Julesz introduced the concept of statistically defined textures and their perceptual discrimination. Julesz showed that discrimination was possible with statistics equated to third-order, specifying fourth-order textures. Klein and Tyler offered a variety of paradigms suggesting that fourth order might be the limit on human texture processing. To go beyond this limit, new texture paradigms are now introduced to avoid contamination by luminance extrema, to control local and long-range texture properties, and to provide textures without global statistical structure. Local luminance contamination is avoided by novel orientation plaids, in which higher-order rules govern the orientation of local elements rather than their coloring. These textures allow evaluation of texture discrimination up to thirty-second order by cortical pattern elements. Long-range processing is studied by random strip rotation and by interlacing of independent textures. Each substantially degrades the visibility of the fourth-order textures, revealing that the fourth-order information is conveyed largely by local rather than long-range perturbations from random statistics. Finally, textures equated at all orders can be defined in terms of their global statistics, but may nevertheless readily be discriminated in human vision. The discrimination on the basis of local perturbations implies that human vision assesses textures through a local sampling window, and is largely insensitive to longer-range statistical properties.