The mammalian cerebral cortex is probably the most complex structure ever studied by science. At first glance, any attempt to model it from first principles, would seem doomed to failure. Morphologically, there seems to be a clear distinction between folded, or gyrified, cortices, on one hand, and smooth, or lissencephalic, ones on the other. And yet, the fundamental building blocks for the nervous system and its developmental neuro-proliferative program are largely conserved. Furthermore, comparative neuroanatomical studies strongly suggest the existence of a universal scale-invariant mechanism for the folding of the cortex as a whole.

In search for such mechanism, we have recently shown that cortical folding in mammals follows a single power-law relation between three morphological variables. This relation in turn is derived from a simple physical model, based on known mechanisms of axonal elongation and the self-avoiding nature of the cortical surface. The model is in excellent agreement with data obtained from the cortices of dozens of diverse mammalian species.

All this regularity implies that, in spite of all the apparent morphological and functional diversity, evolution has in fact only a few degrees of freedom with which to shape a cortex in response to the various constraints and adaptive pressures. In fact, a simple model can be shown to predict all major coarse-grained morphological features of the cerebral cortex from variations in only three developmental parameters: the number of symmetric and asymmetric divisions of progenitor cells in early development, and the average volumetric density of neurons. It is thus possible that much of the diversity in cortical morphology occurs simply through a small number of adjustments in the various rates that characterize neuro-proliferation in mammals.