> Perhaps what I should do instead is set the derivatives to zero for the 
> edge points? But that would still give me a set of points that never 
> actually move... hmm...

No no, set the 1st derivatives outside of the grid to be zero, then when you 
calculate the 2nd derivative you could still get a non-zero value.

So at [0], you would want to calculate:

2nd deriv = (x[1] - x[0]) - (x[0] - x[-1])

What i mean is to replace the (x[0]-x[-1]) term by zero.  I have no idea if 
that will work or not, but it seems like it might.

>> I just checked, a 1024x1024 simulation runs at 240 fps ;-)
>
> NOOOO!! Damn you! >_<
>
> My simulation manages about 2 seconds per frame for 100x100...

Hehe I just worked out how to use YouTube ;-)

http://www.youtube.com/watch?v=0GeDiFxCY9s
(make sure you click the "watch in high quality" text)

That's using a 256x256 grid, but it's drawing it in 3D as well as 2D so it 
runs a bit slower (~150fps).

>> http://www.youtube.com/watch?v=D4FY75GwA00
>
> That's a GPU?? You'd have to have, like, 50,000,000,000 polygons to make 
> it anywhere near that smooth!

Not that many, you just need each polygon to be roughly the size of a pixel.

> (And the RAM requirements alone preclude doing that.)

The results are stored as textures on the GPU, the actual polygon data does 
not ever exist fully, the GPU creates the polys on-the-fly from the texture 
data.  I think every GPU is fine with a few 1024x1024 textures.

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