How to Construct Space-Filling Curves

Abstract

In a mathematical sense, introducing a sequential order on a d-dimensional array of elements (or cells) defines a corresponding mapping – from the range of array indices $${1,…,{n}}^{d}$$ to sequential indices $${1,…,{n}^{d}}$$ , and vice versa. From a practical point of view, such sequential orders should result from a family of orders, i.e. be generated via a uniform construction for arbitrary n (and maybe d).