A Family of NxN Space-Filling Z-Functions, N>1
In , Wunderlich explores variations on Peano's space-filling curve, and in Figure 5 gives a rule, which looks noticeably similar to Hilbert's rule. Up to one initial "+" or "−" sign, the Lindenmayer definition of Wunderlich's Figure 5 can be obtained from the Lindenmayer definition of Hilbert's specimen, simply by concatenating additional symbols to the image words of "L" and "R" axioms. The extra symbols draw a right angle around empty squares in the complements of the and grids.[more]
In general, it is possible to simply draw an extra right angle around the empty squares in the complements of the and grids. Thus by induction of concatenation, a Lindenmayer rule is obtained for any grid, with integer . The Lindenmayer notation explicitly determines the space-filling -function, but more work is necessary to construct the densely-interpolated -function.[less]
For an explicit implementation of the concatenation procedure, refer to the source code above.
 W. Wunderlich, "Über Peano-Kurven," Elemente der Mathematik, 28(1), 1973 pp. 1–10. www.mathcurve.com/fractals/wunderlich/125.pdf.