Lostinidlewonder has made one or two insightful observations here. Improvisation pushes the bounds of rhythm, in particular, far beyond composition. It has to, because notation cannot capture rhythm beyond a certain point at all.
The sort of highly structured, pattern based improvisation, largely dependent on very rapid mental arithmetic, used to be met with in many accomplished professionals. It still is in the jazz field. My teacher was a case in point. He was quite well known, knew many famous musicians, and had musical gifts which approached perfection. In private, he practised the organic, unconscious variety but in public and in lessons he demonstrated the formulated approach.
He would never let me hear his tapes wherein he really let himself go, but left instructions with his widow that I, and nobody else, was to hear them after his death. I couldn't make up my mind whether this instruction was funny or sad. They were, of course, far more vital and interesting than anything I had ever heard him play.
The silly part was that he was always instructing me to "let my mind run free" while maintaining a consciously calculated (but technically and harmonically formidable, I have to say) notation based stance himself. I think he must have worried that his famous friends would consider his private playing unseemly. With my being just the boy down the road, so to speak, it didn't matter and he could be himself, at least in terms of spoken opinion.
Thanks largely to the admirable public examples of Jarrett and others, there is no reason nowadays for anybody to inhibit the unconscious. It is now "legitimate".
Well ... still perhaps not quite, I fear.