The discovery in a difference in the way of thinking of the two halves of our brain can be attributed to research by a psychobiologist named Roger W Sperry. His work revealed that the right half of the brain is responsible for processes that involve intuition and the ability to process information in a simultaneous way. Artists first have to be able to create a complete picture of the art form in their brains and then break it down to make decisions on the color, material, etc. to be used. This would require an extensive use of the right half.
The left half of brain on the other hand is the part that can handle operations which need to be done following a sequential order with the final product emerging as the pieces are put together.
Though, the way the two halves think is not exclusive, the importance of the right half can be judged from the fact that the percentage of artists who are left-handed is substantially higher compared to the percentage of left-handers in the general public where it is one in ten. This follows from the fact that the movement in the right half of our body is predominantly controlled by the left half of the brain and vice versa.