Path: utzoo!utgpu!jarvis.csri.toronto.edu!rutgers!tut.cis.ohio-state.edu!snorkelwacker!bloom-beacon!THINK.COM!bmb From: bmb@THINK.COM Newsgroups: comp.theory.cell-automata Subject: flocking behavior Message-ID: <9002011402.AA06402@aldebaran.think.com> Date: 1 Feb 90 14:02:49 GMT References: Sender: root@athena.mit.edu (Wizard A. Root) Distribution: inet Organization: The Internet Lines: 72 Date: 1 Feb 90 04:19:08 GMT From: zaphod.mps.ohio-state.edu!rpi!hiebeler@Think.COM (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 bmb@think.com 245 First Street Cambridge, Massachusetts 02142-1214