This is something I just heard about yesterday, but seems to me like an idea we've all had and maybe even toyed with, but never had a formal name till now. They're called cinemagraphs, and the the idea of them is to present something that appears to be a still photograph with some minor elements of motion in it to jazz it up. For instance, a woman standing before a building, but with a lock of hair and the folds of her dress around her calves gently moving in the breeze. The effect can actually be kind of compelling.
I started looking through old things I had. The easiest way to create one, really, is to find some video you've shot where the camera was fixed and the frame didn't move, and then take one frame as your base "still" photo, and use a sequence of other frames, strategically masked, to create other frames adding subtle motion to the "still" image. I imagine I have something like that but I'll have to look.
The easiest things for me to find, though, were the long exposure images I took around New Year's of 2008 downtown. They idea was to combine them into high-speed movies with a lot of natural motion blur. They have a strong element of motion, suddenly frozen, in them when they're viewed as individual images. So I took a couple, isolated motion in some of the frames associated with them, and came up with these. One is of a man wandering through a world frozen in time; the other, a young couple chatting animatedly while the world around them simply comes to a stop, and there's nothing going on for them but one another.
FYI: creating the layers was done in Photoshop. Converting the layers in the PSD file, fairly automatically, was done using GIF Movie Gear, a program that finally makes the creation of animated PNGs feasible (what the hell is everyone else waiting for????), although Blogger doesn't seem to recognize an animated PNG as an image file... sigh... these things have only existed since the late 1990s, that's all... so below are animated GIF versions. >:/