Category Archives: growth

5.19 the ‘sand-pile’ forest fire model

This model is an implementation of a simple forest fire model with a primary focus on the size distribution of the fires that are produced. It is based on the model described in

Bak P and Chen K 1990 A forest-fire model and some thoughts on turbulence. Physics Letters A, 147, 297–300.

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.

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.

5.12 Eden growth along a linear invasion front

This model draws on ideas discussed in

Edwards SF and Wilkinson DR 1982 The surface statistics of a granular aggregate. Proceedings of the Royal Society of London. Series A, 381(1780), 17-31.

and allows you to explore the rate of progress made by an Eden invasion process advancing along a linear ‘front’.

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.

5.11 the Williams-Bjerknes Eden growth process model for spread of ‘abnormal’ cells

This model is an implementation of the process described in

Williams T and Bjerknes R 1972 Stochastic model for abnormal clone spread through epithelial basal layer. Nature, 236, 19–21.

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.

5.10 Eden ‘tip’ model

This model is an implementation of the Eden ‘tip’ growth process described in

Sawada Y, Ohta S, Yamazaki M and Honjo H 1982 Self-similarity and a phase-transition-like behavior of a random growing structure governed by a nonequilibrium parameter. Physics Review A, 26, 3557-3563.

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.

5.7 simple Eden growth model

This model is an implementation of the basic Eden growth process as originally presented in

Eden M 1961 A two-dimensional growth process, 4th Berkeley Symposium on Mathematical Statistics and Probability, pp. 223–239, University of California Press, Berkeley, CA.

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.