Abstract: A method is provided for the fractal representation of data in which a representative continuous n-dimensional surface is defined as a first approximation to the original data. Residual data is formed from the date and the n-dimensional surface, and is then divided into a first number of regions. For each of the first number of regions, the following steps are performed: A number of domain regions are determined from the data; for a current one of each of the domain regions, a second representative n-dimensional surface is formed from the current domain; a (domain residual is formed from the current domain region; and the second representative n-dimensional surface, and a closest distance or error measure is determined. After processing each of the regions, the representation of data is stored.

Abstract: A method is provided for the fractal representation of data in which the data (902) is divided into a first series of overlapping regions. A weighting function is applied to the regions. The weighted regions are expanded onto an orthonormal basis, and the orthonormal expansion is truncated at a predetermined point. A residue is formed between the data (902) and the truncated orthonormal expansion, and a fractal approximation to the residue is determined.