I became fascinated with abstract composition because of movie posters. I'd always liked to draw, but posters like the one at the top of this post really captured my imagination. They weren't just drawings of a particular scene, they were a lot of elements carefully woven together. That is, a collage, which is an abstract composition.
This type of design is seen everywhere, and is most popular in movie posters. Back when this movie was new, the transition has begun from hand-drawn illustration to adaptation of photographic images that were enhanced. And it really sets a feeling of action and excitement more than just a photo of the hero and a pretty girl standing next to him would.
Of course, this type of abstract composition isn't easy to do. As I got more interested in pure composition I became interested in the great masters of abstract composition, like Piet Modrian. Little by little I came to understand that it's all a careful balance of shapes, sizes, and colors. And it's not done with a formula, it's done by eye. And once I started to understand that, I started to understand all types of abstract composition, from architectural design to landscape design.
If you're starting out on this, don't expect most people to understand. The poster up there, which to me shows a masterful combination, is not seen that way by most people, nor should it be. Most people just get an impression, and they see actors they may or may not like, or just girls that are scantily-clad. Of course I see that, but I also see the boat coming out of the mouth of the alligator, the girl sitting on a gun barrel, the way that the cards fan out to draw your eye to the center, along with the explosion of color behind Roger Moore's head.
I've had the good fortune to have some awesome design teachers in my life. These were the people who taught me the careful balance, the rearranging of abstract shapes, the juxtaposition of color and form. And I learned that excellent design is something that is easily ruined, by just a small change here or there, like the notes of a song, which is also an abstraction.
Whether you're doing a collage, or scrapbooking, or anything like that, you're dealing with abstract composition. The more you look at it, and the more you experiment with it, the better your design will get. It isn't something that can be translated into words, but just because it can't, doesn't mean that it doesn't exist. As a graphic designer, it's my art form.