Dendritic arbors of retinal ganglion cells (RGCs) collect information over a certain area of the visual scene. The coverage territory and the arbor density of dendrites determine what fraction of visual field is sampled by a single cell and at what resolution. Yet it is not clear whether visual stimulation is required for the establishment of branching patterns of RGCs, and is there a general principle directs the dendritic patterning of diverse RGCs. By analyzing the geometric structures of RGC dendrites, we found that dendritic arbors of RGCs underwent a substantial spatial rearrangement after eye-opening. Light deprivation blocked both the dendritic growth and the branch patterning, suggesting that visual stimulation is required for the acquisition of specific branching patterns of RGCs. We further showed that vision dependent dendritic growth and arbor refinement were occurred mainly in the middle portion of the dendritic tree. This non-proportional growth and selective refinement suggested that the late-stage dendritic development of RGCs is not a passive stretching with the growth of eyes, but an active process of selective growth/elimination of dendritic arbors of RGCs driven by visual activity. Finally, our data showed that there was a power law relationship between the coverage territory and dendritic arbor density of RGCs on a cell by cell basis. RGCs are systematically less dense when they cover larger territories regardless of their cell types, retinal locations and developmental stages. These results suggest that there is a general structural design principle directs the vision dependent patterning of RGC dendrites.