  Axelrod's model for culture dissemination offers a nontrivial answer to the
question of why there is cultural diversity given that people's beliefs have a
tendency to become more similar to each other's as people interact repeatedly.
The answer depends on the two control parameters of the model, namely, the
number $F$ of cultural features that characterize each agent, and the number
$q$ of traits that each feature can take on, as well as on the size $A$ of the
territory or, equivalently, on the number of interacting agents. Here we
investigate the dependence of the number $C$ of distinct coexisting cultures on
the area $A$ in Axelrod's model -- the culture-area relationship -- through
extensive Monte Carlo simulations. We find a non-monotonous culture-area
relation, for which the number of cultures decreases when the area grows beyond
a certain size, provided that $q$ is smaller than a threshold value $q_c = q_c
(F)$ and $F \geq 3$. In the limit of infinite area, this threshold value
signals the onset of a discontinuous transition between a globalized regime
marked by a uniform culture (C=1), and a completely polarized regime where all
$C = q^F$ possible cultures coexist. Otherwise the culture-area relation
exhibits the typical behavior of the species-area relation, i.e., a
monotonically increasing curve the slope of which is steep at first and
steadily levels off at some maximum diversity value.
