Existing models of categorization typically represent to-be-classified items as points in a multidimensional space. While from a mathematical point of view, an infinite number of basis sets can be used to represent points in this space, the choice of basis set is psychologically crucial. People generally choose the same basis dimensions, and have a strong preference to generalize along the axes of these dimensions, but not "diagonally". What makes some choices of dimension special? We explore the idea that the dimensions used by people echo the natural variation in the environment. Specifically, we present a rational model that does not assume dimensions, but learns the same type of dimensional generalizations that people display. This bias is shaped by exposing the model to many categories with a structure hypothesized to be like those which children encounter. Our model can be viewed as a type of transformed Dirichlet process mixture model, where it is the learning of the base distribution of the Dirichlet process which allows dimensional generalization.The learning behaviour of our model captures the developmental shift from roughly "isotropic" for children to the axis-aligned generalization that adults show.