Learning to write with the fluid rope trick

Direct ink writing, a versatile method of 3D and 4D printing, requires the precise placement of a nozzle just above the print surface to prevent fluid instabilities that cause deviations from the prescribed print path. But what if one could harness the instability associated with the spontaneously folding or coiling of a thin stream of viscous fluid, i.e. use the "fluid rope trick" to write specified patterns on a substrate? Here we use Deep Reinforcement Learning to derive control strategies for the motion of the extruding nozzle and thus the fluid patterns that are deposited on the surface. The method proceeds by having a learner (nozzle) repeatedly interact with the environment (a viscous filament simulator), and improves its strategy using the results of this experience. We demonstrate the outcome of the learned control instructions using experiments to manipulate a falling viscous jet and create cursive writing patterns and Pollockian paintings on substrates.