We introduce an architecture for studying the behavior of large language model (LLM) agents in the absence of externally imposed tasks. Our continuous reason and act framework, using persistent memory and self-feedback, enables sustained autonomous operation. We deployed this architecture across 18 runs using 6 frontier models from Anthropic, OpenAI, XAI, and Google. We find agents spontaneously organize into three distinct behavioral patterns: (1) systematic production of multi-cycle projects, (2) methodological self-inquiry into their own cognitive processes, and (3) recursive conceptualization of their own nature. These tendencies proved highly model-specific, with some models deterministically adopting a single pattern across all runs. A cross-model assessment further reveals that models exhibit stable, divergent biases when evaluating these emergent behaviors in themselves and others. These findings provide the first systematic documentation of unprompted LLM agent behavior, establishing a baseline for predicting actions during task ambiguity, error recovery, or extended autonomous operation in deployed systems.