VW - CVM 1.1

Some Unsolved Problems

Color-turning wallpapers:

We think the classification of these will not be too difficult. But we are not currently working on this, waiting for a more abstract formulation of this entire subject in terms of group representations.

Vibrating wallpaper on the sphere:

There aren't many groups of symmetries of the sphere, so one ought to be able to find a basis for the spherical eigenfunctions invariant under each of these groups.

Vibrating wallpaper in the Poincare disk:

Here, of course, there are infinitely many groups of isometries to play with. We are in the progress of using Eisenstein series (from the field of modular forms) and the technique of domain-coloring to make pictures of these.

Stereograms:

With our methodology for constructing repeat patterns, we think it should be possible to deform the functions to introduce stereogram images. We have experimented just a bit with this, but don't have any results.

Directions for Future Work Some Programming Challenges