I think in pictures and patterns. I do a lot of problem-solving in my job, and I can see the situation, the various parts of it, and the solution(s) as a diagram. That means that I've often found the solution when others are still discussing (...arguing over...) irrelevant details.
Of course, being autistic and not great with the whole social dominance games thing, I tend to get ignored.
I see pictures and patterns in other ways, too - when shooting, I can see how the target is moving, how the shot will move, and what I need to do to bring the two into conjunction (of course, doing it is a whole different thing, but hey, at least I know what I'm doing wrong...). It presents itself as a sort of diagram, with the motion of the target and the shot in blue dotted lines.
When flying, I can understand how the forces act on the aircraft to make it do certain things (visualised as more blue lines...).
And to me that is pattern recognition, but then perhaps all artists who are good learn to develop that anyway
I think composition is mostly innate - although you could probably learn it by rote, you'd probably never have that instinct for a great art photo.
Two people I know (husband and wife) are both ex-police officers who were taught photography for surveillance by the police. The guy has often said to me that he can take a very accurate photo through a keyhole of someone doing something they shouldn't... but it's just a photo. When his wife (who had exactly the same training) does the same thing, it's
art.
She is also the person who - during the early years of their relationship - made sure that every time she took a photo of him, it looked like he had something growing out of his head. Probably a different composition skill, there! (It took him years to catch on...)
There's some research indicating that across the whole population, some people think in words and some people think in pictures/patterns. However, picture/pattern thinking is more common in autistic people than in the general population.