A fractal algorithm like Mandelbrot is self-similar in all size scales. This is not the case in nature. A tree is fractal in the sense that each branch is similar to the tree as a whole. But that is only true at a certain range of scales, about 0.1 - 10 meter. The forest does not look like one tree, nor does the texture at millimeter scale or the cellular structure at microscopic scale. At those scales the tree may or not be fractal, but at least it is not fractal in the same way as on the 1 meter size. Nature breaks the fractal regime after only a couple or so self-similar scales.
Are these transitions between fractal regimes studied by biology?
Are there any ideas around about how different fractal regimes might be connected with emergent phenomena? At very small scales there exists no tree, but only elementary quantum particles/waves. Macromolecules and cells and the tree and the forest each emerge as a phenomena on different size scales. I wonder if this emergence is matched by the different fractal regimes at those scales?