My attempts to make a mask with moving ink proved pretty damned impossible with the means in my possession. Theoretically, though, it is possible to achieve that effect.
Basically my plan was to cut a ziploc bag into two sheets of plastic. Then use something (all I could think of was glue) to create "pools" of sorts on top of one sheet of plastic and let it dry. After that, you should have a barrier in which to put in some black ink mixed with olive oil (not sure about the ratio of ink to oil, but I'm going to guess much more ink). Add a little more glue to the barrier and press down the second layer of plastic on top. What should happen after it dries is that you seal the oil and ink into a contained space on the plastic, and when you move around the ink and oil move as well, never mixing. You place the plastic sheet over a plain white mask with eye-holes cut out, and put a thin white legging over that so that the plastic is covered. What should happen is the legging should be thin enough for the ink to come through, but since you're wearing a white mask underneath your facial features don't. It isn't a mask that creates different inkblots, but it will have a sort of motion effect, and that's way better than just drawing a flat ink blot on your white mask.
I had lots of problems with leakage and the glue being very unreliable with containing the other fluids. Anyway, I couldn't get it to work in time for Halloween, but maybe for the movie premiere.
So, giving up on that, I took a photo of my costume with your basic white mask and sharpie marker design. I went for the design used on the screenshot of Rorschach blowtorching a SWAT team member. It's simple, allows for vision through the mask, and it looks very much like a Rorschach ink blot. A lot of people go overboard with the design on the mask and I think it makes it look pretty bad. Other than that, I wish I could have found a darker trench coat, but this was all there was at the Salvation Army (and I checked two or three times).
Anyway, it's a decent Rorschach costume: