No aesthetic rule should be strictly followed, yet rules are there as a guideline for the achievement of that perfect look bonsai trees have.
The aesthetic canon of bonsai art has been gradually developed during centuries of trial and error by fine masters. Those rules are suggested by practical aspects of the bonsai cultivation.
The primary meaning of the bonsai tree is imitating it’s counterpart living in nature, achieving that well balanced look of a “normal” dimension tree. However, on a little bonsai, there’s not room for all of the branches of a big tree, so they have to be screened.
You should leave on the tree just those fundamental branches required to achieve the aesthetic balance. The branches position is fundamental too, and, even if every bonsai style has its characteristics, some overall rule can be listed.
The first branch is bigger and is positioned at about 1/3 of the bonsai height. The other branches are smaller as they reach the top of the tree, alternating the side of the trunk from where they grow. Those branches have to grow about 120° one from the other, having their center in the trunk. No branch should point toward the viewer nor directly backward where it is invisible. The whole foliage should roughly draw a scalene triangle.
The trunk has to be conical; one of the worst mistakes a bonsai cultivator can make is growing a cylindrical trunk.
When we look at big trees we have the feeling their tops dominate us. This should happen when looking at a bonsai too; the trunk of the bonsai should bend a little, as if it gently bows towards the observer.
The pot is always underrated by the beginner, but it is really important for the balance of the bonsai. The pot is part of the bonsai itself, no plant can be called bonsai if it hasn’t a good balance with its pot.
The pot should be of the right colour, contrasting or blending with the bonsai tree. A maple, for example, can have a glossy light blue pot, contrasting the red foliage during fall; a conifer, such as a pine, should have a matte brown pot exalting its noble bearing.
The shape of the pot is important, and it should complement the foliage: a rounded foliage needs an oval pot and a triangular foliage a rectangular pot.
The size of the bonsai pot should be chosen carefully, too often I see little bonsai in large pots, and this destroys the balance. The right pot should blend in the composition. As a general rule the width of the pot is 2/3 of the bonsai height and its height equals the base of the trunk.
All of those rules are just indicative, what makes a great bonsai is the artistic sensibility of the human who cultivates it. None of these rules should be severely followed, every rule is meant to be broken and experimentation is allowed in bonsai cultivation. On the contrary you don’t have to completely change those norms.
It is just like aesthetic canons in sculpture or painting: there are the rules, invisible to the viewer, followed even by great masters; those rules sometimes are broken in a clever way and that transforms a good piece of art in a masterpiece.