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Do you know? Do 'swarms' follow random walks?

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Trucano, Timothy G

Do you know? Do 'swarms' follow random walks?

That sqrt(N) estimate depends on the assumption of random walk in non-random environment, doesn't it? These kinds of estimates change a lot in a random environments? I don't have the time to check this, but this should be presented in detail in existing books. For example, see the two-volume book by Barry Hughes "Random Walks and Random Environments," Oxford University Press, circa 1995. I think the overall question about the detailed random characteristics of swarms is a very interesting one.

Tim

---- Harder ---- Slower ---- Too Expensive ----

Timothy G. Trucano
Optimization and Uncertainty Estimation, 01411
Sandia National Laboratories
MS 0370
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________________________________

From: [hidden email] [mailto:[hidden email]] On Behalf Of Robert Holmes
Sent: Thursday, September 07, 2006 11:15 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Do you know? Do 'swarms' follow random walks?

Phil,

Following on from Steve's comments, the mean distance of a randomly-walking point from its origin is of the order sqrt(N) where N is the number of steps in its walk. Steve's flocks don't exhibit this behaviour, so it's safe to say that no, swarms do not generally display random walk behaviour.

Robert

On 9/7/06, Stephen Guerin <stephen.guerin at redfish.com> wrote:

Phil,

I now see where 'accumulated variance' is used in the context of Principal
Components Analysis where it represents how much of the variance is explained by
a set of component vectors. Is this how you're using the term?

Given this usage, I would guess that if you described the agents' states with
position and velocity vectors, a given number of principal components would have
increasing accumulated variance as the swarm becomes more organized.

Or, perhaps you are talking about describing the motion of the swarm as a single
entity? In that case, I would say it depends on the parameters of the model.
Some settings yield swarms that break symmetry in linear momentum and move at a
constant rate in a given direction. Other settings in a model yield more
stationary swarms that buzz around much like gnats around a light. These swarms
may exhibit random-walk dynamics.

FWIW, We have a swarm model/visualization at
http://www.redfish.com/projects/SwarmEffects/ where you can vary agent behaviors
to get different macro swarms. Focus on changing the "Average Position", "Avoid"
and "Average Direction" sliders. These sliders weight how much a given behavior
contributes to a summed vector that is an agent's next move.

-Steve

> -----Original Message-----
> From: Stephen Guerin [mailto:stephen.guerin at redfish.com]
> Sent: Wednesday, September 06, 2006 11:55 PM
> To: sy at synapse9.com ; 'The Friday Morning Applied Complexity
> Coffee Group'
> Subject: Re: [FRIAM] Do you know? Do 'swarms' follow random walks?
>
> Hi Phil,
>
> > Has anyone checked to see if any alife 'swarms' display
> accumulative
> > variance?
>
> I haven't come across the term 'accumulative variance'
> before. Do you have a web pointer?
>
> As a swarm organizes, the agents' directions and velocities
> become more correlated with each other. ie agents become more
> constrained as they lose degrees of freedom. Would you
> interpret this to be decreasing variance?
>
> -Steve
>
>
>
> > -----Original Message-----
> > From: Phil Henshaw [mailto:sy at synapse9.com]
> > Sent: Wednesday, September 06, 2006 8:24 PM
> > To: 'The Friday Morning Applied Complexity Coffee Group'
> > Subject: [FRIAM] Do you know? Do 'swarms' follow random walks?
> >
> > Has anyone checked to see if any alife 'swarms' display
> accumulative
> > variance?
> >
> > If you were to design one to do that, would it have a structure
> > comparable to populations of organisms living in ecologies?
> >
> > -In case anyone's curious I have a high quality direct measure of
> > accumulative variance.
> >
> >
> > Phil Henshaw ????.?? ? `?.????
> > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> > 680 Ft. Washington Ave
> > NY NY 10040
> > tel: 212-795-4844
> > e-mail: pfh at synapse9.com
> > explorations: www.synapse9.com
> >
> >
> > > -----Original Message-----
> > > From: friam-bounces at redfish.com
> > > [mailto:friam-bounces at redfish.com] On Behalf Of Phil Henshaw
> > > Sent: Tuesday, September 05, 2006 8:30 PM
> > > To: 'The Friday Morning Applied Complexity Coffee Group'
> > > Subject: [FRIAM] nature walks!
> > >
> > >
> > >
> > > I am dually impressed at Amazon's ability to know what
> > undergarments
> > > it's random visitors might be advised to
> > > try....:) (just marvelous!) but still I have some questions about
> > > reality 101.
> > >
> > > If molecules in thermal motion follow random walks, do
> > fluids composed
> > > of molecules in thermal motion do so as well? I've run into the
> > > strangest confusion among Darwinian theorists, both from
> > journals of
> > > paleontology and evolutionary biology. I have a quite good paper
> > > that's unpublishable because I stick my neck out to say
> populations
> > > have no non-extraordinary mechanisms for changing by random walks.
> > >
> > > a) am I wrong and there are some? a.1)clue me in..
> > > b) do you know a journal for people literate in evolution
> > theory that
> > > might be willing to consider the issue based on physical
> mechanisms?
> > >
> > >
> > > Phil Henshaw ????.?? ? `?.????
> > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> > > 680 Ft. Washington Ave
> > > NY NY 10040
> > > tel: 212-795-4844
> > > e-mail: pfh at synapse9.com
> > > explorations: www.synapse9.com
> > >
> > >
> > >
> > >
> > > ============================================================
> > > FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at
> > > cafe at St. John's College lectures, archives,
> unsubscribe, maps at
> > > http://www.friam.org
> > >
> > >
> >
> >
> >
> > ============================================================
> > FRIAM Applied Complexity Group listserv Meets Fridays
> 9a-11:30 at cafe
> > at St. John's College lectures, archives, unsubscribe, maps at
> > http://www.friam.org
> >
> >
>
>
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