The Law of Thirds
Thou shalt subdivide thy image into three parts. This shall be done by inserting two parallel lines both vertical and horizontal across your image. Where the lines are and intersect, though shalt place thy points of interest so that all images shall be composed in such a way to reveal this Law of Thirds.
If lessons in photographic composition were written in scriptural language they might look like the above statement. And if you are a first year student this might be a good way to introduce such an idea. There are advantages to rigidity at first. This is why the military trains as such, this is why robots run by protocols, not by assigning random variables and seeing what comes out.
The Law Of Thirds can be looked as such. When you begin your photographic journey use only the law of thirds. It wont treat you wrong and will probably serve you more than you know. If you are on day one of your photography journey follow such a law.
A prime example of the Law of Thirds
The Rule of Thirds
In composition theory there are various aspects that have been labeled as pleasing. One of these composition theories that have been laid out is the rule of thirds. The rule of thirds is when an artists composes an image so that the points of interest within the image reside on imaginary points within the image. These points or regions for the rule of thirds is 1/3 of the way into the image from either top or bottom or from either the left or right side of the image. If you were to graphically represent these points, draw two parallel lines that come off the bottom and top of the image and sides of the image 1/3 of the way into the frame of view. Use these grid lines to help compose your image. Most cameras will do this for you and require quick setting change to achieve this.
The rule of thirds is a good basis of how to compose an image, but is not the only way. Other methods such as central focal points, rule of odds, repeated patterns can be used as well. Thus the rule of thirds just becomes another arrow in the quiver.
When the rule of thirds is used but does not follow rigidity of the law.
Principles of Thirds
When a rule becomes a principle it becomes non-bindings and may be interwoven with many aspects of your photography. Because principles are non-binding they can be interwoven into many aspects of an image and may actually be strongly present but the main subject may defy the rule and may be closer in line with a single focal point (for example).
In the below image the thirds line is actually at the base of the two mountains and the two mountains follow sort of the horizontal rule of thirds principle. The water on the other hand does not correspond with any aspect of the rule of thirds and mostly is there as a stepping stone into the back of the image.
In the below image the stump in the bottom right could have been placed in the center but when in the center it carried too much weight. So when placed in the bottom right rule of thirds spot it became softer and apart of the scene rather than a major anchor that didnt allow for further exploration. Additionally the horizon line is above the rule of thirds putting more emphasis on the arid landscape below, thus the rule of thirds is only partially followed.
For the below image, the rule of thirds is there, but I originally designed this image so that the viewer would wander through the image back and forth between the sides, rather than having major focus points at the third increments, they you can clearly see that they are, but you have to think about it a bit more.
When should you use the rule of thirds? I don't know it kind of depends. Not every photo needs a rule to run by, sometimes they just need a single focal point and you can stop caring about the rule of thirds. If you get to this point you have arrived at self expression at your own desire.