The Art of the Wunderlich Cube - MathLapse
We define a Wunderlich cube to be a cube whose surfaces contain raised impressions of the reflections of seed shapes resembling the letter S. The video shows how this cube can be rolled leaving a trail which can become the Wunderlich curve.
Walter Wunderlich is attributed with the discovery of three space-filling curves called Wunderlich curves. In contrast to the Hilbert curve, which involves a square of size 2n x 2n, Wunderlich curves involve squares of size 3n x 3n.
A Wunderlich curve is constructed using rotations and reflections of an initial seed shape to create patterns which can be connected to form a space-filling curve. Wunderlich curves can be constructed iteratively in a fairly intuitive fashion. In this video we take a look at the first Wunderlich curve, which we will simply refer to as the Wunderlich curve.
The Wunderlich curve shown in the video is constructed using a seed shape similar to the letter S, and its 90 degree rotation. Using these shapes, a 31 x 31 cell grid can be tiled in a checkerboard-like fashion. The shapes in the tiling can then be connected to create the Wunderlich curve. A larger Wunderlich curve can be created by using the 31 x 31 pattern as the seed pattern to “tile” a 32 x 32 cell grid.
We define a Wunderlich cube to be a cube whose surfaces contain raised impressions of the reflections of seed shapes. The video shows how this cube can be rolled leaving a trail which can become the Wunderlich curve.