Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
1D CAs are used for some real world models, notably simple models of traffic and traffic jams. The simplest example of this is elementary CA rule 84, which shows density-dependent congestion effects, which propogate backward to the direction of motion in a realistic way, eventually sorting out to allow all "particles" to move at their allowed speed to the right. Y
ou can start from that situation (deterministic, only 2 colors) and add additional realistic bits (varying speeds, probabilities, etc) to get reasonable models of the effects of congestion on traffic patterns.
There are also plenty of simple physical problems that contain enough symmetries or simplifications that they can effectively be modeled in a reduced number of dimensions. Diffusion can be modeled in 1D for instance, using a gray level to track a local concentration.
There are many more applications in 2D, including fluid flow models, models of drainage over a surface (with a field of values at each location effectively measuring a third dimension, but not requiring that to extend off the surface), grain boundaries (surface tension effects), terrain and ecological models, etc.
I hope this helps.
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