The four step theory of creativity widely cited in the creativity theory literature is a good place to begin thinking about computational approaches that can augment and supplement the process.
This kind of thinking usually happens in the context of problem solving. It is usually not an open ended creative context, such as the scenario of abstract art I have discussed before. However, on this side note, the abstract art previously discussed enters into this phase after a perceptual logic has been constructed.
The art of science. A seeming dichotomy, which may be less distinct than once imagined. Science is the careful crafting of knowledge through experimentation and verification. Methodology varies, but verification typically relies upon statistical, computational, logical, or a combination thereof in order to make its way into the realm known as knowledge. Science, as a totality of human effort, is an organic being. And knowledge, as its extension, is also an amorphous, far-reaching entity in itself. The digestion and interpretation of knowledge in humans breeds an entirely new creature: thought. (These terms are here loosely defined in order to put forth a feeling of an idea that I have. This may be a typical occurrence in this space, analytic philosophy aside…)