I was asked the following question on Quora recently:
What part of the brain is responsible for linear thinking? What part of the brain is responsible for creativity?
Thinking   is very poorly understood, but broadly speaking in seems to involve the prefrontal cortex (PFC), with a special role for the dorsolateral PFC. Other important areas include the hippocampus and parietal cortex. Ultimately, thinking involves many brain regions, and cannot be localized to one place. Thinking is a distributed process that can incorporate many different parts of the brain. And the specific content of the thoughts will influence which brain areas are involved. If you are thinking about images, visual areas will be involved. If you are thinking about movement, motor areas will be involved.
In my opinion, the distinction between “linear” and “creative” thinking is somewhat vague. At this point, the most important thing to note is that the idea that the “left brain is rational/logical and the right brain is creative/artistic/emotional” is totally wrong  . Both hemispheres contribute to logic as well as creativity. Moreover, the use of logic can itself be a creative activity.