Do you know what a Cinemagraph is? It's better than an animated GIF and catchier than a video. Usually it's a gif with most of it being frozen and only one and only part of it moving in a loop.
There's a free iPhone app that can create those: Cinegram is free, awesome and it's going to keep you busy!
Here's my first one I created just within a couple of minutes:
Now, go play!