Fig. 3: Quantifying effervescence.

a Dynamics within a droplet is slow compared to that in regions where α is much larger, as can be seen from the evolution of ϕ_i with time at a fixed position R. b Probability distribution for ∣ϕ∣ in the steady-state, revealing the coexistence of travelling waves (associated with the peak at ∣ϕ∣ < 1) and droplets (linked with the peak at \(| \phi |={\rho }_{0}=\sqrt{{\alpha }_{0}/{\alpha }_{1}}\)) in which the effective non-reciprocal interaction vanishes. c Probability distribution for the area \({{{\mathcal{A}}}}_{{{\rm{droplet}}}}\) (determined by calculating the area within the contours shown in Fig. 2a, b) of the droplets made of reciprocal granules (in units of \({q}_{0}^{-2}\)). The peak at the origin reveals the existence of a large population of reciprocal granules. The oscillatory motif of the full distribution shows that the droplets are formed as aggregates of a number of similarly sized granules. Inset: the observed exponential decay of the droplet size distribution (as evident in the semi-log scale) verifies the existence of an underlying size selection mechanism. d The persistent fraction ν is plotted against time for α₀ = 5 and α₁ = 4. ν(t) is the fraction of space occupied by droplets of age at least t, implying that ν(0) is the initial average coverage of space by droplets. The bold blue line shows the average over 250 different initial configurations while the fainter lines show the time evolution for a few individual cases. The inset shows the correlation between the droplet lifespan τ and its size \({{{\mathcal{A}}}}_{{{\rm{droplet}}}}\) (see Methods II for details) and the dashed line is a linear fit to the data.