It would also be interesting to see how learning a non-phonetic alphabet, like Chinese or Japanese Kanji affects your brain. Learning tens of thousands of pictographs by heart is no easy feat, and I can tell you that bilingualism does not prepare you for that.
Kanji contain repeated elements ("radicals"), which form something of a graphical alphabet. Learning a new character's form is not too difficult then, you can identify that it's radicals A, B and C, in this kind of arrangement. Basically, it's neatly pre-chunked for memorisation.
The pronunciation of kanji is more difficult than their visual layout, and arguably where most of the burden is in Japanese. A single kanji can have pronunciations it's picked up from several periods in history. In practice, it just means that it might have a handful of different pronunciations in different contexts. Learning all these contexts takes time.
I'm bilingual in English and Japanese (When I am in Japan, people can't tell I'm not from Japan until I tell them).
I seem to have have better than average graphic memory (I remember taking tests and picturing a page in the textbook or a page of my notes in my head, then picturing where the information was on the page, then seeing the info itself on the page).
I have no idea if this is because of learning 2k Kanji characters though.
Learning kanji isn't quite so hard as people often make it out to be... It's not trivial, of course, but you're off by an order of magnitude. :P A native Japanese person once told more she sees kanji as images, so it probably is different, though.
