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A pmg Example

This movie shows the superposition of three wallpaper waves invariant under the group pmg. Each has its own characteristic frequency and so will vibrate at a different rate.

[A wallpaper with pmg symmetry]
[Movie]
A wallpaper with pmg symmetry.

The black bars show how high each of the waves is at any given instant. The initial configuration combines equal amounts of all three waves, but this image is from partway through the movie, so the bars are at different heights. One way have a negative height, while the other two are positive at this point. The color bar at the far right shows how color is used to indicate height, with the highest values colored by the color at the top, and zero at the middle.

The final image in the movie looks almost like a pattern of type p'bmg. This is because the wave that breaks the negating horizontal half-translation has nearly died out at that instant.


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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: Sep 30, 2003 9:27:31 AM
Comments to: CVM@maa.org