Real-Space Cellular Automaton Models
In a vast majority of cases, a numerical model is a set of physical variables
(temperature, pressure, velocity, etc...) that are recalculated over
time according to some
predetermined rules or equations. Then, any point in space is entirely
characterized by a local set of parameters. This is not the case in
Real-Space Cellular Automaton Models where the only local variable is a
state-parameter that represent the different phases involved in the
An elementary cell is a cube of edge length l0
and pairs of nearest neighbour cells are called `doublet'. For each
individual physical process that we take into account, there is a set
of doublet transitions.
Each transition is associated with a rate parameter with units of
frequency that introduces into the model the characteristic time
scale of the corresponding physical mechanism. Doublets are all
supposed to be independent and the occurrence of a transition of
doublet is assumed to follow a stochastic process.
Using this approach we can model a wide range of physical-chemical or anthropological processes.
See applications in geosciences in Narteau et al. (2001)
and Narteau et al. (2009)
For example, we can study molecular diffusion in 2-D, with 2 states (Air =
; Molecule =
) and four transitions for the random motions
particules (see the animation