Orientation maps are a prominent feature of the primary visual cortex of higher mammals. In macaques and cats, for example, preferred orientations of neurons are organized in a specific pattern, where cells with similar selectivity are clustered in iso-orientation domains. However, the map is not always continuous, and there are pinwheel-like singularities around which all orientations are arranged in an orderly fashion. Although subject of intense investigation for half a century now, it is still not entirely clear how these maps emerge and what function they might serve. Here, we suggest a new model of orientation selectivity that combines the geometry and statistics of clustered thalamocortical afferents to explain the emergence of orientation maps. We show that the model can generate spatial patterns of orientation selectivity closely resembling the maps found in cats or monkeys. Without any additional assumptions, we further show that the pattern of ocular dominance columns is inherently connected to the spatial pattern of orientation.