Abstract Ideologically committed minds form the basis of political polarization, but ideologically guided communication can further entrench and exacerbate polarization depending on the structures of ideologies and social network dynamics on which cognition and communication operate. Combining a well-established connectionist model of cognition and a well-validated computational model of social influence dynamics on social networks, we develop a new model of ideological cognition and communication on dynamic social networks and explore its implications for ideological political discourse. In particular, we explicitly model ideologically filtered interpretation of social information, ideological commitment to initial opinion, and communication on dynamically evolving social networks, and examine how these factors combine to generate ideologically divergent and polarized political discourse. The results show that ideological interpretation and commitment tend towards polarized discourse. Nonetheless, communication and social network dynamics accelerate and amplify polarization. Furthermore, when agents sever social ties with those that disagree with them (i.e. structure their social networks by homophily), even non-ideological agents may form an echo chamber and form a cluster of opinions that resemble an ideological group. This article is part of the theme issue ‘The political brain: neurocognitive and computational mechanisms’.