This work examines the integration of large language models (LLMs) into multi-agent simulations by replacing the hard-coded programs of agents with LLM-driven prompts. The proposed approach is showcased in the context of two examples of complex systems from the field of swarm intelligence: ant colony foraging and bird flocking. Central to this study is a toolchain that integrates LLMs with the NetLogo simulation platform, leveraging its Python extension to enable communication with GPT-4o via the OpenAI API. This toolchain facilitates prompt-driven behavior generation, allowing agents to respond adaptively to environmental data. For both example applications mentioned above, we employ both structured, rule-based prompts and autonomous, knowledge-driven prompts. Our work demonstrates how this toolchain enables LLMs to study self-organizing processes and induce emergent behaviors within multi-agent environments, paving the way for new approaches to exploring intelligent systems and modeling swarm intelligence inspired by natural phenomena. We provide the code, including simulation files and data at https://github.com/crjimene/swarm_gpt.