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.

Enamel-calibrated lamellar bone reveals long period growth rate variability in humans.

Mammalian teeth exhibit incremental structures representing successive forming fronts of enamel at varying time scales, including a short daily increment called a cross striation and a long period called a stria of Retzius, the latter of which, in humans, occurs on average every 8-9 days. The number of daily increments between striae is called the repeat interval, which is the same period as that required to form one increment of bone, i.e.

Lamellar bone is an incremental tissue reconciling enamel rhythms, body size, and organismal life history.

Mammalian enamel formation is periodic, including fluctuations attributable to the daily biological clock as well as longer-period oscillations that enigmatically correlate with body mass. Because the scaling of bone mass to body mass is an axiom of vertebrate hard tissue biology, we consider that long-period enamel formation rhythms may reflect corresponding and heretofore unrecognized rhythms in bone growth. The principal aim of this study is to seek a rhythm in bone growth demonstrably related to enamel oscillatory development.