Simulated Flocks

Collision Avoidance
Velocity Matching
Flock Centering

To build a simulated flock, we start with a boid model that supports geometric flight. We add behaviors that correspond to the opposing forces of collision avoidance and the urge to join the flock. Stated briefly as rules, and in order of decreasing precedence, the behaviors that lead to simulated flocking are:

Collision Avoidance: avoid collisions with nearby flockmates
Velocity Matching: attempt to match velocity with nearby flockmates
Flock Centering: attempt to stay close to nearby flockmates

Velocity is a vector quantity, referring to the combination of heading and speed. The manner in which the results from each of these behaviors is reconciled and combined is significant and is discussed in more detail later. Similarly, the meaning nearby in these rules is key to the flocking process. This is also discussed in more detail later, but generally one boid’s awareness of another is based on the distance and direction of the offset vector between them. Static collision avoidance and dynamic velocity matching are complementary. Together they ensure that the members of a simulated flock are free to fly within the crowded skies of the flock’s interior without running into one another. Collision avoidance is the urge to steer away from an imminent impact. Static collision avoidance is based on the relative position of the flockmates and ignores their velocity. Conversely, velocity matching is based only on velocity and ignores position. It is a predictive version of collision avoidance: if the boid does a good job of matching velocity with its neighbors, it is unlikely that it will collide with any of them any time soon. With velocity matching, separations between boids remains approximately invariant with respect to ongoing geometric flight. Static collision avoidance serves to establish the minimum required separation distance; velocity matching tends to maintain it.
Flock centering makes a boid want to be near the center of the flock. Because each boid has a localized perception of the world, „center of the flock“ actually means the center of the nearby flockmates. Flock centering causes the boid to fly in a direction that moves it closer to the centroid of the nearby boids. If a boid is deep inside a flock, the population density in its neighborhood is roughly homogeneous; the boid density is approximately the same in all directions. In this case, the centroid of the neighborhood boids is approximately at the center of the neighborhood, so the flock centering urge is small. But if a boid is on the boundary of the flock, its neighboring boids are on one side. The centroid of the neighborhood boids is displaced from the center of the neighborhood toward the body of the flock. Here the flock centering urge is stronger and the flight path will be deflected somewhat toward the local flock center.