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

Thu Sep 7 13:54:30 EDT 2006

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

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________________________________

From: friam-bounces at redfish.com [mailto:friam-bounces at redfish.com] 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
	> > >
	> > >
	> > >
	> > >
	> > > ============================================================ 
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	> >
	> >
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