Category Archives: diffusion

8.1 leGUME (the Grand Unified Model of Everything)

This is the model presented in Chapter 8 of the book, which combines elements from many of the building-block models discussed in earlier chapters.

You can see a fairly typical example of long-term survival of the island colonisers in the video.

Details of the model are in Chapter 8 and additional information not included in the Chapter can be found here.

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

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.

5.15 Eden spread from a linear front with long-distance dispersal (LDD)

This model shows how Eden spread along a front is dramatically altered by the occurrence of even relatively rare long-distance jumps. The behaviour of this model should be compared with that of the same model without such jumps.

An alternative version of the model is available, which makes use of the netlogo R extension.

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.

4.2 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.

4.1 random walks

This model implements a number of variations on the random walk including the lattice-based walk, the simple random walk, walks with different distributions of step lengths, and correlated (direction) random walks.

Two variants are shown in the videos to the right: a simple random walk, and a directionally correlated random walk.

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.

3.9 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.