Why do languages parcel human experience into categories in the ways they do? Languages vary widely in their category systems but not arbitrarily, and one possibility is that this constrained variation reflects universal communicative needs. Consistent with this idea, it has been shown that attested category systems tend to support highly informative communication. However it is not yet known what process produces these informative systems. Here we show that human simulation of cultural transmission in the lab produces systems of semantic categories that converge toward greater informativeness, in the domains of color and spatial relations. These findings suggest that larger-scale cultural transmission over historical time could have produced the diverse yet informative category systems found in the world’s languages.