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A Gallery of Movies

Here are five more movies showing the vibration of a wallpaper drum. Each shows the superposition of three wallpaper waves, but without the vertical bars to give the height of each wave at each instant.

One thing to notice in these movies is that a single wallpaper wave is traveling fastest when it passes through its equilibrium position, f = 0. This is when the temporal cosine function is zero, and its derivative, a sine function, is highest. In the movies, watch for a sort of "swoop" effect when the membrane is moving quickly.

Another thing to observe is that occasionally there are instants when one of the component waves is zero and the pattern takes on a higher symmetry than it had exhibited originally. Some of the patterns have instants where they look pretty much like checkerboards or hexagonal grids of dots.

[p4g movie]
[Movie]
A p4g movie.
[p3 movie]
[Movie]
A p3 movie.
[p6 movie]
[Movie]
A p6 movie.
[cm movie]
[Movie]
A cm movie.
[cmm movie]
[Movie]
A cmm movie.

There are many more movies waiting to be made: movies showing a 3D view of the wallpaper, movies with other color models than the ones we used here, and movies of vibrating wallpaper with negating symmetries.


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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 9:27:33 AM
Comments to: CVM@maa.org