Programmable assembly of particles on a Chladni plate.

In nature, simple building units can be assembled into complex shapes through long-term time-varying external stimuli that are often spatially nonlinear. In contrast, most artificial methods of externally directed assembly rely on field- or template-based energy minimization. However, methods directing the assembly process by controlling time-varying external stimuli instead of attaining the lowest-energy state remain largely unexplored. In this study, we introduce a method that applies time-varying and spatially nonlinear vibration fields to assemble particles into a desired two-dimensional shape. Our assembly method predicts, controls, and monitors the vibration-induced particle motion to iteratively minimize the difference between the desired shape and the actual particle distribution. We applied our method to a centrally actuated vibrating plate, also known as a Chladni plate, and assembled up to a hundred submillimeter particles into complex recognizable shapes. The method allows programmable formation of shapes beyond the intrinsic limits of periodic patterning of the plate.