One of my pet peeves about most agent-based models is that they ignore energy. The boids model does too. But what happens if we include energy considerations?
We could assume that the boids move in a frictionless medium and that they never touch each other. So the only energy issue is the energy expended in following the rules. (Here's Craig Reynolds' page<http://www.red3d.com/cwr/boids/>describing his original boids work, which describes the rules.) It's easiest to assume that each boid has access to an unlimited supply of energy which it uses to accelerate itself according to the rules. Obviously it's unrealistic to assume that any agent has access to an unlimited supply of energy. But most agent-based models do! Being a far-from-equilibrium system, energy enters the model through the boids. It dissipates (without warming the environment) as the boids use energy to accelerate themselves. Since there are no internal energy transfers, the energy issues should be fairly easy. Given the boid rules and the availability of unlimited energy, can anything be said about how an arbitrary boid collection will evolve? Will it evolve, for example, to a state that requires the minimum total energy expenditure? If that's the case, can something similar be said about other emergent entities and phenomena? This is a somewhat different question than is normally asked about far-from-equilibrium systems. More frequently one assumes that energy is *pumped into the system at a constant rate*. One then asks what happens. One gets Bénard cells <http://en.wikipedia.org/wiki/B%C3%A9nard_cells> and similar phenomema. But here energy is being *pulled into the system **as needed*. It's pull rather than push! I sincerely hope that someone who can work with the physics of this takes it up. If so, I'll do whatever I can to help. -- Russ On Sun, Sep 6, 2009 at 4:32 PM, Russ Abbott <russ.abb...@gmail.com> wrote: > 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 <teds...@gmail.com> 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 <russ.abb...@gmail.com>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 >>> >>> >> >
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