1. A computer-implemented method for generating a portion of an image, the method comprising using a computer to perform the following actions: receiving an identification of an image texture region stored in a computer storage device; calculating a differential representation for pixels in the image texture region, wherein the differential representation represents a rate of change between pixels across the image texture region; generating a synthesized differential representation of a new texture region by sampling differential representations of pixels in the image texture region; and generating the new texture region based on the synthesized differential representation, wherein the new texture region includes a plurality of pixels stored in a computer storage device.