Free convection schema defines the shape of the human brain: brain and self-organization.

As a fundamental rule of nature, the shape of a functioning organ should never be considered accidental. Since the principal rules for a self-organizing neural network are not sufficient for determining the shape and anatomic features of the brain, these must be governed by other rules. Ontogeny of the global shape of the brain is guided by radial glial fibers. The rules defining the growth pattern of radial glial fibers, therefore, should be the rules for a self-organization for the shape of the brain. In this work, the overall shape and structural anatomic detail of the human brain was successfully simulated utilizing self-organization rules of heat convection represented by Boussinesq partial differential equations. The result suggests that radial glial fibers may grow in Markovian fashion, guided by gaseous substrates moving miniature distances according to a convection schema. The result also holds implication that the shape of the brain has specific physical meaning in the creation of a virtual sphere, which in turn ensures equivalence of columns within the entire cortex, the well-known vital fundamental of brain organization.