  The observation of strongly interacting many-body phenomena in atomic gases
typically requires ultracold samples. Here we show that the strong interaction
potentials between Rydberg atoms enable the observation of many-body effects in
an atomic vapor, even at room temperature. We excite Rydberg atoms in cesium
vapor and observe in real-time an out-of-equilibrium excitation dynamics that
is consistent with an aggregation mechanism. The experimental observations show
qualitative and quantitative agreement with a microscopic theoretical model.
Numerical simulations reveal that the strongly correlated growth of the
emerging aggregates is reminiscent of soft-matter type systems.
