💎 Amethyst Crystal Growth Simulator (2D)

This 2D companion replaces the 3D version's static, hand-modelled amethyst geode with the actual growth process behind it: a diffusion-limited-aggregation (DLA) engine in which free ions perform a genuine random walk through solution, their step size set by temperature through the Einstein diffusion relation, and stick onto the growing cluster with a probability that combines a kinetic sticking factor with a six-fold angular bias mimicking quartz's real hexagonal crystal symmetry. A live readout tracks particle count, cluster radius, a fractal-dimension estimate (D = ln N / ln R, which drifts toward the textbook off-lattice DLA value of roughly 1.71 as the cluster grows) and the current growth rate, so instead of orbiting a finished crystal you watch one form, particle by particle, from nothing.