ABSTRACT

Many scientists have attempted to express the group behavior of flocks of birds and schools of fish, using a variety of methods. Two of the most well-known of these scientists are Reynolds and Heppner, who simulated the movements of birds. Reynolds was fascinated by the beauty of bird flocks [101], and Heppner, a zoologist, had an interest in finding the hidden rules in the instantaneous stops and dispersions of flocks [50]. These two shared a keen understanding of the unpredictable movements of birds; at the microscopic level, the movements were extremely simple, as seen in cellular automata, while at the macroscopic level, the motions were very complicated and appeared chaotic. This is what is called an “emergent property” in the field of Artificial Life (Alife). Their model places a very high weight on the influence of individuals on each other. Similarly, it is known that an “optimum distance” is maintained among individual fish in a fish school (see Fig. 6.1).