The final three or four prey fish are often the most difficult to catch because they have more room to run without colliding with another fish.
Captured fish are removed from the population
When the predator is successful in eating a prey fish, that fish is removed from the prey-fish population causing the prey-fish population to decrease overtime. Also, each time the predator eats a prey fish, the program emits an audible beep to provide feedback to the player.
The other GUI components
In addition to the elapsed time indicator and the Attack button, the GUI contains an input text field by which the player can specify the number ofprey fish that will be in the population when the game begins. The GUI also contains a Start button and a Stop button. Finally, the GUI contains check boxes that allow the player to display points only, directionvectors only, or both for the prey fish. (Only the direction vector is displayed for the predator.)
Playing the game
In practice, the player specifies the number of randomly-placed prey fish that will be in the population and clicks the Start button to start the game. At this point, the prey fish swim in a large swirling cluster and thepredator swims around them encouraging them to form a tighter cluster as shown in Figure 5 .
Prey fish motion is random but each prey fish generally tends to spiral toward the center of the cluster. When the user clicks the Attack button, the predator turns and swims rapidly into and through the center of the clusterof prey fish. If the predator manages to get to within a specified distance from a prey fish, that prey fish will be deemed to have been eaten, and will beremoved from the population. However, each prey fish will sense that the predator is coming and will try to escape. Whether or not an individual preyfish manages to escape the predator when an encounter between the two occurs is based on a random number generator.
The Start and Stop buttons
The animation continues until all of the fish have been eaten or the user clicks the Stop button. The user can click the Stop button at any time, change any of the parameters, and then click the Start button again to re-start the game with zero elapsed time and different parameters.
Displaying the vectors
The animation is most impressive when the direction vectors are displayed for the prey fish because the vectors provide a lot of visual information about howthe prey fish are reacting to the predator.
A spherical playing-field boundary
In addition to the school of prey fish and the predator, the graphical output also shows a large circle drawn with broken lines, as shown in Figure 5 . This circle represents the intersection of a sphere and the x-y plane.
The purpose of the sphere, which is centered on the origin, is to provide a soft boundary for keeping the prey fish and the predator inside the 3D playingfield. The prey fish and the predator all have a tendency to remain inside the sphere, but they may occasionally stray outside the sphere. If they do, theprogram code will encourage them to return to the 3D playing field inside the sphere.