Blame it on the Greeks and Italians
Beginning photographers are often criticized for weak composition and seek a set of rules that will help them "fix" their images. Rules are meant to be broken, and no sooner will you read this than you will see an astounding photograph that breaks all of the rules. So, who wrote the rules?
The rules or concepts of composition are derived from observations of nature and the success of images that emulate nature in their design. Design in nature has a certain order about it, and our brains are naturally wired to recognize and appreciate those relationships. The Egyptian pyramids are a prime example of mathematical balance. The Greeks analyzed composition and understood the relationship between the height and width of images and the space within them. The Greeks and Italians were good at analyzing nature mathematically and applying their studies to various aspects of life, like architecture, sculpture, and painting. Mathematics was simply the means of communicating the concepts.
If you examine nature you find Fibonacci numbers (0 and 1 and each subsequent number is the sum of the previous two), and a variety of terms derived from them; the Golden Mean, the Golden Section, the Golden Rectangle, the Golden Spiral, etc. They are mathematical representations of natural patterns that comprise the everything; galaxies, conch shells, sunflowers, trees and leaves. They are essentially the mathematical explanation for the patterns in nature. They may be interesting to explore for a few moments on a rainy day, but the intellectual exercise can be boiled down to a simple concept. We intuitively recognize composition based upon the visual clues that nature provides for us. Over the centuries art has used this natural composition as it represents successful balance in visual media, whether it be painting, sculpture, or photography. We like what we see when the visual clues in an image follow the "rules" of nature and the balance it provides.
The image of a sailboat on the water shows the rule of thirds grid of the crop tool over the image. The darker blue outside of the crop is the part of the image to be removed (the original image was cropped to square to make this illustration fit better). As you move the crop the grid lines move to assist you in visualizing the balance of your image. The grid overlay is symmetrical and centered and can assist you in making decisions for symmetrical crops and crops with perspective considerations. The lines can also be turned off completely. Not only is the sailboat a consideration for the crop, but the wake and the larger lighter area that extends into the center of the image influence the overall balance of the composition.
If you divide any quadrangle into thirds you establish 4 intersections of the lines and these points are what people mean when they refer to the rule of thirds. The rule of thirds is a simplification of the balance points. Most photographers learn about the rule of thirds as a tool for learning composition. The intersecting points are where the brain will presumably delight in the positioning of primary subject matter or visual weight. It does not mean that the subject must be precisely at those points. If you determine the division of space with the Golden mean or Bakker Saddle you find points slightly closer to center than the rule of thirds. The Bakker Saddle divides an image with a line from opposite corners, and lines from the other corners that intersect the diagonal at 90 degrees. The Golden Mean and Bakker Saddle methods are virtually identical and very close to 60/40.
There is also the consideration of formal vs. informal composition; symmetry vs. asymmetry. Symmetry is when a subject sits so that the left and right sides (or top and bottom) of the image mirror or balance each other. When this happens and the center line is not accurately centered it sets up a tension that cries to be resolved. For this reason, if you have an image that tends to want to be symmetrical and centered, you should take efforts to make sure it is accurately done. The visual pull of a line in an image to be near an asymmetrical point is not nearly as strong as the pull of a line to be dead center if it is close to already being there. In an asymmetrical or informal composition the primary lines are not centered but closer to the off-center points. Most images tend to be asymmetrical.
If you make a grid with the Golden Mean numbers and overlay it on paintings of the masters such as Leonardo Da Vinci's The Last Supper, you will see how effectively he used the mathematics of composition. The Last Supper is especially interesting as it is formal and symmetrical with respect to the overall composition, while incorporating the Golden Mean for the supporting elements of the composition, which are assymetrical. It is no wonder it is considered to be "perfect" when it comes to composition.
If you apply Fibonacci numbers and include zero, or use the Bakker Saddle and divide a square, you add the center point of the composition to the other four sweet spots for positioning subject matter. Therefore, the center arguably becomes a legitimate compositional point despite the horror some would apply to placing a subject there. The argument is that a centered subject tends to be static rather than dynamic, ignoring the fact that a static composition may be the intention of the artist. The difficult thing for a beginner to understand is why a composition fails when a subject appears to require a dynamic composition, but is placed in a static position. This is a legitimate compositional criticism. Imagine a runner, an obvious dynamic subject, placed in the center of a composition. The visual subject and the psychological composition are in conflict. How we perceive balance in a composition is therefore not strictly based on the placement of the subject, but the placement with consideration for the implied movement of the subject.
The primary four points of asymmetrical composition created by any method are close enough together. The points themselves are not the specific locations where a subject must be, they are the areas where the primary visual weight of the composition will appear to be most comfortable. This is why the rule of thirds is the easiest to apply and to learn, but also why it should not be taken too literally. A subject usually has a natural balance point and that will find visual rest near a compositional sweet spot. Since subject matter is rarely a point but rather an area, the specific location is rather ambiguous, and most artists will tell you that it is felt more than reasoned.
