In this work, it is taken into account that in nature, due to pressure and temperature, water drops in general are either spherical or ellipsoidal. Thus, starting from a more general structure, a 3D elliptical surface (oblate spheroid) is constructed, which, by means of parameters, can be turned into a spherical shape. Hexagons are built on a rectangular horizontal plane, then this plane is passed through an elliptical surface at height h, which is determined by a parameter $\theta$. As a result of the cutting of these surfaces, a curve and a plane are obtained, both horizontal ellipsoidal; if these hexagons are within the perimeter of the horizontal ellipse obtained as a function of $\theta$, they are marked with an N, and if they are outside the perimeter, they are marked with an E. Several frozen nucleation centers are established, either in the same layer or in different planes, marking them with an F and their first eight neighbors with a B. The calculations based on a modified snowflake model are carried out tile by tile and layer by layer, governed by the thermodynamic factors $\alpha$, $\beta$, and $\gamma$, leading to results that depend on the position of the nucleator, which can be symmetrical or asymmetrical for a snowflake with more than one nucleation center and an external surface formed by water vapor that functions as a membrane.

This work explores the morphogenesis of the skeletal mineral component, with a specific emphasis on hydroxyapatite (HAp) crystal assembly. Bone is fundamentally a triphasic biomaterial, consisting of an inorganic mineral phase, an organic matrix, and an aqueous component. The inorganic phase (hydroxyapatite), is characterized by its hexagonal prismatic nanocrystalline structure. We leverage a cellular automata (CA) paradigm to computationally simulate the mineralization process, leading to the formation of the bone’s hydroxyapatite framework. This model exclusively considers the physicochemical aspects of bone formation, intentionally excluding the biological interactions that govern in vivo skeletal development. To optimize computational efficiency, a simplified anatomical segment of a long bone (e.g., the femur) is modeled. This geometric simplification encompasses an outer ellipsoidal cylindrical boundary (periosteal envelope), an inner ellipsoidal surface defining the interface between cortical and cancellous bone, and a central circular cylindrical lumen representing the medullary cavity, which accommodates the bone marrow and primary vasculature. The CA methodology is applied to generate the internal bone microarchitecture, while deliberately omitting the design of smaller, secondary vascular channels.