Using State Diagrams for Hilbert Curve

The Hilbert Curve describes a method of mapping between one and n dimensions. Such mappings are of interest in a number of application domains including image processing and, more recently, in the indexing of multi-dimensional data. Relatively little work, however, has been devoted to techniques for mapping in more that 2 dimensions. This paper presents a technique for constructing state diagrams to facilitate mappings and is a specialization of an incomplete generic process described by Bially. Although the storage requirements for state diagrams increase exponentially with the number of dimensions, they are useful in up to about 9 dimensions.