Fast N-Dimensional Hilbert Mapping Algorithm

To address the problem of complexity of the high dimensional Hilbert curve, we present a novel way for analyzing Hilbert curve, which is based on a static evolvement rule table, called Hilbert gene. Based on the Hilbert gene, we present algorithms for implementing N-dimensional Hilbert mappings. According to the commands of the Hilbert gene, through performing the coordinate transformations, it can implement highly efficient Hilbert mappings. The experimental results show that our method can perform Hilbert mappings as efficiently as Z-order mappings in up to about 10 dimensions. It indicates that Hilbert mapping can take the place of Z-order mapping in practice.