This Demonstration shows how a bifurcation diagram for a simple nonlinear optical fiber ring resonator changes with the fiber coupling ratio, kappa, which determines how much light circulates in the fiber loop. There is an isolated bistable (hysteresis) cycle for a narrow range of parameter values. The bistable cycle can give 0s and 1s to be used in computing. There is potential to replace electronic computers with all-optical computers in the future.