I've got a friend whose grandfather was, in his heyday, a famous muralist. As an aside, I've never met him but I did work with his wife for a semester when I was at school. My friend is a very accomplished sculptor who has also studied painting and printmaking but I think he still somewhat lives in the shadow of his grandfather. At any rate, he's never quite completed a degree although he probably has more than enough coursework under his belt. He told me he really only took the classes he wanted to take -- the classes he thought he'd get something out of. However, he did share this piece of advice with me which his grandfather told him some time ago. If you're going to make a masterpiece, plan it out. Have a good idea of what you want it to look like and then make it look like your idea -- no happy accidents along the way. Once you've made one, make another to prove that wasn't just a one off. After you've made a second, make a third to prove you can do it any time you darn well please. Then you can do pretty much whatever you darn well please.
Needless to say, he was rather amused at me one day when he was over at my house and I was rather busy making happy accidents. Can't help it.... they're so much fun!!!