If you have an iPhone, you may already be familiar with the Live Photo feature that it has. When Live Photos are enabled, whenever you take a picture, the iPhone will also capture a few seconds before and after the shot is taken. This gives the photo some motion, almost like a very short video clip. But you may not know that it can actually go beyond just that basic functionality. After you take a photo of something that moves, go to edit the photo and swipe up. This will reveal a few different effects that you can apply. You can select "Loop," which will loop the Live Photo with a slight dissolve, or "Bounce" which will play it forwards, then in reverse. There's also a "Long Exposure" selection.
Once you've created your Live Photo, you can use the GIF Toaster app on iOS to turn it into the more standard GIF format.