Schooling of Fish

Try out the applet at Ref.[17] Does it not look like a very realistic simulation of fish swimming? The motion of each individual fish is not scripted right from the beginning but rather each individual follows just three simple local rules: cohesion, alignment and separation. Each of the rules is sensible from the biological perspective and so the model is plausible. What is remarkable of course is how the realistic and complicated collective behaviour emerges from the few simple local rules. There is no leader and none of the individuals has a global plan or perspective, (the motion is not orchestrated from the beginning). This example is an example of self-organisation. Other examples are the herding behaviour of humans, say for example in the stock-market, and the alignment of magnetic spins to form a ferromagnet. Many such examples will be studied later.