Center composition puts the subject in the center of the frame. If it's done well, the symmetry and intricate detail makes it aesthetically pleasing. I really enjoy this composition, but it is very hard to create a center composition that is very visually appealing and memorable. For inspiration, here are some of my favorite Wes Anderson's shots that use the center composition:
The rule of thirds divides the image into nine equal parts. Using the rule of thirds makes it easier to create an interesting image, as the off-center subject creates more tension in the shot.
The golden triangles divide the image into three or four triangles with a strong diagonal line, called the "major line," and another diagonal line that goes from one corner to the major line, connecting perpendicularly. That line is called the "reciprocal line." This creates a more dynamic photograph, as seen below. Just look at that bridge and its diagonal line. Powerful stuff.
The two types of diagonals are Baroque and Sinister. Baroque are read from left to right and Sinister are read from right to left.
The golden ratio is all about geometry and proportions. The largest shape is divided by a perfect square, and the remaining portion is the same proportions as the first shape. Then that shape is divided by a perfect square, and so on and so forth. It creates somewhat of a spiral on the frame:
This ratio also works on other shapes and is seen in the Great Pyramids, Stonehenge, the Parthenon, on the human body, seashells, and hurricanes.
Knight also focuses on other important concepts and theories that help make photographs more dynamic, such as a frame within a frame and the Gestalt Principles.
A frame within a frame is an extremely important theory that uses objects to frame the main subject. It's good to have a foreground frame that is darker than the background because our eyes go to the brightest parts of the image.
Some of the Gestalt Principles are figure/ground, proximity and grouping, symmetry and balance, similarity, continuity, and closure.
Figure/ground means the subject and everything surrounding it is very contrasting. Using either chiaroscuro, strong contrasts between light and dark, and/or negative space, it enhances the illusion of depth.
When elements are placed together, they become a group. When similar objects are placed together, it becomes a whole. And elements with similar characteristics can be viewed as a group or pattern and can be very nice to look at.
Symmetry creates an equilibrium. As long as you make the center composition purposeful and dynamic, the symmetry is strong and appealing. Also, balance does not always mean perfect symmetry.
Continuity deals with leading lines. They can be straight or curved, but they're not alway obvious. They guide the viewer's eye to continue through the object.
Last, but not least, is closure. The subject is not fully seen, but the image gives your brain enough to form the rest. It "leaves a little to the imagination."
For me, learning the five main compositions was very helpful. I've learned the rule of thirds before, but learning and seeing the other compositions in use will help me frame my own shots and understand why certain photographs are more aesthetically pleasing than others.