Emergence in flocking

Laplace’s demon has given way to claims that all that constitutes nature, can be derived and explained by understanding how their composing parts work. This idea of reductionism is often speculated upon by a portion of scientists who disapprove such approach whose limits are evident in complex systems.
Emergent behaviour is said to exist in systems where complex and collective organization is formed by interactions that result from simple rules.
Emergence according to complexity theorists is “the process whereby the global behaviour of a system results from the actions and interactions of agents”.
The flocking behaviour of birds portrays this kind of collective and decentralized behaviour. Natural flocks are comprised of two "balanced, opposing behaviours": the need to stay close to the flock and the need to avoid collisions with other members of the flock.
In order for the flocking to work each bird in the flock must apply three rules:

Collision Avoidance

“Steer to avoid crowding local flockmates.” Each bird of the flock must avoid having another bird of the flock closer than a set threshold in order to avoid collision. If a bird enters another bird’s “space”, both must correct their position.

Velocity Matching

“Steer towards the average heading of local flockmates.” All birds should flock towards the same direction.

Flock Centering

“Steer to move toward the average position of local flockmates.” This allows the flock to stay together.

A video of flocking starlings:

For more info on how to simulate a flocking behaviour check Craig Reynold's website.