The Rules of Composition

Composition guides the viewer's eye. During the compositional stage artists determine important areas in a painting use lines to lead the viewer to them. The arrangement of shapes play an important factor as well as colour. Despite many artists using intuition to compose their artwork, a few important elements such as Rhythm, Balance and Unity are to be found.

Rhythm
Rhythm helps guide the eye through the artwork. It can be seen as a method to organize the painting. There are two basic types of rythm, the dynamic and the controlled type.
The dynamic impression is created through diagonal lines, patches and varying spaces between shapes and creates a sense of activity.

If the spaces are repetitive and even, the painting is dominated by vertical and horizontal lines and the colours are analogous the composition tends to have a more controlled and static pattern.  

Balance

Again two contrasting aspects can be used to describe balance best; symmetrical or asymmetrical. Balance can be achieved through 

the arrangement of shapes and colours. Important to realize is that regardless if its symmetrical or asymmetrical, the artwork will still be balanced in some way.

Unity
This element can be described as the consistency among the various elements to create a unifying art piece. This can for example be achieved by using colour schemes to guide the eye around and also unify the picture.
A further facet of unity is the feeling of “completion.”  In an unified artwork no part can be added or subtracted without destroying the whole.

So now lets have a look at some example compositions. "Dream Worlds: Production Design for Animation" has a nice section on composition and depicts the different compositional structures and layouts precisely. The following images are from the book Dream Worlds. (Bacher, H. 2007. Dream Worlds: Production Design for Animation. Focal Press)

Afterword: Sometimes Less is More

A complicated composition is not always the best solution in art. Simplicity can be stronger than a cluttered or complicated composition due to its effectiveness.

”Simplicity does not imply starkness. A simple composition is economical in use of line, form, mass and movement; includes only one center of interest; has a unified style which harmoniously integrates camera angles, lighting, tonal and color values” (Mascelli, J. 1998. The Five C's of Cinematography: Motion Picture Filming Techniques. Scb Distributors.)

Consequently everything decreasing the pictures effectiveness should be removed since it has no real purpose and only distracts.