The receptive fields of simple cells in visual cortex are composed of elongated on and off subregions. This spatial arrangement is widely thought to be responsible for the generation of orientation selectivity. Neurons with similar orientation preferences cluster in "columns" that tile the cortical surface and form a map of orientation selectivity. It has been proposed that simple cell receptive fields are constructed by the selective pooling of geniculate receptive fields aligned in space. A recent analysis of monosynaptic connections between geniculate and cortical neurons appears to reveal the existence of "wiring rules" that are in accordance with the classical model. The precise origin of the orientation map is unknown, but both genetic and activity-dependent processes are thought to contribute. Here, we put forward the hypothesis that statistical sampling from the retinal ganglion cell mosaic may contribute to the generation of simple cells and provide a blueprint for orientation columns. Results from computer simulations show that the "haphazard wiring" model is consistent with data on the probability of monosynaptic connections and generates orientation columns and maps resembling those found in the cortex. The haphazard wiring hypothesis could be tested by measuring the correlation between the orientation map and the structure of the retinal ganglion cell mosaic of the contralateral eye.