Re: Cellular Automata vs. Agent-Based Models

[gross]

Jason Alexander writes:
> 
> Really?  Suppose I want to compare a spatial IBM containing 100 agents
> in Euclidean 2-space (say, in the rectangular region R between (0,0)
> and (10,10)) and a 10x10 CA.  Take a state to be a function mapping
> the set of agents into the underlying set.  Since CAs are based on
> discrete lattices, there are only finitely many states for the CA
> whereas, for the IBM, if we seriously allow R to be a subregion of the
> plane there are infinitely many states.
> 
This is reasonable if indeed we could do any analysis at all on the 
underlying continuous 2-d agent model. The only way I know to do this 
(perhaps I'm just ignorant - anyone know of another way?) is to look at 
some pde approximation for the 100 agent model. If you aren't doing 
analysis, then you have to discretize anyway on finite machines. Then 
the question is what is the appropriate spatial resolution for
the problem, based upon whatever data limitations you have, set 
the spatial resolution at that, and use that as an underlying CA grid.
Of course, a 10x10 may not be sufficient, but handling grids many
orders higher are no problem these days for simple CA's. This is
not to say that CA's are useful, but rather to point out that I think
the difficulty in translating a spatial agent model to a CA that is
usable and saves us something is not because agent models can live in
continuous space. Rather the large potential state space for an individual 
agent makes the local CA state space far too complex. 

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)


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