This paper compares a series of traditional and deep learning methodologies for the segmentation of textures. Six well-known texture composites first published by Randen and Hus{\o}y were used to compare traditional segmentation techniques (co-occurrence, filtering, local binary patterns, watershed, multiresolution sub-band filtering) against a deep-learning approach based on the U-Net architecture. For the latter, the effects of depth of the network, number of epochs and different optimisation algorithms were investigated. Overall, the best results were provided by the deep-learning approach. However, the best results were distributed within the parameters, and many configurations provided results well below the traditional techniques.