  We present the first experimental study on the simultaneous capillary
instability amongst viscous concentric rings suspended atop an immiscible
medium. The rings ruptured upon annealing, with three types of phase
correlation between neighboring rings. In the case of weak substrate
confinement, the rings ruptured independently when they were sparsely
distanced, but via an out-of-phase mode when packed closer. If the substrate
confinement was strong, the rings would rupture via an in-phase mode, resulting
in radially aligned droplets. The concentric ring geometry caused a competition
between the phase correlation of neighboring rings and the kinetically
favorable wavelength, yielding an intriguing, recursive surface pattern. This
frustrated pattern formation behavior was accounted for by a scaling analysis.
