Percolation and growth

The models in this chapter provide a basis for both models of landscape pattern, and for diffusive spread through such landscapes. The underlying basis of all these models is percolation which partitions a space into either occupied or unoccupied sites either all at once, or sequentially according to some simple rule, to yield a wide variety of models of growth processes.

5.1 Site percolation

This model demonstrates site percolation and displays the largest and spanning clusters (if the latter exists).

5.2 The ant in the labyrinth

This is an implementation of the classic ant in the labyrinth problem, discussed in

5.3 Site percolation forest fire model

A simple site-percolation based model of a forest-fire (or any other contagious process).

5.4 The percolation backbone

This model demonstrates the identification of the backbone of a spanning cluster in site percolation. See

5.5 Invasion percolation

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

5.6 Invasion percolation drainage basin model

This model is an implementation of the drainage model presented in

5.7 Simple Eden growth model

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

5.8 Inverted Eden process

This model is an implementation of the simple inverse Eden process presented in

5.9 The Eden tree

This model is an implementation of an Eden tree growth process as discussed in

5.10 Eden ‘tip’ model

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

5.11 Williams-Bjerknes Eden growth model for abnormal cells

This model is an implementation of the process described in

5.12 Eden growth a linear invasion front

This model draws on ideas discussed in

5.13 Eden epidemic process

This model simulates an Eden epidemic process as described in

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

5.15 Eden spread on 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…

5.16 Diffusion limited aggregation (DLA)

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

5.17 Neutral landscape generation by percolation processes

This model implements a number of different percolation-based neutral landscapes.

5.18 The SIMMAP neutral landscape model

This model implements the SIMMAP process for generation of neutral landscapes as described in

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…

5.20 Forest fire model with age-related flammability

This model is a forest fire model where the flammability of sites changes with the time elapsed since the site last burned. The focus of this model is on the relationship…

5.21 Stark model of gullying

This model is an approximate implementation of the model described in