Date: 01 Aug 2012

How to Construct Space-Filling Curves

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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 \(\{1,\ldots ,{n\}}^{d}\) to sequential indices \(\{1,\ldots ,{n}^{d}\}\) , 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).