Unfortunately neither the images or video show the beauty of watching these run at full speed in their native environment. The video is not good at all. I haven't found a nice way to capture video on my computer yet, the files are huge, the quality is poor, and the worst part is that doing the capture bogs down my computer making the sketch run abnormally slow and choppy. At least you can get a sense of what the motion looks like though. The images, while free of these issues, just don't capture the beauty of watching the plane freely wave and ripple. I think that, despite the limitations, these images and videos are still pretty awesome though and I hope you enjoy them.
Note: I forgot to turn off the [non-working] sound when doing the screen capture. Thats why the video has those crazy sounds.
This is a basic sign wave propagating from the center pf the plane.
From straight above:
and from other perspectives:
The next image are of the plain with 3D Perlin noise applied to it. Often 1 dimension of Perlin noise is used to create movement; in this case the movement in the 3rd dimension is controled by the sine wave function used in the previous images.
This last set was made by simply increasing the amplitude of the previous noisy waves. It goes to show how simple changes to this set up can yield nearly infinite variations on the final outcome. In many ways, it's hard to find an outcome that isn't beautiful.