Taffy Pulling Apart
Nonlinear iteration can be pictured as a taffy puller or a baker kneading bread dough. Indeed, mathematicians call what happens when nonlinear equations iterate, “the baker transformation” as nonlinear iteration is similar to what occurs when a baker stretches out dough and folds it back again. What began as neighboring points, say raisins, in the dough can end up very far from each other. One of the strange attractors, the Roessler attractor, is actually based on the equations to describe the taffy puller. These examples demonstrate how quickly things can become very complicated and unpredictable (Briggs & Peat, 1989).
Another fitting visual that is used to show chaos theory at work is a picture of Poincaré as it is playfully stretched and folded back on itself, after the first iteration he is diagonal, and by the 10th iteration there is no trace of him, only striped lines, on the 48th iteration he comes back into view briefly a multiplicity of times and then again after 241 times he is back to his old self.
This brings us to a discussion of strange attractors, as “mathematically this process of stretching and folding takes the form of a strange attractor” (Briggs & Peat, 1989, p. 71). The strange attractor branch of chaos theory is so named to reflect the notion that deterministic chaos contains within it deeply encoded structures known as strange attractors. Stewart (2002) sees that something is going on beneath the surface, things coincide too much to be just coincidence. In his segue into speaking about strange attractors, remarking about this coincidence of things, Stewart playfully notes “unless you agree with Kurt Vonnegut in Cat’s Cradle, that the Deity made the universe as an elaborate practical joke” (p. 84). Casey (1996, cassette) reports that a cloud of NO2 or laughing gas, has been found at the center of the galaxy, and so maybe we should not laughingly dismiss Vonnegut’s idea. But just as Stewart segued, we must, too, because it is now time to see what these strange attractors are, how they work, and how they relate to the psyche.