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The global structure of a pulse-modulated 13.56-MHz asymmetric surface barrier discharge plasma has been investigated in atmospheric-pressure air. Intensified-CCD images were exposed over 20- μs radio-frequency pulses for three input power cases. The discharges do not appear to move significantly during the pulses, even though they are integrated over more than 200 oscillations of the applied voltage, and this allows for the observation of organized filamentary structures. The quantity and propagation length of the discharges are observed to increase with increasing input power, and the onset of branching occurs at a uniform propagation length. Subsequent to branching, a distinct decrease in luminosity is observed as the branches realign to propagate parallel to the original discharge. The spacing between the tips of the filaments is very similar to that of small indentations present on the surface of the dielectric barrier.