Space-Filling Curves in Generating Equidistrubuted Sequences and Their Properties in Sampling of Images

A simple algorithm for computing a multi-dimensional the Sierpiński space-filling curve generalization

“…) is an upperbound. The same bound is valid for the multidimensional Hilbert curve [37], [11]. Furthermore, it is known that for the 2-D Sierpiński curve, the smallest possible constant equals 2 [26] or is close to 6 1/2 for the 2-D Hilbert curve [10], [37].…”

“…We present a simple algorithm for computing a transformation of multidimensional data points onto the unit interval using the proposed a Sierpiński type space-filling curve generalization. Specific ideas regarding the generalization of the Sierpiński curve were considered in the author's monograph [37], but the algorithms presented in this work are new and have not been published anywhere.…”