The fractal geometry of convoluted brains

The evolution of the brain in mammals is characterized by an overall size increase and structural reorganization. Consequently, the brain's geometry has changed notably since the late Cretaceous. Here I show that the mammalian brain is a fractal structure, the dimensions of which can be described in mathematical terms. Application of the scaling principle to convoluted brains shows that the cortical surface area, with its fractal dimension of D = 2.70 +/- 0.07, is geometrically similar with the amount of white matter, i.e., with the number and length of the interconnective nerve fibers. The hypothesis is put forward that the potential for brain evolution results from a combination of fractal folding and compartmentalization of neurons into modular circuits. The close correspondence between the form and fractal dimensions of the brain and a geometric model provides further evidence that the macroscopic organization of the brain in mammals is governed by a few simple generative rules and that these internal factors of brain design, bearing no relation to the selective reasons of initial enlargement, may be the primary determinants directing the evolution of the brain.