Control of Coulomb expansion in charged particle beams is of critical importance for applications including electron and ion microscopy, injectors for particle accelerators and in ultrafast electron diffraction, where space-charge effects constrain the temporal and spatial imaging resolution. The development of techniques to reverse space-charge-driven expansion, or to observe shock waves and other striking phenomena, have been limited by the masking effect of thermal diffusion. Here we show that ultracold ion bunches extracted from laser-cooled atoms can be used to observe the effects of self-interactions with unprecedented detail. We generate arrays of small closely spaced ion bunches that interact to form complex and surprising patterns. We also show that nanosecond cold ion bunches provide data for analogous ultrafast electron systems, where the dynamics occur on timescales too short for detailed observation. In a surprising twist, slow atoms may underpin progress in high-energy and ultrafast physics.