Fractal Cellular Textures

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.

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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.
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