Re: Formalization of the Artificial Life Systems

[Catherine Dibble]

> For those who aren't familiar with it,
>(from Mumford),
>
>"Pattern theory aims at constructing knowledge representations of complex
>systems using an algebraic foundation that describes typical pattern
>structures in terms of their compositions (configuratin spaces) and
>invariances (similarity groups).  To represent the variability of the
>patterns probability measures are defined on the resulting image algebras."
>
>It turns out to be a nice framework to implement a complex adaptive system.
>The image algebras in question are actually partition quotient groups
>defined on equivalence relation identification rules.  For those who know
>about pattern theory SFI just released a paper, "Complexity of
>Two-Dimensional Patterns", by Lindgren, Morre and Nordahl.  For those who
>want to know more, you might try the book, "Elements of Pattern Theory", by
>Ulf Grenander, Johns Hopkins University Press, 1996.  


Greetings Kerry,

I too have been working with Grenander's Pattern Theory as part of my
dissertation work on formalizing my Swarm models and characterizing/
generalizing  Swarm simulation results (re computational laboratories as
a general complement to theory).  I'm just beginning to work through
the Lindgren/Moore/Nordahl paper (thanks for that pointer, I hadn't seen
it yet).  I loved your Mumford quote, that is, of course, exactly the point of 
all this!  But I am not familiar with this Mumford source -- reference?

May I ask you more about your formalization work?  This has been a
central interest of mine, but I didn't find quite as much discussion of
this at SwarmFest as I'd hoped.  I am of course thrilled to see both
swarm-modelling (finally) and especially this recent thread.  In addition
to Mumford, I am especially curious about further references on partition
quotient groups, since I've been emphasizing the central importance of
group theory and equivalence classes and detection / identification / 
characterization thereof, but partition quotient is a modifier new to me 
and perhaps exactly the missing piece I've been seeking.

best regards,

Catherine

*----------------------------------------------------------------*
| "Topsight---an understanding of the big picture---is ...       |
|  the most precious intellectual commodity known to man. ...    |
|  It is *the* quality that distinguishes genius in any field."  |
|                                     -- David Gelernter (1992)  |
|----------------------------------------------------------------|
|  Catherine Dibble              http://www.geog.ucsb.edu/~cath  |
*----------------------------------------------------------------*




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