common way for electrical circuits, computer programs, brain mechanisms and other complicated systems, even cultural or spiritual movements, to behave when one or more important control parameters crosses a threshold. Doyne Farmer of the Los Alamos’s Prediction Company once said about this vulnerability in complex system, “Those things can hardly wait to roll up.” The /imit cycle lock-up occurs most often as a sudden, discontinuous change, called a_ bifurcation, into autonomous Sself-oscillations from an equilibrium state around which there was some random variation. A bifurcation, a discontinuous change in outcome from a smooth changes cause, characteristically occurs when the amount of an important influence, a metabolic state, a drug, a psychodynamic conflict or level of emotional stimulation crosses some critical value. The switch from one type of dynamical behavior to another looks like the system has suddenly changed into something else with an entirely new kind of life of its own. In the new life of rolled up, locked-up repetitious motion, almost all new starting conditions follow pathways that lead into the same limit cycle pattern. Evangelical Christians talk about a// born again life being in Jesus, fixed in a complete set of moral, social and political beliefs, ideas and judgments. The limit cycle gets its name because the end state of the orbits of almost all starting points of the dynamics winds up being drawn into the same fixed, repetitious pattern of a stable cycle. Visualizing the simulation of one kind of bifurcation to a limit cycle on a computer screen, we see a slightly jiggling point explode suddenly into an orbit of ceaseless rotations around a circle. Ralph Abraham, the University of California at Santa Cruz pioneer in graphical approaches to nonlinear systems, describes, cinemagraphically, the emergence of limit cycles from a single point. He starts with a picture of an attractor of water flow in the shape of a basin. All water that enters