Folding of the cerebellar cortex is clade-specific in form but universal in degree

Like the cerebralcortex, the surface of the cerebellum is repeatedly folded. Unlike the cerebralcortex, however, cerebellar folds are much thinner and more numerous; repeatthemselves largely along a single direction, forming accordion-like folds transverseto the mid-sagittal plane; and occur in all but the smallest cerebella. We haveshown previously that while the location of folds in mammalian cerebral cortex isclade-specific, the overall degree of folding strictly follows a universalpower law relating cortical thickness and the exposed and total surface areas predictedfrom the minimization of the effective free energy of an expanding, self-avoidingsurface of a certain thickness. Here we show that this scaling law extends tothe folding of the mid-sagittal sections of the cerebellum of 53 speciesbelonging to six mammalian clades. Simultaneously, we show that each clade hasa previously unsuspected distinctive spatial pattern of folding evident at themid-sagittal surface of the cerebellum. We note, however, that the mammaliancerebellum folds as a multi-fractal object, because of the difference betweenthe outside-in development of the cerebellar cortex around a preexisting coreof already connected white matter, compared to the inside-out development ofthe cerebral cortex with a white matter volume that develops as the cerebralcortex itself gains neurons. We conclude that repeated folding, one of the mostrecognizable features of biology, can arise simply from the interplay betweenthe universal applicability of the physics of self-organization and biological,phylogenetical clade-specific contingency, without the need for invokingselective pressures in evolution.