Fig. 2: Effervescence, reciprocal granules, and droplets.

a Snapshot of a part of the field ∣ϕ∣ in the steady state for α₀ = 5, α₁ = 4 illustrating reciprocal granules (highlighted by the red arrows) and droplets with red contours at ∣ϕ∣ = 0.8. The configuration changes entirely in finite time, as seen in the next snapshot, emphasising the chaotic nature of the creation-annihilation processes that occur continuously in the steady state. b To highlight the processes involved in granule and droplet production and annihilation we now focus on the contours only. Each image in the series is produced by superimposing the contours over an interval of time between 30 and 250, in increments of 10 until the time indicated in the label, thus showing the evolution history of the granules and droplets. The final configuration is highlighted using thick lines and the preceding contours are shown in progressively lighter hues. A reciprocal granule -- so called because the strength of net non-reciprocity is suppressed within the domain -- as marked with a red arrow disappears within t = 10. This is a fast process, as it occurs while the surrounding larger droplets are virtually unchanged. Droplets are formed by coalescence events to form larger droplets and dissolve either by shrinking or splitting. The droplets drift and diffuse while their interfaces strongly fluctuate. The series of events shown here are typical of the dynamics seen in the steady state. c The definition of effervescence, as realised through spatiotemporal chaos in non-reciprocal systems with number conservation showing hallmarks of both chasing dynamics and phase separation. d At nonzero mean composition, smaller droplets fuse to form a persistent phase-separated domain (i.e., very large droplet) with pulsating interfaces. This stable domain coexists with reciprocal granules that form and dissolve as described above. e Fluctuations of the interfaces in the steady state are illustrated using the same method as adapted for (b).