Alignment is a social phenomenon wherein individuals share a common goal or perspective. Mirroring, or mimicking the behaviors and opinions of another individual, is one mechanism by which individuals can become aligned. Large scale investigations of the effect of mirroring on alignment have been limited due to the scalability of traditional experimental designs in sociology. In this paper, we introduce a simple computational framework that enables studying the effect of mirroring behavior on alignment in multi-agent systems. We simulate systems of interacting large language models in this framework and characterize overall system behavior and alignment with quantitative measures of agent dynamics. We find that system behavior is strongly influenced by the range of communication of each agent and that these effects are exacerbated by increased rates of mirroring. We discuss the observed simulated system behavior in the context of known human social dynamics.