Hexagonal CNN and its applications in sphalerite banding texture simulation

A cellular nonlinear network (CNN) has been developed in the literature to characterize complexity, especially for reaction-diffusion dynamic systems. This CNN includes models that describe periodic precipitation and banding pattern formation in minerals. Banding textures are commonly observed in mineral crystals, including sphalerite crystals in Mississippi Valley-type deposits. A CNN model in a hexagonal coordinate system is developed in this paper to simulate the process for the hexagonal growth of minerals such as sphalerite. The model involves dividing the hexagonal space into triangular cells for which a coupling law can be defined. The model was used by referring to the initial conditions in the literature. The agreement of the simulated results with the observations demonstrates that the CNN model introduced in this paper is reasonable and can be used to interpret the mechanism for hexagonal growth of various textures such as banding in sphalerite.