To the layman, chaos means undesired randomness or disorder. In mathematics, chaos theory (also known as dynamical instability) began as the study of the evolution in time of systems that are extremely sensitive to initial conditions. The usual example is how the flapping of a butterfly’s wings in South America can change the weather in Kansas. Chaos theory has evolved into the study of the behavior of physical systems that at first seem entirely random but in fact are not entirely so. Physical systems in general are said to inhabit “phase space,” a multidimensional universe where each point corresponds to a fixed value for every variable describing the system, and the evolution in time of such a system can be described as a path (or trajectory) from one point to another. The physical systems described by chaos theory are deterministic, meaning that if it were possible to exactly quantify the variables describing one point, the trajectory leading to the next point in a time sequence could be entirely predicted. The basis of dynamical instability lies in the precept that these variables cannot be completely and exactly described; the initial conditions are subject to minute uncertainties, and thus the trajectory may change in a seemingly random manner. In general, any trajectory in phase space is said to occur in response to an “attractor,” which determines the direction of movement. Trajectories that move toward an equilibrium position respond to a “point attractor”; trajectories that retrace a path in a strictly periodic movement are responding to “periodic attractors”; and trajectories that describe broad cycles of behavior within certain boundaries, but never exactly retrace the same path, are, by definition, responding to a “strange attractor.” The latter systems are said to be chaotic but not random. Such a system is still deterministic but is nonlinear in that its future state cannot be precisely predicted over the long term. The beginning of chaos theory was prompted by the problem of predicting the movements of three interacting astronomical bodies. Examples of other such physical systems abound and include the stock market, traffic flow, fluid turbulence, population dynamics, and a myriad of biological processes.