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It has been hypothesized that the different appearance of oculardominance bands in the cat and the monkey is a consequence of thedifferent mapping geometries in these species (LeVay et al.1985; Anderson et al. 1988). Here I investigate the impactof areal geometries on the preferred direction of ocular dominancebands in two adaptive map formation models, the self-organizingfeature map and the elastic net algorithm. In the case of theself-organizing feature map, the occurrence of instabilities thatcorrespond to ocular dominance bands can be analyticallyinvestigated. The instabilities automatically yield stripes ofcorrect orientation. These analytic results are complemented bysimulations. In the case of the elastic net algorithm, simulationsreveal two different parameter regimes of the algorithm, only oneof which leads to stripes of correct orientation. The resultssuggest that neighborhood preservation in visual maps is enforcedin the backward direction, such that neighboring cells in thecortex have neighboring receptive fields, and not vice versa.