If you didn't see the 2011 action film "Drive," directed by Nicolas Winding Refn, you should definitely check it out. Apart from it gratuitous violence, it is a fantastic work of complex cinematography and artistic storytelling. In this video review, Tony Zhou puts together another great analysis discussing how the use of quadrants add a unique dimension to the overall film. Zhou is also known for his breakdown of Edgar Wright's use of visual comedy in his ongoing series (and Vimeo Staff Pick), "Every Frame a Painting."
Zhou uses examples where splitting the frame into an upper and lower half, as well as right and left half, can split the scene to tell two different yet paralleled stories. Breaking down a frame into quadrants, thirds, or halves has been an ongoing practice in cinema. However, "Drive" serves as a great example to using these very simple composition breakdowns to bring a film to life.
The framing technique additionally allows us to be constantly entertained in our viewing experience. Though the storytelling is similar across each quadrant, the allowance for our eyes to wander through the frame keeps us engaged and "in" the film. Zhou does a fantastic job explaining these principles. His Vimeo page is full of great shorts, much like this one, that give a very simplified breakdown to complex yet simple composition techniques.