Protein Crystallization: 2D Nucleation & DLA Precipitate

This is the 2D counterpart to the 3D protein-crystallization phase-diagram simulator, working from the same classical-nucleation-theory phase diagram but computing its droplet cross-section natively in two dimensions. Free protein monomers undergo Brownian motion inside a flat box; crossing the solubility curve lets an existing crystal grow by filling a true 2D square lattice cell by cell, and crossing the supersolubility curve spawns new nuclei with a nucleation rate that turns on almost like a switch as classical nucleation theory predicts. Push concentration far enough past the precipitation threshold and growth switches to diffusion-limited aggregation — each new molecule sticks to whichever cluster tip a random-walking particle would statistically reach first, producing the same branchy, fractal-like amorphous clumps real over-supersaturated protein precipitate forms. Move the protein, precipitant and temperature sliders to hunt for the metastable growth window crystallographers actually target, and compare the resulting lattice-vs-DLA morphologies directly.