Low-level "adaptive" and higher-level "sophisticated" human reasoning processes have been proposed to play opposing roles in the emergence of unpredictable collective behaviors like crowd panics, traffic jams, and market bubbles. While adaptive processes are ubiquitous in mechanistic theories of emergent social complexity, complementary theories understand incentives, education, and other inducements to rationality as able to suppress such outcomes. We show in a series of laboratory experiments that, rather than suppressing complex social dynamics, sophisticated reasoning processes can support them. Our experiments elicit flocking behavior in groups and show that it is driven by the human ability to recursively anticipate the reasoning of others. We identify this sophisticated flocking in three different games—the Beauty Pageant, Mod Game, and Runway Game—across which game theory predicts no formal similarity. The persistence of sophisticated flocking across unrelated game types not only speaks to the phenomenon's robustness, it also suggests that people are treating three supposedly different decision settings as conceptually similar, implicating a second sophisticated cognitive ability: human concept formation. We also find in participants' underlying reasoning that the number of recursions they perform is limited not by any individual's cognitive abilities, but by a social norm that emerges during flocking. By implicating both recursive reasoning and concept formation in complex dynamics, we support interdisciplinary perspectives that emergent complexity is typical of even the most intelligent populations and carefully designed social systems.