The three rules

Each boid looks only at the neighbours inside its sight radius, then nudges its own velocity a little toward the average of three urges:

• Separation steers away from neighbours that get too close, so nobody collides.
• Alignment steers toward the average heading of the group, so the flock moves as one.
• Cohesion steers toward the average position of the group, so it stays together.

That is the whole algorithm. Crank cohesion up for a tight ball, alignment up for streaming rivers of boids, or separation up for a nervous, spread-out crowd. The trick that keeps it fast even with hundreds of boids is only ever checking neighbours in the same patch of space, not the entire flock.

Based on Craig Reynolds' original boids work.