Streamlines tracing out a vector field are important for graphics and visualization, yet the way of controllably arranging the streamlines in unsteady flows, even in 2D, has not been well studied to this day. We thus propose an unsteady streamline synthesis framework that can create a full set of coherent streamlines following certain inputs under 2D and 3D time-varying scenarios while satisfying coverage, continuity, and controllability purposes. Our key concept is to treat the time-varying streamline arrangement like a dynamic packing of anisotropic elements with deformability such that both quality and efficiency can be fulfilled. Specifically, we devise a synthesis process based on inter- and intra-streamline relationships to dynamically synthesize all the coherent streamlines in parallel and incorporate a regulation mechanism with primitive operations to timely adjust each streamline’s continuity and the overall streamline coverage. With specification, our framework can further controllably produce desired streamline arrangements for various application demands.