Category Archives: aggregation

5.16 diffusion-limited aggregation (DLA)

This is an implementation of an on-lattice (i.e. grid-based) diffusion-limited aggregation process. See

Witten TA and Sander LM 1981 Diffusion-limited aggregation, a kinetic critical phenomenon. Physical Review Letters, 47, 1400–1403.

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

5.14 Benguigui’s Eden process based model of urban growth

This model simulates a version of Benguigui’s highly abstract model of urban growth, as discussed in

Benguigui L 1995 A new aggregation model. Application to town growth. Physica A: Statistical Mechanics and its Applications, 219, 13–26.
Benguigui L 1998 Aggregation models for town growth. Philosophical Magazine Part B, 77, 1269–1275.

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

4.7 flocking

A flocking model loosely based on ideas in

Czirók A and Vicsek T 2000 Collective behavior of interacting self-propelled particles. Physica A: Statistical Mechanics and its Applications, 281, 17–29.
Grégoire G, Chaté H and Tu Y 2003 Moving and staying together without a leader. Physica D: Nonlinear Phenomena, 181, 157–170.
Vicsek T, Czirók, A. A, Ben-Jacob E, Cohen I and Sochet O 1995 Novel type of phase transition in a system of self-driven particles. Physical Review Letters, 75, 1226–1229.

This model also includes various different implementations of the idea of ‘flock-mates’ which demonstrate the importance of basic spatial properties (in this case proximity or ‘neighbourhood’) in many spatial models.

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

4.2 demonstration of the correlation length effect in random walks

This model demonstrates how a correlated random walk, when consecutive steps are aggregated, reverts to a simple random walk without correlation but with a longer mean step length. This effect means that correlated random walks are ultimately diffusive (not super-diffusive) like simple random walks.

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.

3.10 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.

3.6 grass – bush – trees IPS succession model

This model is an implementation of the simple grass – bush – trees model of

Durrett R and Swindle G 1991 Are there bushes in a forest?. Stochastic Processes and their Applications, 37, 19–31.

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

3.5 Competing contact processes

This is an implementation of competing contact processes in two dimensions, including an option for one of the processes to spread over long distances. Models of this kind are discussed in

Durrett R and Levin SA 1994b Stochastic spatial models: a user’s guide to ecological applications. Philosophical Transactions of the Royal Society of London. Series B. 343, 329-350.

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