It sounds great if you have the time to do the experiments. :) It's an interesting observation that two boids in a torus will eventually flock. Suppose that they started off moving both orthogonally and out of phase. There is no reason for that to change since they are never in each other's neighborhood.
But if you add some random drift effects, then presumably they will eventually begin to affect each other and over time move closer and closer together until they become a flock. By the way, I would define a flock as a collection of boids that form a persistently fully connected network where the boids are the nodes, the links are between boids that are in each other's neighborhoods, and persistently means that the entire collection is always fully connected. Given that definition, given a flock will it eventually settle into a fixed network, i.e., with no link changes? It's conceivable that a flock may remain a flock even though there are continuing internal link changes. So the question is will every flock eventually find a fixed network configuration. Since by my definition of a flock, the entire collection will always be fully connected, then it would seem that internal forces will pull it into a fixed (minimal energy) state. Someone must have proved some results along those lines already. -- Russ On Sun, Sep 6, 2009 at 3:48 PM, Ted Carmichael <[email protected]> wrote: > Hi, Russ. Thanks for the post. It's always interesting to think about > these things. > Offhand, I think the most relevant factors would be the number of > interactions (how often one boid affects another) and the strength of those > interactions (to what degree one boid affects another, and in what ways). > > In a torus, I believe two boids will always - eventually - flock, > regardless of how seldom or weak the interactions are. (Of course, this > assumes that the interactions will occur at some point and that they are > formulated to induce flocking ... probably it would be possible that their > path/speed was such that they reach a point where they stop interacting, > even in a torus.) > > It would also depend on how you define a 'flock,' I suppose. Probably > based somehow on the rules for moving closer or farther apart. > > I think this way would simplify things. I'd guess the boids would keep > getting closer together until the number of "move apart" interactions > approximately equals the number of "move closer" interactions. This would > be the equilibrium point - assuming both types of interactions are equal in > their degree of effect). Probably the rate of movement towards a flock > would change over time as the % of interactions gets closer to the > equilibrium point. I reckon the speed of change in these percentages would > decrease as you approach the equilibrium point. > > Anyway, it should be easy to test ... if all that is correct, you just have > to count the interactions of each type over time, and see when (if) they > begin to fluctuate around some equilibrium point. > > How does that sound? > > Cheers, > > Ted > > On Sun, Sep 6, 2009 at 5:37 PM, Russ Abbott <[email protected]> wrote: > >> In a recent discussion about emergence I wrote the following (somewhat >> edited). >> >> Emergence is what happens when components of the emergent entity act in >> such a way as to bring about the existence and persistence of that entity. >> For example, when "boids" follow their local flying rules, they create (* >> implement*) a flock. It's not mysterious. We know how it works. >> >> That's all emergence is: coordinated or consistent actions among a number >> of elements that result in the formation and persistence of some aggregate >> entity or phenomenon. The "coordination" doesn't have to be top-down. In >> flocking, for example, there is local (or networked) coordination. The >> flying rules for on each boid depend on that boid seeing neighboring boids. >> One can even say that there is some overall coordination: all the boids >> follow the same rules. ** >> >> It's worth pointing out that in biological and social emergent entities, >> the components may come and go while the entity persists. What emerges is a >> pattern of activities, not a physical thing. That's one of the reasons >> people get confused. (And that's why subvenience is not particularly useful >> in these cases.) >> >> But if you just think about emergence as a persistent pattern of >> activities, that pretty much takes care of it. It's the fact that the >> pattern persists that matters, not the elements that are acting to produce >> the pattern. >> >> One of the more interesting issues in complex systems is the formation of >> entities --. that "boid attraction" creates flocks is a simple example. >> >> With that in mind, it might be interesting to do some experiments. For >> example, How dense does a collection of boids have to be for a flock to >> form? Or more to the point, if the boids are confined to a limited, e.g., >> toroidal, space, how does their initial density determine the rate at which >> the flock forms? What about the other parameters such as the distance each >> individual boid can see (that is, which boids become neighbors) and the >> velocity at which the boids are moving compared to the "attraction" they >> have on each other? This is like gravity and asking whether two passing >> bodies will form an orbiting system or simply affect each other's velocities >> as they pass and separate. >> >> What if the environment included obstacles that the boids had to avoid. >> Some of those obstacles could presumably break up a flock. So how do flock >> formation and flock disintegration interact? There might be other >> disintegration forces such as boids moving a bit more randomly. >> >> How do these results relate to similar results in networks such as network >> formation and connectivity, etc.? >> >> Do any "self-organized criticality" effects appear? >> >> Does anyone know whether experiments of this sort have been done, and if >> so, what the results were? >> >> Having written this down, these feel like questions that should have been >> asked a decade ago. But perhaps there might still be something there. Entity >> formation is an open and important issue. Perhaps experiments of this sort >> might shed some light on it >> >> -- Russ >> >> >
============================================================ 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
