# Bird Flocking Simulation

Bird flocking is an extremely interesting natural phenomenon that have been widely studied as witnessed by the number of papers in literature). I will present here a work on aggregate motion of large number of boids in a virtual environment with the presence of predators using CUDA as computational framework.

Beautiful Flocking motion

Collective motion or flocking appears at different fields and scales in nature and several mathematical tools have been developed for analyzing such motions

1. organism are threaten as particles in Brownian motion combined with attraction/repulsion forces
2. Differential equation models
3. Agent based models.

The model presented here is based on a work of Reynolds (1987) which is based on three key behavioral rules:

• Cohesion: to attempt to stay close to nearby flock-mates;
• Collision avoidance: to evade objects that are too close;
• Velocity/Heading Matching: to head in the same direction of nearby flock-mates

and extends it adding predator avoidance and multiple species and bird groups interaction

# Bird Flocking Model

The environment is parameterized using the following a set of parameters that describe the size of the virtual environment and the duration of a timestep. What is really interesting is the set of bird's parameter that describe how a bird behave and react to event in its surrounding. Some notable parameters  include the Fyeld Of View (FOV), peak velocity $v_p$, thrust $a$ and others (see figure).

Bird Parameters

The environment is partially observable and the portion of space that is visible to each bird is defined by its FOV. FOV is defined as follows:

Let  the position vector of the object  in the 's frame of reference, then  is 's neighbor if and only if the followings hold:

where  is the maximum horizontal range of view, $s_v$ is the maximum vertical range of view and

## Cohesion

In formal terms , the bird 's centroid at time , is given by:

Cohesion

which is basically a weighted average of neighbors position.

## Separation

A bird try to keep certain distance between itself and
its neighbors. Bird 's separation vector  at time  is given
by:

where  determines how strong is the repulsion against to the neighbor .

Alignment

Bird's alignment is computed as follows

It is a weighted average of the neighbors's heading direction.

Other species and predator avoidance
Other species avoidance is a behavior pretty much similar to the separation. The only difference is that only birds that belong to other species contribute to the result.

Predator avoidance is also a "flee or separation" behavior, but what happens here is that we do not take into account the current predator position, but instead, birds try to "separate" from predators's next position (the prediction is made from current position and velocity and acceleration of the predator).

The predator avoidance vector  is defined as follows:

where:

•   is the 's set of predators
•  
is the predator avoidance coefficient, where  is the minimum distance bird avoid predator.

The model has been implemented in CUDA to speedup the simulation. The following is a short video which I used during my presentation at PDP16 conference.  The model and the implementation described in this article are much more greatly described in the following slides (download here).