  We investigated the effect of time delays on phase configurations in a set of
two-dimensional coupled phase oscillators. Each oscillator is allowed to
interact with its neighbors located within a finite radius, which serves as a
control parameter in this study. It is found that distance-dependent
time-delays induce various patterns including traveling rolls, square-like and
rhombus-like patterns, spirals, and targets. We analyzed the stability
boundaries of the emerging patterns and briefly pointed out the possible
empirical implications of such time-delayed patterns.
