Strong activity. Shown are velocity (full line) and network (dashed line) dynamical correlation functions for natural swarms (orange) and near-critical ISM simulations (purple). The network correlation function measures the fraction of particles remaining within the n c nearest neighbours after time t (Supplementary Section III ), so it quantifies how quickly the interaction network reshuffles with time. In both natural swarms and ISM, the network decorrelates on the same timescale as the velocity, so they are strongly active systems. Here, n c = 18, which is the mean number of interacting neighbours in simulations. In Supplementary Section III and Supplementary Fig. 15 we show that in natural swarms the two timescales are the same over all spatial scales.
