We describe the primary visual cortex (V1) as a system of maps. The global retinotopic map distorts the visual field coordinates in a manner that enables efficient computation of rotation and scaling. We describe the non-retinotopic response properties in V1 in terms of a repeated tiling of local maps, each the size of an orientation pinwheel. Together these two mappings can be formalized as a four dimensional representational, space, in which two dimensions are tiled locally within two global dimensions. We present evidence from brain anatomy and function to support this formalism. A consequence of V1 conceptualized at a four dimensional representational space is that it enables rotation and scaling of visual objects about arbitrary points in the visual field.
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