Category Archives: chapter 3

3.16 evolutionary spatial prisoners’ dilemma

This model demonstrates how different strategies in a two player game compete with one another in space, when players ‘evolve’ by changing their strategy to match successfully strategies either globally (the non-spatial case) or locally (the spatial case).

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.14 spots and stripes: a discrete reaction-diffusion model

This model implements the cellular automaton model described by

Young DA 1984 A local activator-inhibitor model of vertebrate skin patterns. Mathematical Biosciences, 72, 51–58.

which is itself a cellular automaton discretisation of Turing’s reaction-diffusion model of morphogenetics.

Turing AM 1952 The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London. Series B, 237, 37–72

The reaction-diffusion model is a fundamental process model across many scientific domains.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.13 centroidal Voronoi tessellation

The Voronoi tessellation is an ‘all at once’ subdivision of a landscape based on proximity to a set of generating points. Many possible iterative processes based on the Voronoi tessellation are possible. This model demonstrates one example, the centroidal Voronoi tessellation where successive generations of generating points are placed at the centroids of the previous generation of Voronoi tiles. See

Du Q, Faber V and Gunzburger M 1999 Centroidal Voronoi tessellations: applications and algorithms. SIAM Review, 41, 637–676.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.11 the Schelling model implemented as an interacting particle system

This model demonstrates how the Schelling model can be implemented as an interacting particle system exclusion process.

The video shows the emergence of segregated regions of different types (red and blue) separated by the vacant (grey) state.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.10 the Schelling model of segregation

This model is one possible implementation of Thomas Schelling’s simple model of residential segregation. This implementation shows how changing the criterion for how a household decides that a prospective new location is acceptable or not can change the overall outcome quite dramatically.  The original papers on this model are:

Schelling TC 1969 Models of segregation. American Economic Review. 59, 488–493.
Schelling TC 1971 Dynamic models of segregation. Journal of Mathematical Sociology. 1, 143–186.
Schelling TC 1978 Micromotives and Macrobehavior. Norton, New York.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.9 voter model with dispersal and mutation

This model implements a simple voter model with two non-local processes. One admits succession at a distance, while the other (mutation) allows the appearance of completely new states in the lattice.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.8 simple voter model

This model is an implementation of a simple voter model.

The video demonstrates how regions of each original class or type develop and persist.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.7 Simple rock – scissors – paper IPS model

This model is an implementation of a rock – scissors – paper succession model.

In the video you should be able to see how red invades yellow invades blue invades red, in a cyclic relationship.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.