Herself’s Artificial Intelligence

Using potential functions for predator prey movement gives a more realistic chase than using line of sight or other line algorithms.

Potential functions are well known in physics and describe attraction and repulsion due to electricity, gravity etc.

Potential_Energy = – Attraction/distance^j + Repulsion/distance^k

A strong attraction will cause the predator to chase the prey, a strong repulsion will cause the prey to flee the predator. Either of these can be set to zero. Predators may only be attracted to prey, prey may only be repulsed by predators. Various prey and predators can be given slightly different numbers for attraction, repulsion, j, k allowing them to behave differently.

To chase or run a character using potential functions use this algorithm:

Move_Predator (){

double attraction = some_constant; // experiment with these, the size of your game
double repulsion = some_constant; // area will determine good choices
double j = some_constant; // try something between 1 to 3 for these numbers
double k = some_constant; // higher number mean smaller results
double x_predator;
double y_predator;
double x_prey;
double y_prey;

//distance between predator and prey
double distance_x = x_predator – x_prey;
double distance_y = y_predator – y_prey;

double distance = sqrt ( distance_x*distance_x + distance_y*distance_y);

//normalized distance vector
distance_x = distance_x / distance;
distance_y = distance_y / distance;

//see what our attraction or repulsion is
double potential = -attraction/distance^j + repulsion/distance^k;

//now use that attraction/repulsion to see how far we move
double move_x = potential * distance_x;
double move_y = potential * distance_y;

//new location for us
double new_x = predator_x + move_x;
double new_y = predator_y + move_y;

}

More information:
The use of potential functions on modelling animal movement
Advanced Movement Model of Crowd Robots ( pdf )

Books:
AI for Game Developers