Fractal interpolation of images and volumes

We present a method for constructing fractal interpolation surfaces and volumes through points sampled on rectangular lattices. Unlike other surface constructions ours uses rectangular rather than triangular tilings, halving the number of required parameters. This method is no more complex than previous constructions and yet does not suffer from their limitations. Additionally, our construction extends easily to volumetric interpolation, for which there were no previous (continuous) constructions. In addition to an example with synthetic data, a real image is interpolated using a fractal surface. Limitations and possible improvements are mentioned.