Generating texture maps for use in rendering visual output. According to a first aspect, there is provided a method for generating textures for use in rendering visual output, the method comprising the steps of: generating, using a first hierarchical algorithm, a first texture from one or more sets of initialisation data; and selectively refining the first texture, using one or more further hierarchical algorithms, to generate one or more further textures from at least a section of the first texture and one or more sets of further initialisation data; wherein at least a section of each of the one or more further textures differs from the first texture.