Consequences for retinal growth when vision occurs in S² space

Abstract

We postulate that the process of vision occurs in the S² space. The retina is endowed with the topology of a part of a two-sphere S², roughly, the topology of a hemisphere. There is a corresponding topology on the tectal surface, induced by the anatomy of the retino-tectal connections. Our analysis predicts the experimentally observed "near-neighbour" relationships between points in the visual field and their representation in the tectum. Further, in this context, topological arguments are presented to indicate that if the normal developing retinal disc in goldfish undergoes a process of deformation, a discontinuity is generated at the retinal surface. This discontinuity makes the differential patterns of the retinal and tectal tissues more compatible, and also enables the retina (which grows throughout the life of the animal) to conveniently connect to the tectum.