# A Family of NxN Space-Filling Z-Functions, N>1

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In [1], 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.

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Contributed by: Brad Klee (October 2019)

Open content licensed under CC BY-NC-SA

## Details

For an explicit implementation of the concatenation procedure, refer to the source code above.

Reference

[1] W. Wunderlich, "Über Peano-Kurven," *Elemente der Mathematik*, 28(1), 1973 pp. 1–10. www.mathcurve.com/fractals/wunderlich/125.pdf.

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