We study a one-dimensional version of Axelrod\'s model of cultural transmission. We classify the equilibrium configurations and analyze their stability. Below a critical threshold, an initially diverse population will converge to a monocultural equilibrium, or ordered state. Above this threshold, the dynamics settles to a multicultural or polarized state. These multicultural attractors are not stable, so that small local perturbations can drive the system towards a monocultural state. Cultural drift is modeled by perturbations (noise) acting at a finite rate. If the noise rate is small, the system reaches a monocultural state. However, if the noise rate is above a size-dependent critical value, noise sustains a polarized dynamical state.
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