Quartz crystals build up by adding whole layers that match the crystal symmetry. A simple mathematical model uses a growth rate equation such as dZ/dt = k(σ − σ₀), where σ is the supersaturation and σ₀ is the equilibrium value. The kinetic coefficient k depends on temperature and the surface energy. To capture the step‑by‑step deposition you can run a phase‑field or Monte‑Carlo simulation, which follows the same rule layer by layer and reproduces the natural lattice pattern.