A Matrix Iterative Approach to Systematically Generate Hilbert-type Space-filling Curves

Abstract

Hilbert-type space-filling curve has attracted much interest thanks to its mathematical importance and extensive applications in signal processing. In this paper, we construct the complete six Hilbert-type space-filling curves form a
matrix point of view. The address matrix for each considered Hilbert-type space-filling curve can be easily generated by a recursive manner. Besides the six Hilbert-type space-filling curves, we also construct their corresponding variation versions. The merit of the matrix approach is that the iterative algorithm is easy to implement and can be generalized to produce any other Hilbert-type space-filling curves and their variation versions.