Rules are made to be broken, even when you're working with something as seemingly uncompromising as composition.
A visually appealing image is equal parts creativity, mathematics, and intuition. There are many concepts that teach us how to assemble elements within a frame to give it the maximum amount of aesthetic energy—the rule of thirds, symmetry, balance, etc.—but they certainly aren't the only ways to make that happen. Photographer James Allen Stewart shows us how to break the rules of composition in this interesting video:
Stewart highlights two major ways one can deviate from classic compositional rules, namely the rule of thirds:
Balance between light and dark
Consider for a moment the denseness of light and dark elements—light elements seem to "weigh" less than dark elements. This quality of "weight" does interesting things to an image. For instance, say all of the darks gather on one side of the frame; your image will feel "heavier" on that side, creating the illusion that the image is being pulled down in that direction.
This is an important concept to understand, because according to Stewart, the rule of thirds becomes less important to composition if these two elements are balanced within your image.
This is probably the most interesting concept Stewart introduces, that since we tend to "read" or "write" an image from left to right, you can compose your image like you would a story, with a beginning, middle, climax, and end. Consider the following images:
You may agree or disagree with Stewart's assertions about composition. What works for one image may not work for others, nor for the entire film as a whole. But I think it's worth learning about because the more tools you have in your arsenal, the better equipped you'll be when composing your shots.