with applications to the shell of snails.

Presentation: PDF (low resolution, 506kB) or PDF (high resolution, 4.0MB)

Additional Material:

  • Mirek's Cellebration: Online Java applet and downloadable Java programme for running cellular automata

4 Mar. 2013: Fractals

Leaves, trees, river systems and other fractal systems.

Presentation: PDF (low resolution, 1.3MB) or PDF (high resolution, 22MB)

11 Mar. 2013: Perception and related topics

(Human) perception of randomness and patterns.

Presentation: PDF (low resolution, 1.0MB) or PDF (high resolution, 7.9MB)

Additional Material:

  • Cecilia Burman: Face blindness explained with stones. Original site no longer available, but there is an archived version.

18 Mar. 2013: Summary and Discussions

Patterns, self-organization and emergence.

Presentation: PDF (low resolution, 1.0MB) or PDF (high resolution, 17.8MB)

Additional Material:

25 Mar. 2013: Additional session

This is an additional, optional session where we can recapitulate some of the topics again.