In the synthesis of natural-looking textures, it is common to mimic the self-similarity found in many natural (fractal) systems by mixing copies of a synthetic texture generated at different scales. A "fractal" texture is typically produced by summing the first few "octaves" of a particular texture function. In this case, we use Worley's cellular texture, which combines the first few nearest-neighbor distance functions, to , for a set of random feature points. Adjust the weights of to with the sliders. Interesting results can also be obtained using alternate distance metrics.
This Demonstration is based on S. Worley, "A Cellular Texture Basis Function," in SIGGRAPH '96 Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, New York: Association for Computing Machinery, 1996 pp. 291–294.
Given a set of random feature points, we can compute the distance from any point to the nearest feature point. Call this nearest-feature distance function . The function that returns the distance to the second nearest feature is , and the nearest-feature distance, . Cellular textures, Worley observed, can be generated from linear combinations of the first few . Producing fractal versions of these texture functions can reproduce interesting natural-looking textures with minimal information input.