Environmental Engineering Reference
In-Depth Information
Fig. 8.5 The pattern on a triangular grid (three neighbours to each cell) was obtained by applying
the following rules: The initial configuration is a random distribution. If the state of the majority of
the neighbours differs from the focal cell's state, it has a 50% probability to change to the state of
its neighbours. After a number of iterations, the pattern reaches a stable state, where each cell's
state conforms to the majority of its neighbours. Shown are the iterations 0, 2, 5, 8, 11, and 14
(Fig.
8.6
). Comins et al. (1992) used a cellular automaton employing deterministic
rules to explore the spatial dynamics of a host-parasitoid interaction resulting in
spiralling spatial patterns.
Diffusion-Limited Aggregation
Diffusion-limited aggregation is a process that can be observed in the successive
growth of river systems, in certain forms of organic growth, involving branching,
and in some inorganic immobilization processes. Again, the basic underlying rules
are relatively simple. Cells can be in three types of states, which can be called
“empty”, “mobile” and “fixed”. A “mobile” cell shifts the state of any (randomly
chosen) “empty” neighbouring cell into “mobile”, while turning back to an
“empty” state. This simulates random movement of a particle across the grid. If
a cell is in the state “mobile” and has a cell with the state “fixed” in its neighbour-
hood, the “mobile” cell changes its state to “fixed” and remains in this state for the
rest of the simulation, regardless of the states of neighbouring cells. To obtain
non-trivial results, it is required that a sufficiently large number of “mobile” cells
