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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.

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