Fish do not need a leader or external stimuli for their school organiz
ation. The model presented shows that the group movement of a school c
an be maintained by interactions in which each individual controls its
movement in relation to its neighbours. Our three-dimensional simulat
ions reproduce the typical characteristics of real schools, if the beh
aviour of the single fish is based on four patterns: attraction, repul
sion, parallel orientation and averaging the influences of at least fo
ur neighbours. The results of our simulations agree with experimental
data in many points, as is demonstrated here for the polarization, nea
rest neighbour distance and internal dynamics.