I love Kurt Vonnegut's book Breakfast of Champions. In this book, a modern artist is one of the main characters, and he paints minimalist paintings featuring an "unwavering band of light" which represents all that is "alive and maybe sacred" in all of us. The artist's paintings are simple straight lines painted on canvas.
In my first novel Paper Tiger (okay, it's my only completed novel), the main character connects with a wacky and passionate art teacher who pushes her to explore her creative voice. Toward the end of the book, the teacher has her student create a sloppy, expressive collage. Then she cuts a small window out of cardboard and has the young girl "frame" small, essential areas of her collage (using the cardboard window as you would the viewfinder of a camera). The girl moves the frame over different areas of her artwork until she finds one perfect curve of red sliced by a sliver of yellow. Then, she creates a giant painting of this one small area--the essence of everything that she has learned over the course of a year. The painting itself is rich and painterly--not a simple minimalist rendering--but it's structure remains that one curving arc.
I just read a great post by the Disco Mermaids in which Robin talks about the theme of her book which magically presented itself to her--kind of like Vonnegut's "unwavering band of light." It's a tricky and often elusive thing to find--that essential thing that makes our artwork or book exist and breathe.
I do believe that once you find that fundamental core in your writing, you can and should exploit it. This makes the cutting and revising process so much easier, almost sublime--everything that supports the soul of your story should stay and be made stronger, while those extraneous plotlines and characters should be eliminated . . .but, you can always leave some Jackson Pollock splatters in there--as long as they give support to the story at its heart.
(photo: Onement 1 by Barnett Newman 1948)