Re: Cellular Automata vs. Agent-Based Models

[gross]

Hi folks,
    Good discussion. In my lectures on individual-based models, I've
always argued that these are really CA's but typically with such a 
complex state structure that viewing them as CA's gains us nothing. 
The available theorems on CA's are pretty limited, dealing as they do 
mainly with stationary (long-term asymptotic) behavior in situations
with small state spaces. Certainly you can view any IBM that operates
in Euclidean n-space as a CA, but the state of a particular cell
then requires dynamic allocation (think of individuals dragging all
their state structure around, and the possibility of having large 
numbers of these in any particular CA cell) or enormous fixed-length
state vectors. This is in part the reason why the GIS people haven't
jumped on the dynamic modeling bandwagon - GIS approaches are 
inherently flat map with no easy way of dealing with dynamic local
allocation. A CA need not at all be restricted to Euclidean space
of course - after all these are just collections of finite state 
automata with some metric describing where these FSA are relative to 
each other, and rules for interaction between the FSA's. So the 
advantage of viewing an agent model as a CA is that the metric is 
inherently defined. For economic agents, it seems to me that there
is no inherent reason why such a metric, based upon nothing whatsoever
to do with physical space, cannot be defined. It just might be 
very difficult to come up with a reasonable one. 
    As for PDE's, there are now a number of people who are working very 
hard to find appropriate analytic analogs to IBMs. This offers some 
hope of developing general macrodescriptor systems that provide similar 
behaviors to complex models without their large data requirements. As a
theoretician, the possibility of finding these offers great appeal. As 
someone who has to deal with the reality of biological complexity 
coupled to unpredictable abiotic influences, I am often doubtful of
the practicality in application of such abstractions. 
    Cheers,
        Lou Gross
Professor of Ecology and Evolutionary Biology
    and Mathematics
Director, The Institute for Environmental Modeling
University of Tennessee - Knoxville
address@hidden
http://www.tiem.utk.edu/~gross/
http://atlss.org/ (ATLSS Project Home Page)
http://archives.math.utk.edu/mathbio/ (Math Archives for Life Sciences)


                  ==================================
   Swarm-Modelling is for discussion of Simulation and Modelling techniques
   esp. using Swarm.  For list administration needs (esp. [un]subscribing),
   please send a message to <address@hidden> with "help" in the
   body of the message.
                  ==================================