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Wunderlich, Hilbert, and Moore fractal curves

The Wunderlich curves are a family of three plane-filling curves. Each curve is created by beginning with a seed shape, and for each iteration arranging copies of the seed shape in a 3×3 grid in such a way that the "end" point of one copy is adjacent to the "start" point of the next copy. Connecting the figures results in a plane-filling curve.

The Hilbert curve and the Moore curve are two famous plane-filling curves. They have similar recursive constructions, constructed here using L-systems. Such curves map points in multi-dimensional space to points on a one-dimensional line, and thus have properties that make them useful for certain types of data manipulation (such as image processing).

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Notes and References

[1] Wolfram Math, 'Hilbert and Moore Fractal Curves'. Internet Reference, 2010.

[2] Wolfram Math, 'Wunderlich Curves'. Internet Reference, 2010.