Squares this time. Both applets give you two squares that you can move around, scale, rotate. One applet emphasizes the intersection of the two squares; the other, the union. The aesthetic this time seems to be big blocky lines. I'm not quite sure why, but there's something large and monumental about squares.
I'm happier with the intersection graphic. The vertical bar density works well with the square frame size, I think. Also, the coarseness of the bars means that you can't quite make out the intersection shape, blurs out that hard polygon a bit. When I first worked on this problem I wanted to solve for the polygon of intersection explicitly and manipulate that. Because everything is convex it shouldn't be too hard, and we even came up with an algorithm to do it, but it would be a lot of work to implement. So instead I just test a lot of points to see if they're inside both polygons. Ick!
The union applet doesn't feel quite finished. When both squares are lined up right the resulting picture is quite beautiful. But there are a lot of ugly pictures there, too, especially when the negative space inside is concave. The line between the two dots is only drawn when the shapes are "close enough", where close enough roughly means that the interior space is small enough to feel like its own object.
The keyboard interface to both applets is pretty awful. It'd be much better to be able to grab a corner of the square and drag it around, but that wasa too much to implement just now.