Visual experience is critical to the development of the structure of the primary visual cortex and, in turn, normal functional vision. The primary visual cortex contains maps of multiple features of the visual input, and these maps are characterised by specific types of geometric relationships. Manipulations of the visual environment during development in animals such as ferrets, cats and monkeys provide an opportunity to probe the rules governing map formation via their effect on these relationships. Here we use a computational model of map formation based on dimension-reduction principles to predict the effect on map relationships of presenting only a single orientation to one eye and the orthogonal orientation to the other eye. Since orientation preference and ocular dominance are now tightly coupled one might expect orientation and ocular dominance contours to lose their normally orthogonal relationship and instead run parallel to each other. However, surprisingly, the model predicts that orthogonal intersection can sometimes be preserved in this case. The model also predicts that orientation pinwheels can migrate from the centre to the borders of ocular dominance columns, and that the wavelengths of the ocular dominance and orientation maps can become coupled. These predictions provide a way to further test the adequacy of dimension reduction principles for explaining map structure under perturbed as well as normal rearing conditions, and thus allow us to deepen our understanding of the effect of the visual environment on visual cortical development. Copyright © 2009 Elsevier Inc. All rights reserved.