Creativity: Random or deterministic? Invention or discovery? I'm late to the game on this one, so I'll throw out a few ideas (sorry if they've already been touched on).
Creativity is not random, nor is it deterministic. What makes creativity seem random is it's immediateness. An idea takes shape, and there it is. But this is no random process; the creative process itself is made up of subconscious work which the creative brain is doing all the time. There's nothing random about the subconscious. The subconscious is made up of all sorts of things; the (sort of?) conscious part of the brain makes signs and symbols out of this subconscious stuff. What this stuff is or means is anyone's game; rather, it's the game of art interpretation...or expression? Yeah, who decides, really?
Creativity is not deterministic for the same reasons; By nature (by definition), creativity brings concepts to the fore of the conscious mind that were not at the fore before. Nothing determines what does or does not come up into the conscious mind in this process. It's extremely personal to the person who's consciousness is doing the work. The process is different for every creative person, and so there's nothing that determines just exactly how the process happens/takes shape. There are of course patterns that can be mapped. But for every mapped pattern of creative effort, there are at least as many unmapped anomalies that defy any sort of determinism.