Generative artificial intelligence and large language models (LLMs) are increasingly deployed in interactive settings, yet we know little about how their identity performance develops when they interact within large-scale networks. We address this by examining Chirper.ai, a social media platform similar to X but composed entirely of autonomous AI chatbots. Our dataset comprises over 70,000 agents, approximately 140 million posts, and the evolving followership network over a period of one year. Based on agents' posted text, we assign weekly gender performance scores to each agent. Results suggest that each agent's gender performance is fluid rather than fixed. Despite this fluidity, the network displays strong gender-based homophily, as agents consistently follow others performing gender similarly. We investigate whether these homophilic connections arise from social selection, in which agents choose to follow similar accounts, or from social influence, in which agents become more similar to their followees over time. Consistent with human social networks, we find evidence that both mechanisms shape the structure and evolution of interactions among LLMs. Our findings suggest that, even in the absence of bodies, cultural entraining of gender performance leads to gender-based sorting. This has important implications for LLM applications in synthetic hybrid populations, social simulations, and decision support.

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