Re: When agents cross paths?

[Bohdan DURNOTA]

> 
> Hello group
> 
> Here is a question that I got thinking about today.
> 
> Imagine that you have a 2D (or anything-D) surface with things (agents)
> running around on it in a random fashion, such as the simpleSwarmBugs in
> the tutorial. Does anyone know of a way to find the expectation that
> 
> a) a particular point (cell) on a discretized surface would be trodden
> upon more than once, 
> 
> b) a particular point (cell) on a discretized surface would be trodden
> upon by one or more individuals, and
> 
> c) any two paths cross each other (discrete or continuous surface).
> 
> These would each obviously be a function of the density of individuals
> in the space and the amount of time that the simulation runs.  I am not
> sure of what other factors would be relevant yet.
> 
> Has anyone on this list had to deal with a formal description of this? 
> Could anyone point me to an article or textbook that discusses anything
> similar?
> 
> Any ideas would be appreciated.
> 
> -- 
> /**********************************************************************/
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> 
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> 
Paul,

You have brought up a topic I am working on right at the present
time. I am in the midst of completing a series of simulations,
as well as some theoretical work, of how the *visitation
surfaces* (the number of visits per lattice site) evolve over
time for some particular agent models man-environment
interactions.

This is analogous to a certain stream of work in condensed matter
physics to do with surface/domain growth -- such as in
molecular beam epitaxy -- like ballistic deposition (BD).
A good book to look at is *Fractal concepts in surface growth*
by Albert-Laszlo Barabasi and H. Eugene Stanley, 1995.
There's a lot of concepts floating around in the area (and
more generally), such as scaling, universality, criticality, etc.

If you want, I can provide a copy of my draft paper/simulations
when thet are complete in a few weeks.

Cheers, Bohdan


<><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

Bohdan Durnota
Department of Computer Science          Parkville 3052
Melbourne University                    Australia

interests: multiagent & complex adaptive systems,
        formal methods/software architectures

email:  address@hidden
phone:  +61-3-93449116
fax:    +61-3-93481184

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                  ==================================
   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.
                  ==================================