We report results of directional solidification experiments conducted on board the International Space Station and quantitative phase-field modeling of those experiments. The experiments image for the first time in situ the spatially extended dynamics of three-dimensional cellular array patterns formed under microgravity conditions where fluid flow is suppressed. Experiments and phase-field simulations reveal the existence of oscillatory breathing modes with time periods of several 10's of minutes. Oscillating cells are usually noncoherent due to array disorder, with the exception of small areas where the array structure is regular and stable.