On Multidimensional Curves with Hilbert Property

Indexing schemes for grids based on space-filling curves (e.g., Hilbert curves) find applications in numerous fields, ranging from parallel processing over data structures to image processing. Because of an increasing interest in discrete multidimensional spaces, indexing schemes for them have won considerable interest. Hilbert curves are the most simple and popular space-filling indexing schemes. We extend the concept of curves with Hilbert property to arbitrary dimensions and present first results concerning their structural analysis that also simplify their applicability