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The human visual system encodes spatial relations along the anatomical scaffold of retinotopic organisation, yet top-down control can flexibly change the encoding of visual space. We investigated this flexible encoding of space by means of population receptive field (pRF) mapping. In separate conditions, participants performed a titrated two-alternative forced choice task on either fixation luminance, or the color or speed of elements in a bar aperture systematically traversing the visual field. Single-voxel pRF parameters were fit for each of the conditions, and their spatial characteristics were compared across conditions and retinotopic regions. Over and above changes in pRF amplitudes, voxels' preferred visual-field position and size changed as a result of stimulus-based attention. Notably, visual-field position changes were restricted to radial movement, ie to changes in eccentricity. The sign of changes in …