Layered patterns in nature, medicine, and materials: quantifying anisotropic structures and cyclicity.

Various natural patterns-such as terrestrial sand dune ripples, lamellae in vertebrate bones, growth increments in fish scales and corals, aortas and lamellar corpuscles in humans and animals-comprise layers of different thicknesses and lengths. Microstructures in manmade materials-such as alloys, perlite steels, polymers, ceramics, and ripples induced by laser on the surface of graphen-also exhibit layered structures. These layered patterns form a record of internal and external factors regulating pattern formation in their various systems, making it potentially possible to recognize and identify in their incremental sequences trends, periodicities, and events in the formation history of these systems.