

Article 318 of comp.theory.cell-automata:
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>From: [email-masked]
Newsgroups: comp.theory.cell-automata
Subject: flocking behavior
Message-ID: <[email-masked]>
Date: 1 Feb 90 14:02:49 GMT
References: <[email-masked]>
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   Date: 1 Feb 90 04:19:08 GMT
   From: [email-masked]  (Dave Hiebeler)

     I am interested in learning some basics about flocking behavior, for
   example in birds and fish.  I'm not interested in how the physiology
   of particular animals drives flocking.  What I am more interested in
   is phenomenology of flocking, that is, classifications of different
   types of flocking behavior, some relevant parameters, and maybe some
   mathematical models of such behavior.  I am most interested in
   "homogeneous" flocking, that is, where there is no "leader", although
   that is not a strong requirement.
   ...

Hi Dave

This is going to sound bizarre, but it's something I've noticed for some time
now and haven't mentioned to anybody (perhaps out of fear of having people
think that I've truly gone off the deep end...)

I've spent quite a bit of time over the last year and a half experimenting with
the Rothman-Keller lattice gas for two-phase Navier Stokes flow (two immiscible
fluids with a surface tension interface).  If you start out with a homogeneous
mixture of the two phases, you can watch them separate like oil and water.  

The model is basically an FHP-type lattice gas where the particles can have one
of two colors, say red and blue.  Red particles, blue particles, and total
momentum are conserved.  Collisions involving particles of the same color are
exactly FHP collisions; collisions involving particles of different color are
chosen to preferentially send each particle toward neighboring sites that are
dominated by like color particles.  (This rule is carefully quantified in the
paper by Rothman and Keller.)  It is this affinity of particles for other
particles of the same color that gives the fluids cohesion and gives the
interface surface tension.

Once two fluids separate, it is interesting to look at their interface.  Though
it is quite stable, there are microscopic fluctuations: Occasionally a particle
of red fluid will break away and wander into the blue fluid, and vice versa.
When this happens, these "vapor" particles execute Brownian motion in the
foreign fluid until they hit the interface again and stick there.  Thus, there
is some small equilibrium level of foreign particles.  This is identical to the
physical phenomenon of vapor pressure.

Once in a great while, two individual vapor particles will come near each other
in the foreign fluid.  When this happens, there is a bit of a tendency for them
to stay together, according to the above rules.  I've watched this happen on
Connection Machine simulations on large grids at a few frames per second.  The
two particles execute a fascinating little dance.  They come together, dance
about, split apart, come back together, dance some more, etc.  I find it
incredibly reminiscent of the way that butterflies and moths flutter about
together while mating.

The biochemistry of mating butterflies and moths is governed by attractant
chemicals called pheromones.  (A neighbor of mine once experimented with using
pheromones to keep gypsy moths out of our neighborhood.  A few drops on a rag
hanging from a tree will keep a flock of butterflies about for quite some
time.)  In any event, it may be possible that the cohesion between like
particles moving in an incompressible Navier-Stokes background fluid in the
Rothman-Keller model is sufficiently similiar to the pheromone-induced
attraction of mating butterflies and moths moving through air (well
approximated by an incompressible Navier-Stokes fluid under most meteorological
conditions) to capture their motion in some qualitative way.

Just a suggestion.

Best regards,

Bruce M. Boghosian                               (617)-876-1111
Thinking Machines Corporation                    [email-masked]
245 First Street
Cambridge, Massachusetts  02142-1214