Getting the Program Running

Abstract

Chaotic dynamics has a long history that can be traced back to the papers of Henri Poincaré and James Clerk Maxwell. That history is quite thin compared with the volumes written on how to study small perturbations of a stable equilibrium point. The field of chaotic dynamics did not come alive sufficiently to affect scientists until chaotic systems could be studied on small interactive computers with good graphics. Edward Lorenz’s studies in 1963 were carried out on a desk-sized computer. One day after having previously made a long computer run he entered an intermediate result, a vector giving an intermediate state of the system. But the intermediate result had less precision than the true computer state. To his surprise he found this tiny change caused the system to evolve in quite a different manner. This was the first computer study illustrating sensitivity to initial data. Now with the advent of personal computers with good graphics, now that we know what to look for, it is easy to see chaotic trajectories.