Title: Strange attractors from Lorenz to turbulence Abstract: Typical trajectories of some dynamical systems separate rapidly even if they begin at nearby states, yet repeatedly approach their starting states. Symbolic dynamics uses these two properties, namely sensitive dependence on initial conditions and recurrence, to obtain short codes for long segments of trajectories. Symbolic dynamics makes possible very accurate computations of chaotic differential equations such as the Lorenz equations, leading, for instance, to explicit plots of the fractal structure of the Lorenz attractor. The same methods may be applicable to the study of turbulence in fluid flow, as will be demonstrated using accurate and well-resolved computations of periodic motions within plane Couette turbulence.