Space filling curve method:An implementation and applications

The formulation of space filling curves for one-to-one bidirectional mappings between multidimensional and one-dimensional spaces is presented. The method, based on the original mathematical formulations from the late 19th century, can be implemented by using modern computer technolology. Computer implementations of the method have several potential application areas such as digital image processing in the two-dimensional case and associative data bases in the general multidimensional case. The report consists of three major topics. First, the properties and different realisations of space filling curves are described. Second, a computer implementation of the corresponding algorithms is presented. Third, some potential application areas of the method are shown. Detailed descriptions of the installed algorithms are given in the appendix