The finished product:

(the colors in this photo aren't great - the background animation is more of a teal color and the time is in white)

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The animation is a simple Perlin Noise scroll, with the frame rate limited in steps by one of the encoders.  I took a few swings at the height field water simulation but I'm not much of a programmer and I wasn't able to get anything to look very good on the matrix.  Maybe I'll come back to it in a few months/years.

The animation plays smoothly, but I've been leaving it turned down to 1 frame per minute so the the motion isn't distracting out of the corner of your eye.  The time moves up and down the display twice over the course of a day, too.  At first I set a static brightness that looks good during the day or with the room lights on, but that level lights up practically the whole room by itself at night - so the potentiometer controls the brightness of the matrix.