A selection of textures common in face-centred cubic (fcc) materials have been modelled using a computer simulation technique. Orientations were arranged on a grid of hexagons in order to represent a two-dimensional microstructure, and the statistics of the resulting microstructures were analysed with respect to low-angle boundaries (LABs) and I-lines/U-lines. Most of the results pertain to a single reference texture of varying intensity, with deviations progressively reducing from to away from the exact texture. Two types of microstructural unit are recognized: `clusters', which are groups of grains joined by low-angle boundaries, and `clumps' which are connected U-lines. It is evident that there is considerable clumping of U-lines in these simulated microstructures. The effects of clusters, and more particularly clumps of U-lines, on material properties are discussed.