In addition to the intersections themselves being sweet spots, the divisions are places within the composition where primary lines, like horizons and such, tend to want to be. While this is interesting and often true, there are many reasons why this is a rule begging to be broken, and the complexities of the composition of any image can overrule this positioning. If you work too hard to specifically place a particular line in a specific location you can cheat yourself out of interesting and compelling compositional choices.
Your goal as an image maker is to become comfortable with the concept of composition to the point where rules are not an issue, but a natural result of analyzing your images. Cropping images then becomes an instinctive tool which you apply while feeling how the elements balance themselves rather than whether or not you follow the rules. When you work this way you may find some of your images fall outside of the bounds of the rules, but still sit comfortably within the frame.
So, the rules are learning tools, but ultimately the decision on placement of elements in an image is up to the artist. Balance in a composition is not simply the application of something like the rule of thirds to every image. The rules are simply a means of helping you initially train your eye to see balance. As much as possible other methods should be incorporated into the learning process, and analysis of your images should be done as consistently as possible. One of the advantages of the digital processing tools is the opportunity to work with a dynamic cropping tool so you can play with composition and instantly see and feel the results of your decisions. The more you refine your vision, the more satisfying even the simplest images can be. In Photoshop's crop tool, once you make a crop you can turn on an overlay which will place either grid lines or rule of thirds lines over the image to assist you in making decisions. This is unfortunately not available in Elements. Also unfortunate is the lack of a grid with the Golden Mean as an option for comparison.
The cathedral image is naturally symmetrical as the building was designed and built that way. If photographed away from the center line you should go far enough away to create an obviously asymmetrical balance to the composition. Otherwise, you should carefully adjust the natural center line to satisfy the formal balance of the composition. Both horizontal and vertical convergence are removed. The symmetry is obvious, and the image satisfies the brain as the elements are properly aligned. Care should be taken in an image with obvious vertical and horizontal lines to remove pincushion or barrel distortion. Both Adobe Camera Raw (ACR), Lightroom and other editing programs have tools for this purpose. For most current cameras and lenses it is automatic, but may not be on by default.
The leading lines in the image draw your attention to certain areas regardless of their relationship to the borders. Only the base of the gold structure over the altar sits at a point defined by a rule of thirds or other specific compositional target. While the left and right of the image mirror one another creating the horizontal symmetry, the low position of the camera creates an assymetrical view of the vertical space. It is interesting to note how the light from the very high stained glass windows plays against the far walls in a non-symmetrical counterpoint to the structural symmetry of the overall image.
A common problem with some images is a symmetrical subject which is not carefully aligned. This will throw the image out of balance, and while it may be a subtle mistake it is one that will make an image "unsettling" to viewers. Training yourself to see symmetry and using the crop tool and other methods of correcting the balance in your images will make your results more satisfying.
feeling balance - positive and negative space
In this image of the bridge the leading lines of a typical asymmetrical composition lead your eye to a vanishing point. The light standard is certainly not in a proper location by the rules, but the image works. This is because you need to consider the entire space occupied by the light standard, the bridge abutment and the horizon line as a larger compositional element rather than the individual items themselves. There is a tension to the light standard that is anchored by the overall composition in a complex manner and that is why learning to "feel" balance is more important than simply applying rules to composition.
A balanced composition often relies on complex interactions between elements in the image rather than on a single element. The horizon line falls at almost precisely the Golden Mean. It was not measured to be that way, but when analyzed later was discovered to be there. The horizon is a rather small element of the image but acts as an anchor for the more complex interactions in the composition. Several triangular shapes divide the image in ways that serve to balance the image. The negative space between the bridge and the lamppost are a tension point. If the lightness of the snow in the central river area continued to the bottom of the image the sense of a base or support would be missing, so the shadowed snow tones contribute to the balance. The visual weight of the large bridge abutment on the left is the balance point around which the entire image is anchored.
The total visual weight of the space defined by the abutment, the horizon and the lamppost sit at a compositional sweet spot but there is no single element at that spot in the image. The space between the elements is the negative space that becomes an element of its own in composition. This is where learning to feel composition becomes necessary because no set of rules or guidelines in a camera viewfinder or a Photoshop tool will guarantee you that the image you make will work visually. Only your sense of balance and the experience of seeing many images will make that happen.
An exercise to teach yourself to understand positive and negative spaces is to photograph pennies on a piece of white paper. Take three pennies and position them on a piece of paper folded in half so it creates a 5.5 x 8.5 inch space. Position the pennies in different relationships and see how the visual tension of the pennies on the paper and the spaces between them change with small adjustments to their position. This is the same exercise that you employ when you hang several framed images on a wall. The balance of the elements as they relate to each other is as important as the elements themselves and the space they occupy.
“Now to consult the rules of composition before making a picture is a little like consulting the law of gravity before going for a walk. Such rules and laws are deduced from the accomplished fact; they are the products of reflection.” – Edward Weston