The observation that suicides sometimes cluster in space and/or time has led to suggestions that these clusters are caused by the social learning of suicide-related behaviours, or "copycat suicides". Point clusters are clusters of suicides localised in both time and space, and have been attributed to direct social learning from nearby individuals. Mass clusters are clusters of suicides localised in time but not space, and have been attributed to the dissemination of information concerning celebrity suicides via the mass media. Here, agent-based simulations, in combination with scan statistic methods for detecting clusters of rare events, were used to clarify the social learning processes underlying point and mass clusters. It was found that social learning between neighbouring agents did generate point clusters as predicted, although this effect was partially mimicked by homophily (individuals preferentially assorting with similar others). The one-to-many transmission dynamics characterised by the mass media were shown to generate mass clusters, but only where social learning was weak, perhaps due to prestige bias (only copying prestigious celebrities) and similarity bias (only copying similar models) acting to reduce the subset of available models. These findings can help to clarify and formalise existing hypotheses and to guide future empirical work relating to real-life copycat suicides.