Deltas are complex ecogeomorphic systems where features such as channels and interchannel islands are present over a wide range of spatial scales. A quantitative description of the morphology of deltas is fundamental to address how they react to changes in climate forcing and human pressure. In particular, it is interesting to ask how the distributary patterns we observe in coastal areas around the world result from processes and external forcing acting on deltas, and how such patterns might be related to deltaic function, vulnerability, and resilience. Using the example of the Ganges-Brahmaputra-Jamuna Delta, we show that the statistics of island size, shape factor, aspect ratio, and nearest-edge distance show distinct spatial patterns. Comparison between regions identified by our statistical analysis and a physiographic zonation of the delta suggests that the planform extracted from satellite imagery carries the signature of processes responsible for delta formation and evolution and of vegetation. The tidal region is characterized by high channel density, small islands, and short nearest-edge distance (shortest straight-line distance to the nearest water). The results suggest that regions of the delta characterized by presence of vegetation and active transport of water and sediment are statistically distinct from less active regions. Further, we perform a weighted connectivity analysis of the channel patterns based on channel width. The analysis suggests that channels connecting the upper portion of the delta to the coast do not play a significant role in the transport of water and sediment.