Culture represents the broad range of things over which people influence each other, and frequently contributes to the behaviour, interaction and outlook of groups. Although it has been studied in the context of humans, it is also relevant to future intelligent cognitive systems, that could have the capability to update their disposition and strategy based on the influence of others.In this work we transfer concepts from social sciences to the computing sciences and examine the effect of peer influence on culture. We consider the notion of "peer pressure", being the combined effect from all an individual's neighbours exerting influence at the same time, and also through influence flowing from indirect sources. This approach is derived using Social Impact Theory. We benchmark this against the cultural polarisation model from Axelrod, which involves influence being restricted to dyadic interactions between agents.We find that peer pressure provides complex contagion with a significant impact on cultural evolution. Greater cultural diversity is maintained, with indirect paths mitigating this by effectively forming disruptive weak links. This reaffirms that maintaining diversity in social ties, as well as a wide breadth, supports the mitigation of cultural isolation and polarisation. The model provides a platform to explore culture in a wide range of further scenarios, including electronic, coalition and organisational contexts.