Finding order in disorder is a hallmark of science and art. In the time of Leonardo da Vinci, the schism between science and art had yet to arise. In fact, Leonardo freely used scientific methods for his art and vice versa; for example, when he used his observations of turbulent, whirling water to guide his artistic imagination. Half a millennium later, a cornerstone of modern biology is the continuing search for order in dynamic processes. In neuroscience, the search has focussed on understanding complex spacetime brain dynamics. Recently, turbulence has been shown to be a guiding principle underlying the necessary information processing, supporting Leonardo's search for order in disorder. Here, we argue that Leonardo's seminal insights have ongoing relevance for modern neuroscience.