lol, that recent one was REALLY random as of now. A crazy bunny with dislocated eyes, each different colors and carrots around him! Awesome drawing, made my day O.o
If you use the GIMP or some version of PhotoShop (e.g CS2), then what you do is:
1) Create each frame of the animation in a separate layer. 2) Arrange the layers sequentiallly (make sure they line up fine by looking at each layer individually) 3) In the GIMP, there's a plugin that optimises (cuts out the redundant parts of the image) and converts into .gif ready format. This is done by: a) optimising b) converting the file from a RGB format to either grayscale or indexed (255 or less color palette), c) giving the layers attributes to determine how the animation plays.
4) The layer should then read something like "Layer 1 (replace)(100ms)"
(replace) means that the previous frame is replaced. There is also (combine) which means the frame is simply placed on top of the previous frame. (100ms) means that the frame is shown for 100ms, and this can be fiddled with too.
5) After that, use the playback function (if you can find it) and save as gif! If you haven't already converted to indexed/grayscale mode and set your layer attributes, you will need to do this now, but I highly recommend doing all that *before* saving as this saves space.
Otherwise the filesize will kill your connection. I estimate that properly optimised, a eight frame animation (that should cover your funky rabbit pic if the ears, the eyes and the carrot moved) would be about 100kb at most.
Another example of a (rabbit-themed, lol) .gif animation is the 5th post here (yes, shameless plug, sorry :P) I embedded it because the animation is a whopping 32 frames but the filesize is a bare 210kb. How did I do this? Really strict optimisation and indexing.
I'm not sure what image editor you use so I'm sorry if this is a bit confusing. I could probably make it clearer, and even include pics or some kind of animated walkthrough!
(p.s. if you want, I can even do it for you as an example, but of course I will not show it publicly, just send it to you to show you what it might look like)