pattern theory

[David Sumpter]

Maybe I should read all the modelling messages before I comment on one.....

Dr. Christopher Landauer writes:
>i am very interested in hearing more about the styles of formalism 
>that pattern theory provides,
>and in the kinds of descriptions that are allowed -
>a formalism that only provides description is still useful,
>because the units of description become better understood
>and reasoning with them becomes easier,
>but a formalism that allows analysis is better,
>in my opinion
>(this turns out to be the same argument i made about ODEs and PDEs
>compared to ABMs a week or so ago)

This is exactly right. I think the key here is in what we are trying to 
formalise. Formalising the description of agent behaviour and environment and 
then expecting to be able to prove great and wonderous things about their 
behaviour when thrown together in a big simulation is beyond the scope of 
anything I could presently hope to do.

However, creating a differential equation model of some global behaviour of a 
Swarm simulation in a similar way to Mathematical biologists have always done 
for reality is an extremely useful formalism (I know this is probably a 
controversial view here). This formalism would allow analysis but it does 
suffer 
from the old problem of no longer being derived exactly from the agent 
descriptions.

Add me to the Mumford reference list too please!

David Sumpter,
Maths Depatment,
UMIST.


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