This is the first cool looking demo. For each frame, the bottom two lines of the applet are filled with random noise, the buffer is gently blurred, darkened, and everything is moved up one line. Add a black-red-orange colormap, and it looks remarkably like fire.
The resulting patterns interact with one another and exhibit fairly complex behaviour. This is one of my favorite demos, because it produces intricate, nonrepeating patterns; yet underneath it's simple.
I think this is the effect behind the logo in the game select screen of Unreal (an excellent game).
Link to the source code.