Cognitive and neural representations of fractals in vision, music and action.

Mandelbrot popularized the concept of fractal as a tool to tame the geometrical structure of objects with infinite hierarchical depth. The key aspect of fractals is the use of simple parsimonious rules and initial conditions, which, when applied recursively, can generate unbounded complexity. Fractals are ubiquitous structures in nature, present in coastlines, bacteria colonies, trees, and physiological time series. However, within cognitive science, the core question is not which phenomena can generate fractal structures but whether human or animal minds can represent recursive processes and, if so, in which domains. In this chapter, we will explore the cognitive and neural mechanisms underlying the representation of recursive hierarchical embedding. Language is the domain in which this capacity is best studied. Humans can generate an infinite array of hierarchically structured sentences, and this capacity distinguishes us from other species. However, recent research suggests that humans can represent similar structures in music, vision, and action and has provided additional cues as to how these capacities are cognitively implemented. Using a comparative approach, we will map the commonalities and differences across domains and offer a roadmap to understand the neurobiological implementation of fractal cognition.