Could we think of the rules and the effects they produce as some sort of relaxation process? If so, toward what end?
-- Russ On Sun, Sep 6, 2009 at 11:37 PM, Russ Abbott <[email protected]> wrote: > 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 <[email protected]> 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 <[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
