ABSTRACT In one of his lesser-known studies of flow, Leonardo da Vinci in 1513 came upon yet another question he could not answer: When blood hits the wall of the heart, does the flow split in two? In 1977, this question was answered by Albert Libchaber in an experiment that became a cornerstone of chaos theory. Can Leonardo's question, Libchaber's solution and notions of integrated systems be drawn together to create a whole? While this trajectory has its limitations, the journey has some rewards, taking in Leonardo's cosmology, chaos theory, poststructuralist philosophy, the Polynesian worldview, the Internet and the weather.