A method and apparatus are provided to generate automatically a mip-map chain of texture images from a portion of texture image data such that it may be used in texturing a computer graphic image. A portion of the texture image data is stored temporarily and is filtered to generate at least one lower level of mip-map data from the texture data. This lower level of mip-map texture image data is then stored for use in texturing. Preferably these are stored on a tile-by-tile basis where a tile is a rectangular area of the image being displayed.