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.
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
Wolfram Demonstrations Project
Published: March 7 2011