Large language models (LLMs) like ChatGPT now power many everyday applications, from auto-completion to writing assistants to conversational text generation. Yet the candidate outputs these systems consider during their search process remain poorly understood and rarely explained. We address this gap with a visual representation of the search tree the LLM uses to generate the output text. To support this approach, we present «generAItor», a visual analytics technique that enhances this search tree with specialized modules offering visualizations and interactive controls.