Self-Similarity in Biological Structures
If you take a look at the nearest tree, you can notice how the leaves are all similar to each other. Some leaf might be smaller or larger than the nearest one, but the characteristic structure of the leaf is singular enough that we could split the three into “leaves” and “non-leaves” parts.
The branches of a tree all share a similar structure, but at different scales. Closer to the stem, the branches are larger in diameter, gradually decreasing in diameter toward the leaves.
The thick and the thin branches all share the same “procedure”: i) grow in length, away from the tree; ii) subdivide into smaller instances of itself; and iii) repeat.
We can draw from this observation that the pattern that we see at the macro level, on the fully developed tree, stems from the pattern encoded in its growth.
Many other biological structures in ourselves present analogous self-similar structures, such as: blood vessels, pulmonary tissue, and neural tissue.
The “problem” that a self-similar structure solves, from the organism's perspective, is encoding a larger and more complex system with less genetic information.
Every protein and structure ever to exist in an organism must be encoded by its genetic code for synthesis. Thus, it is simpler and more efficient -- in the sense that evolutionary pressures favor it -- to describe a smaller self-replicating recipe.
This kind of structure resemble mathematical fractals: infinitely recursive structures defined in terms of itself. Of course, reality is not infinitely dividable -- a tree branch or capillary vessel can only be so thin -- but, in the same sense, a great amount of observed complexity stems from a very small set of simple underlying mechanisms.