I like processing for quick visualizations of stuff.
I'll do simulations in it because the animation is so easy. No overhead of setting up the gui or anything.
Most recently I've been working out the best way to do inverse kinematics on it. Just about 5 lines of GUI related code makes an animated view of what would happen to the robot. The rest of the code is math and physical part classes(arms/joints/etc).
I also made a quick program to do visualizations of adding waves and standing waves when I was bored a few weeks back.
Also, the page you linked to is the Arduino, which if you'll read is based on Wiring. It's just the IDE that's based on Processing. Strangely enough, you posted a link to that site as well.