Composite is, as the name states, an effect that can composite images together. It uses the Porter-Duff blending modes named after the writers of the paper, where it was published. For those of you with ACM Digital Library access, here's a link to the original paper: Compositing Digital Images: Porter, Duff.
The Porter-Duff blending modes are basically logical operations applied to images. For example, you can go and take an exclusive or of two images. In the original paper there was a table showing an example of each mode and some variation of that has been included in most places, where these modes are explained. Now that I have my two test subjects, Max the rat and Gina the rabbit, I can use them instead of boring triangles.
From this image, one can notice several useful relations between the different modes: over is actually the ordinary alpha compositing, out and atop are complete opposites of each other, as are in and xor.
There is a gotcha for making this kind of images: whenever you use the Background Image you need to enable it and to remember that the filter output doesn't replace the background but instead is composited over it. So, if you just created composite filter with xor mode, you'd notice that it just seems to change the compositing order. The gotcha is that the area where the both objects are atop each other is transparent and shows through the original background. So, to make these images, I actually created a solid background inside the filter to hide the original background.
There is also a sixth mode called Arithmetic. It allows you to specify the result as linear combination of input image colours. Put other way, you can specify four constants K1-K4 for the equation (result colour) = K1 * (input 1 colour) * (input 2 colour) + K2 * (input 1 colour) + K3 * (input 2 colour) + K4. With these, you can take sum of two colours (K1 = 0, K2 = 1, K3 = 1, K4 = 0), product of two colours (K1 = 1, K2 = 0, K3 = 0, K4 = 0) and plethora of other combinations. Here are a couple examples
