The four most important lines of any image are the ones that are often least recognized consciously: the frame itself. Second only to these are the lines that divide the frame, creating frames within the frame. Becoming more aware of how the frame can be used and how it can be divided will help you make more successful compositions.
There are many ways the frame can be divided. You can divide the frame horizontally, vertically or diagonally; in each case, the layers included define the virtual space presented. Different areas in an image can be divided differently. You can divide the frame (or a frame within the frame) multiple times; the more times the frame is divided, the more packed and dynamic it becomes, progressively growing more design-oriented and finally being reduced to pure texture. Each operation has significant consequences.
The only way to understand this intuitively is to explore your options. The development of new possibilities encourages us to ask new questions and develop new habits.
One of the most significant results of dividing the frame is the creation of specific proportions. The combination of the individual aspect ratios of each element creates a new unified aspect ratio. Much has been made of the Rule of Thirds. Dividing the frame into three parts (left/center/right or up/ middle/down) is a simple and often useful strategy for making images more directed, by prioritizing one element over another, and dynamic, through imbalance. Too little has been made of other ratios. What of fourths, fifths, sixths, sevenths or eighths? No musician would be content to only divide an octave into halves and thirds. Every proportion produces particular effects, which are further modified by placement (high/low or left/right) and content. Rather than a rule to be adhered to, proportion is a force to be explored expressively.
When it comes to controlling the division of the frame in your images, you have more options available to you than you may think. You can crop, composite, retouch or distort.
Cropping, either through placing the frame during exposure or by eliminating framed information during postprocessing, which changes the aspect ratio, has been the most traditional way of dividing the frame.
Compositing to extend the frame is a comparatively new practice that has become widely adopted, typically used to produce images with panoramic formats, but not exclusively.