The Normal of a Fractal Surface

The Visual Computer 17(4), June 2001, pp. 209-218

We have discovered a class of fractal functions that are differentiable. Fractal interpolation functions have been used for over a decade to generate rough functions passing through a set of given points. The integral of a fractal interpolation function remains a fractal interpolation function, and this new fractal interpolation function is differentiable. Tensor products of pairs of these fractal functions form fractal surfaces with a well defined tangent plane. We use this surface normal to shade fractal surfaces, and demonstrate its use with renderings of fractal mirrors.

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