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 mirror.
- Fractal function
- Fractal terrain
- Iterated function system
- Recurrent modeling
ASJC Scopus subject areas
- Computer Vision and Pattern Recognition
- Computer Graphics and Computer-Aided Design