Hierarchical textures

Rich, interesting patterns create an oasis of aesthetic pleasure between the arid lands of complete randomness and complete order. In addition to their inherent beauty, patterns prove useful in graphics when we use them as textures. Textures were originally used to add color detail to shapes. Today, textures control everything from shape details to the placement of extras in digital crowd scenes. Though not appropriate for everything, such patterns can be used for applications from ornamentation to creating complex 3D structures and motion. One easy and powerful way to create rich textures is to start with something simple, and then use that seed along with some rules to "grow" something more complicated. Lots of growing schemes produce both repeating and non-repeating patterns. One of the simplest techniques is called "tiling", where you place down multiple copies of a single starting shape, or tile, according to some (usually simple) rules. You can create rich tilings in surprisingly many ways. I look at a tiling technique based on using a set of simple symmetry operations.