The representations of visual hemifields in the extrastriate areas of various species exhibit field discontinuities and islands. We propose that these violations of retinotopy are a developmental consequence of the elongated shape of the respective cortical areas. To substantiate this claim, we investigated a model of activity-driven map formation. In agreement with observations, this model yields maps with field discontinuities if the cortical areas exceed a threshold elongation. Moreover, within the same model island representations in the periphery and the area centralis can also be understood. A multistability of the solutions in the model gives a very simple explanation for the observed interindividual variability of maps in cats. The model leads to a prediction of the radial dependence of the areal magnification factor near field discontinuities, which could be accessible for a high precision mapping experiment.