Abstract
Peano, who presented the first space‐filling curve, did so by means of an arithmetic‐analytic definition. Hilbert recognized that such a curve can be generated by a geometric iteration process and defined his own space‐filling curve at the outset by such a process. It appears that an arithmetic‐analytic definition of the Hilbert curve was never attempted. The four similarity transformations that are needed to generate Hilbert's curve are used to obtain such an arithmetic‐analytic representation in closed form. It so happens that this new representation lends itself readily to evaluation by computer.
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