All my creativity was focused, a result of my profession as journalist. Let's say my assignment is to report on the growing number of mortgage defaults in my hometown. Let's assume I know next to nothing. My first job is to find out what's going on enough to understand it. Then I cram more information in on top of that. Then I do nothing - like Cognisant, I don't think about it. Usually, within 24 hours of stopping information intake, an idea, insight, epiphany, whatever, comes bubbling up without conscious effort on my part. That's what I then base the writing around, usually with the background paradigm that I also know how I want people to feel after reading about what I've figured out. "Writing for effect" or something. It has broader application, and seems to be something that INTPs get immediately because so many of us have at least some innate desire to figure things out and then share it.
Immersion, saturation, then a rest spell, then pow. That's one way.
The more recommended way to be creative, which also works for us, is to see the goal, then work backward through the steps you think are needed to reach the goal, then take the steps and revise as necessary. That's a different kind of creativity. But it always seems like "get more information about x" is one of the steps. :-)
We think. Thinking works best at generating creative ideas when it has lots and lots of raw information to chew on. It's fertilizer, which non INTPs often refer to as bullshit. However, we grow the biggest corn.