Re: Cellular Automata vs. Agent-Based Models

[jalex]

address@hidden writes:

> 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.

It strikes me that whether IBM's are CA's or whether CA's are a
subclass of IBM's depends entirely on how we formalize these two
notions.  
 
> 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, 

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.

Obviously any implementation of an IBM will be equivalent to some
suitably complicated CA, but I'm not sure what this gains us.  If I
had to prove a theorem about an IBM like the one described above, my
first inclination probably wouldn't be to treat it as a CA since I
suspect that assuming the agents live in a continuous space makes it
much more amenable to analysis.  Yet since this misrepresents the
number of possible states, I would be concerned about how this
assumption could lead one astray.

Cheers,

Jason Alexander
Logic & Philosophy of Science
University of California, Irvine



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