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Wunderlich 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.

Contributed by: Robert Dickau

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Snapshot 1: the first and second types of Wunderlich curve begin with an S-shape, where the start and end points of the larger figure and each copy of the figure are at opposite corners of its bounding square; the third type has start and end points at adjacent corners of the bounding square.

Snapshot 2: hiding the connections between copies of the figure makes the relationship to the seed shape clearer

Snapshot 3: as with any plane-filling curve, the limit of any of the Wunderlich curves is the unit square

Fractal (Wolfram MathWorld)

Peano Curve (Wolfram MathWorld)

Recursion (Wolfram MathWorld)

"Wunderlich Curves" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/WunderlichCurves/

Contributed by: Robert Dickau

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