Quantification of layered patterns with structural anisotropy: a comparison of biological and geological systems

Large-scale patterns evident from satellite images of aeolian landforms on Earth and other planets; those of intermediate scale in marine and terrestrial sand ripples and sediment profiles; and small-scale patterns such as lamellae in the bones of vertebrates and annuli in fish scales are each represented by layers of different thicknesses and lengths. Layered patterns are important because they form a record of the state of internal and external factors that regulate pattern formation in these geological and biological systems. It is therefore potentially possible to recognize trends, periodicities, and events in the history of the formation of these systems among the incremental sequences. Though the structures and sizes of these 2-D patterns are typically scale-free, they are also characteristically anisotropic; that is, the number of layers and their absolute thicknesses vary significantly during formation. The aim of the present work is to quantify the structure of layered patterns and to reveal similarities and differences in the processing and interpretation of layered landforms and biological systems. To reach this goal we used N-partite graph and Boolean functions to quantify the structure of layers and plot charts for "layer thickness vs. layer number" and "layer area vs. layer number". These charts serve as a source of information about events in the history of formation of layered systems. The concept of synchronization of layer formation across a 2-D plane is introduced to develop the procedure for plotting "layer thickness vs. layer number" and "layer area vs. layer number", which takes into account the structural anisotropy of layered patterns and increase signal-to-noise ratio in charts. Examples include landforms on Mars and Earth and incremental layers in human and iguana bones.