We present research on tree structures using hexagonally and quarternarily organized imagery. The purpose is to determine and compare benefits from applying these pyramidal representations. Our motive is to develop new approaches to image computing. We compare space and time requirements of two hierarchical data structures. The basic image representation is by the septree and the quadtree data pyramids. A septree is a seven-descendant tree; values stored are found by decomposing a roughly-hexagonal planar region into its central hexagon and its six uniformly-adjacent neighbors. A quadtree is a four-descendant tree; its values are similarly obtained using the more common rectangular decomposition of a planar image. Today's technology (i.e., CCD arrays; VLSI chips) enables both the hexagonal and quartering tesselations to co-exist; likewise, lower-cost hardware trends encourage innovative computer systems for image analysis. Both image data structures presented here for static two-dimensional scenes can be extended to three-dimensional analogies. These can be used in computer vision models and in time-sequences of images for robots.