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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.


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Communications in Visual Mathematics, vol 1, no 1, August 1998.
Copyright © 1998, The Mathematical Association of America. All rights reserved.
Created: 08 Jul 1998 --- Last modified: 18 Aug 1998 23:59:59
Comments to: CVM@maa.org