Laura T. Thomas and Alejandro Lleras, researchers from University of Illinois at Urbana-Champaign, confirmed earlier findings that tracking even an unrelated pattern with your eyes can improve your problem-solving performance. Here's their 2007 Psychonomic Bulletin & Review paper.

I think it might explain that drawing things out during a problem-solving session, e.g. The Three Magicians exercise, helps people come up with better ideas.

Also, a recent book by Dan Roam, The Back of the Napkin, describes some really cool methods to "solve problems by drawing".