Discrete model of fish scale incremental pattern: a formalization of the 2D anisotropic structure

The structure of growth patterns on fish scales is characteristically anisotropic: the number of circuli and their widths significantly vary with the direction of measurement. We show, however, that because of anisotropy, fish scale growth rate variability can be described in fuzzy terms. The index of structural anisotropy is introduced, which serves as a measure of the fuzziness of growth-rate quantification. A discrete model of fish scale incremental pattern is proposed, which takes into account the incremental structure in 2D. This model is based on a representation of the fish scale pattern as a relay network, taking anisotropy in the form of discontinuities and convergences of incremental structural elements into account, and the widths of growth increments in different directions. The model is used to formalize procedures necessary for the quantification of fish scale growth rate. The capability of the model for analysing objects with similar structural attributes as found in fish scale incremental patterns, such as those found in coral, otoliths, shells, and bones, is demonstrated.