When an oil bath is vertically oscillating with an acceleration above some critical value, known as the Faraday threshold, the bath surface becomes unstable and nonlinear standing wave patterns emerge. One phenomenon that has been observed above the Faraday threshold is the formation of Faraday-Talbot carpets, resulting from near-field diffraction. The optical Talbot effect occurs when a monochromatic wave passes through a diffraction grating. In the near-field, the formation of self- images is observed at integer multiples of what is known as the Talbot length. These two-dimensional patterns have various applications including X-ray imaging and atom and particle trapping. Two- dimensional Faraday-Talbot wave patterns have been observed in an oil bath oscillating above the Faraday threshold containing a row of evenly spaced, protruding pillars. These pillars generate sloshing waves which serve as active sources of monochromatic Faraday waves, the interference of which generates the Faraday-Talbot wave patterns. These patterns were observed to trap bouncing and walking droplets at the location of the pillar images. As an extension of the two-dimensional linear Faraday-Talbot effect, we present novel stable and transient Faraday-Talbot carpets created from a circular array of evenly spaced pillars. An understanding of the formation of stable Faraday- Talbot carpets can act as an analogy to atom and particle trapping and may provide insights into particle trapping mechanisms
