Many species of fish schools organize for short or longer periods of time without a leader. We searched for the behaviour patterns of the individual fish, which allow movement of such a school. On the basis of biological facts we constructed a number of behaviour models and tested them with computer simulations against biological reality.

Basic assumptions of our simulations are: (1) The motion of a fish is only influenced by the position and orientation of its nearest neighbours. (2) The new velocity and the turning angle of each fish (after a time step) are calculated by probability distributions taking into account random influences. (3) The movement of each model fish is based upon the same behaviour model, i.e. the modelled fish group swims without a leader.

The basic behaviour patterns are attraction, repulsion and parallel orientation. Our investigations show that it is very important how a fish mixes the influences of its neighbours. If a fish averages the influences of its neighbours, the model fish group shows the typical characteristics of a real fish school: strong cohesion and high degree of polarization. If a fish only responds to a single neighbour, the model creates a confused fish group.