How do people think about complex relational phenomena like the behavior of the stock market? Here we hypothesize that people reason about such phenomena in part by creating spatial analogies, and we explore this possibility by examining people’s spontaneous gestures. Participants read a written lesson describing positive and negative feedback systems and then explained the key differences between them. Though the lesson was highly abstract and free of concrete imagery, participants produced spatial gestures in abundance during their explanations. These spatial gestures, despite being fundamentally abstract, showed clear regularities and often built off of each other to form larger spatial models of relational structure—that is, spatial analogies. Importantly, the spatial richness and systematicity revealed in participants’ gestures was largely divorced from spatial language. These results provide evidence for the spontaneous use of spatial analogy during complex relational reasoning.