Supercontinents like Pangea impose a first-order control on Earth's evolution as they modulate global heat loss, sea level, climate, and biodiversity. In a traditional view, supercontinents form and break up in a regular, perhaps periodic, manner in a cycle lasting several 100 Myr as reflected in the assembly times of Earth's major continental aggregations: Columbia, Rodinia, and Pangea. However, modern views of the supercontinent cycle propose a more irregular evolution on the basis of an improved understanding of the Precambrian geologic record. Here we use fully dynamic spherical mantle convection models featuring plate-like behavior and continental drift to investigate supercontinent formation and breakup. We further dismiss the concept of regularity but suggest a statistical cyclicity in which the supercontinent cycle may have a characteristic period imposed by mantle and lithosphere properties, but this is hidden in immense fluctuations between different cycles that arise from the chaotic nature of mantle flow.