We present extensive numerical simulations of the Axelrod's model for socia
l influence, aimed at understanding the formation of cultural domains. This
is a nonequilibrium model with short range interactions and a remarkably r
ich dynamical behavior. We study the phase diagram of the model and uncover
a nonequilibrium phase transition separating an ordered (culturally polari
zed) phase from a disordered (culturally fragmented) one. The nature of the
phase transition can be continuous or discontinuous depending on the model
parameters. At the transition, the size of cultural regions is power-law d
istributed.