CLICK TO SEE IT MOVE.
You see these on Tumblr a lot, sometimes as photos and sometimes as 3D generated. Fortunately, the 3D kind are easier to work with since you get perfect camera control.
Essentially, you’re hijacking the brain’s sense of parallax to create depth. The background is moving left and right, the foreground is a little bit. Whatever the camera pivot point is stays “fixed” as the depth when the brain puts it together.
So. Super simple setup, and you can use basically any model for this, though some will look cooler / work out better. Ideally, you have three planes: foreground, focus point, background.
So you have your model – whatever it is – and your first camera positioned where you’d normally put it. I just UV mapped a spiral image to this wavy line I rotated; whatever. The important thing here is that my focal point is the cursor and that I’ve rotated two extra cameras around that point (+/- 5 degrees, but that’s arbitrary. Too much angle will lose focus because you only have three frames to work with – jumping around too much is just confusing strobe. Try less, maybe, for a more subtle wobble). The only thing that matters is your cameras make an arc (so they’re the same distance away. You can use constraints against an Empty if you want, but rotating in one axis works too) and the angles converge on the focal point.
Render the three frames. I’m labeling them here that the left camera is 1, middle is 2 and right is 3. Protip: you can activate another camera as being the camera to be rendered from by using CTRL-0 on the numpad with that camera selected. It’s exactly like the normal 0 going into the camera view, but the CTRL bit also makes that camera the active one.
You can use GIMP / Photoshop or any number of .gif assembler programs for this part. I Googled this and it seems to work well, but my five minute using it isn’t exactly a full review. Take your frames and assemble them 1, 2, 3, 2 which creates that loop back to the beginning frame. Mine is a 50 ms delay, but play with that too, probably working in conjunction with how far apart the cameras physically are. If it’s a more subtle wobble you don’t need it to go as slowly, simulating your one physical head moving around the object and the time it takes.
That’s basically it. It’s super easy, you just need to take a little care with how the cameras are positioned.