Chaos: Making a New Science

by James Gleick

This branch of dynamics concerned itself not with describing the final, stable behavior of a system but with the way a system chooses between competing options. A system like Lorenz’s now-classic model has just one attractor in it, one behavior that prevails when the system settles down, and it is a chaotic attractor. Other systems may end up with nonchaotic steady-state behavior—but with more than one possible steady state. The study of fractal basin boundaries was the study of systems that could reach one of several nonchaotic final states, raising the question of how to predict which. James Yorke, who pioneered the investigation of fractal basin boundaries a decade after giving chaos its name, proposed an imaginary pinball machine. Like most pinball machines it has a plunger with a spring. You pull back the plunger and release it to send the ball up into the playing area. The machine has the customary tilted landscape of rubber edges and electric bouncers that give the ball a kick of extra energy. The kick is important: it means that energy does not just decay smoothly. For simplicity’s sake this machine has no flippers at the bottom, just two exit ramps. The ball must leave by one ramp or the other. This is deterministic pinball—no shaking the machine. Only one parameter controls the ball’s destination, and that is the initial position of the plunger. Imagine that the machine is laid out so that a short pull of the plunger always means that the ball will end up rolling...