structural information inside DNA

I had always thought that structural symmetry was strictly a product of evolution due to its phenotypical advantages. Most animals for example have bilateral symmetry. Plants on the other hand exhibit other types of symmetries. In nature one rarely encounters structures that are devoid of such geometrical patterns.

While reading an article on algorithmic complexity, it immediately dawned upon me that there may be another important reason why symmetry is so prevalent.

First, here is a short description of algorithmic complexity:

Given an entity (this could be a data set or an image, but the idea can be extended to material objects and also to life forms) the algorithmic complexity is defined as the length (in bits of information) of the shortest program (computer model) which can describe the entity. According to this definition a simple periodic object (a sine function for example) is not complex, since we can store a sample of the period and write a program which repeatedly outputs it, thereby reconstructing the original data set with a very small program.

Geometrical patterns allow economization. Presence of symmetries can drastically reduce the amount of information that needs to be encoded in the DNA for the orchestration of biochemical processes responsible for the structural development of the organism. Same may be true for more complicated morphological shapes that are still mathematically simple to describe. An example:

Researchers discovered a simple set of three equations that graphed a fern. This started a new idea - perhaps DNA encodes not exactly where the leaves grow, but a formula that controls their distribution. DNA, even though it holds an amazing amount of data, could not hold all of the data necessary to determine where every cell of the human body goes. However, by using fractal formulas to control how the blood vessels branch out and the nerve fibers get created, DNA has more than enough information.