The normal of a fractal surface

We have discovered a class of fractal functions that are differentiable. Fr actal interpolation functions have been used for over a decade to generate rough functions passing through a set of given points. The integral of a fr actal 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-defin ed tangent plane. We use this surface normal to shade fractal surfaces, and demonstrate its use with renderings of fractal mirrors.