Boids

More interesting examples than the termite model above concern self-organisation that arises only when the agents interact among themselves. One of the earliest examples is Craig Reynold's "boids" model that simulates the motion of a flock of birds. In this model, each boid is an agent that follows a few intuitive rules meant to optimize some objective(s):

1. Separation: Reduce chance of collisions by moving away from boids that are too close.
2. Alignment : Fly in the average direction that the flock is moving.
3. Cohesion : Move towards the center of the flock to avoid exposure at the exterior.
4. View : Move sideways from any boid that is blocking the view.

The first three rules are Reynold's while the fourth is that of Flake. The rules are illustrated in the figure below


The next figure shows the result of a simulation in which only the first three rules were active. An initially unorganised collection of boids comes together to form a single flock.(Note: The position of a boid after each increment in time step, assumed here to be of unit length, is obtained by adding to the old position the new weighted velocity that takes into account the above rules.)


The final figure shows what happens when the fourth rule is activated. The largest flock arranges itself into a classic "V" formation.


Though these examples and those in the exercises look realistic, one must still be cautious in interpreting them as sole explanations of observed animal behaviour. The flocking discussed above can be studied in a quantitative way using the methods of physics. See, for example, Ref.[10].