Iterative structures

Seemingly complicated forms arising out of simple iterative structures is more than just intriguing. Traditional Euclidean geometry is just incapable of identifying the regularity in these structures. Ironically nature is predominantly composed of such iterative structures, what we call as "fractals". Fractal geometry to a good extent can represent these structures mathematically is quite satisfying.

Apparently, scaling in nature seems to happen in "fractals". While the traditional examples of ferns, blood vessels, corals, mountains, trees, etc., perhaps best represent these fractal structures in nature. I stumbled upon this documentary where scientist studying "rain forests" in Costa Rica, seem to have extended this a little further. What they claim is that the distribution of width of the branches of a single tree matches the distribution of the width of the trees in the forest. In medicine, apparently it can be used to identify cancers at an early stage. The idea being, the networks of a blood vessel in a healthy person is different from that of a network that usually accompanies a tumor.

I can't help but wonder how the same principles could be used to study brains. Perhaps the seemingly complicated personalities, which if I may assume are products of thought processes, could be mathematically represented using fractals. After all thought process, in simple terms, itself is just a product of neural feedback system. Of course this would require phenomenal mapping of sections of brain along with their synapses.