Wunderlich Curves

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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 (March 2011)
Open content licensed under CC BY-NC-SA



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

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.