David Peat

From Clockwork to Chaos 135though behavior may on the surface appear totally chaotic and infinitelycomplex, it nevertheless originates from an underlying pattern,for the strange attractor itself has an underlying fractal structure.Fractals are complex patterns in which a particular element of the patternis repeated at ever decreasing scales ad infinitum. Likewise, whilethe behavior of a system in the grip of a strange attractor is chaotic,varying unpredictably from moment to moment, these jumps in behaviormirror each other at ever decreasing scale and take place withina certain zone, or range, of possibilities.Economists have compared the behavior of the stock market to asystem in the grip of a strange attractor. While there are overall trendsthat indicate which stocks are going to rise over the next weeks andwhich will fall, within these trends can be found fluctuations that, atfirst glance, appear random. Yet the “random” fluctuations that occurover say, one hour, mimic similar random fluctuations over a day, andover a week. Mathematicians call this self-similar behavior. A fractaldisplays similar patterns at ever decreasing scales, likewise small fluctuationswithin the stock market have a fractal structure, and whileremaining unpredictable in their fine details, the overall patterns areimitated at smaller and smaller time intervals.Although the detailed moment-to-moment behavior of a chaoticsystem cannot be predicted, the overall pattern of its “random” fluctuationsmay be similar from scale to scale. Likewise, while the finedetails of a chaotic system cannot be predicted one can know a little bitabout the range of its “random” fluctuation.IntermittencyUp to now we have looked at systems in which simple order breaksdown, or disappears, into that highly complex swirl of behavior calledchaos. Yet the theory of nonlinear systems presents us with a paradox,for behind the door marked “chaos” lies a world of order, and behindthat door marked “order” can be discovered chaos.Let us return to the sudden burst of noise from an electronic apparatus—anamplifier connected to a loudspeaker perhaps. Electronic