[FRIAM] Do you know? Do 'swarms' follow random walks?

[Robert Holmes]

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
> > >
> > >
> >
> >
> > ============================================================
> > 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
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: /pipermail/friam_redfish.com/attachments/20060907/940568fd/attachment.html