Category Archives: spread

5.5 invasion percolation

This model demonstrates invasion percolation in a landscape with randomly assigned resistance values.

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.

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.

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.