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.
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