Fractal Interpolation Surfaces and a Related 2-D Multiresolution Analysis

AbstractWe consider the theory of fractal interpolation surfaces. Algorithms are given allowing the construction of these surfaces over polygonal regions with arbitrary interpolation points. A class of invariant measures supported on these surfaces is introduced and discussed as is the fractal dimension of some simple surfaces. Using these surfaces we construct a sequence of nested subspaces forming a generalized multiresolution analysis