The Julesz paradigm involving statistical constraints for the study of texture discrimination is extended to continuous-contrast repetitive patterns by using nth-order autocorrelation functions rather than Julesz's nth-order statistics. Second-order autocorrelations specify the power spectrum of the pattern, and the higher-order autocorrelations specify different levels of phase relationships in the pattern. A method is presented for generating patterns with statistical constraints of any order, in one and two dimensions. We show that, without scrutiny by foveal attention, discrimination of continuous textures fails at about the level of fourth-order constraints. An explanation for this failure based on the bandwidth of spatial-frequency-tuned mechanisms is excluded. The autocorrelation approach therefore may provide a general metric for the description of phase discrimination of repetitive textures.