Do Highly-Logical Activities Impair Creativity?

 

This is a question I've had for a while. When a person frequently participates in a highly-logical activity (such as computer programming or Sudoku), does that strengthen or weaken their ability to think creatively?
 
**DISCLAIMER - I don't know much about psychology, so if there's a simple answer, please leave me a note in the comments.
 
I am a computer programmer. In fact, aside from writing, it's really the only major thing I spend my free-time doing. I just love the way it challenges me to break down problems, analyze the components, and put all the little pieces back together in a cohesive, efficient manner. But I also feel like a robot, doing the same calculations over and over and over and over in slightly different contexts. And when I sit down to write after working on my 2D-Shooter, it feels like the only things coming to mind are a bunch of stereotypes. The same ones, over and over and over.
 
That's normal, right? It seems like most writers have trouble with stereotypes, regardless of their favorite pass-times. I have no frame of reference, though. There's no way for me to get inside your head, see what it's like to write from your perspective, and compare to see who has the hardest time. The result is that I have no idea how close I am to meeting my creative potential. It’s maddening, actually.
 
But then there’s the possibility that spending equal times using both hemispheres of the brain (yes, I know neuroscientists have disproved the whole left/right brain thing) can actually greaten one’s creative power. Prominent historical figures like Da Vinci, who were known for both scientific and artistic contributions, seem to be concrete examples of this.

So the question really comes down to: do “left” and “right-brained” activities counteract one another, or are they additive? Was Da Vinci just a prodigy, or did his practice of art and science strengthen him as a whole?
I’m curious to hear what you think!