I don't know if I can answer properly here. As I don't have the ability to discern other people's types, I have no clue what the type is that I'm attracted to.
Currently, I am attracted to *what I perceive* as INTJ. I could be way off, and probably am, but that's what I think.
Qualities I noticed in these types of people were as follows:
Introversion. There was no awkward feeling to talk, or keep a conversation flowing. We both were content being together in silence, speaking only when needing to. When we did talk, it was usually about something technical, and those talks come naturally and flow smoothly with me. If I'm explaining something in detail, I could do it to a complete stranger and be comfortable. (While on that "professional" level.)
Intuition. I believe this is where the endless font of ideas comes from. I'm not too good at generating ideas. But I greatly enjoyed watching her come up with something (we were in photography at the time) and then I assist with implementing it. (I had a greater knowledge of how Photoshop worked, so I was able to do the technical stuff.)
Thinking. I liked this attribute because it seemed we were in the same boat. Everything I said was understood, and everything I heard I comprehended. Communication was never an issue. And never did I have to hear about her other friends. I know it sounds rude to some, but unless other people or other things are related to the matter at hand, then I really don't care for the moment. I point this out because my other friend in the same class talked a lot about her boyfriend. And other things that mattered very little when put in the grand scheme of things.
Judgement. Well, what can I say? I'm a creature of order and all that good stuff, and I can't stand the thoughts of being with someone who doesn't create/maintain order as well. I clean up other people's messes enough ---- I wouldn't want to waste energy doing that in a relationship. Relationships should work together for the greater good.