Pass a current through tin(II) chloride and a silver forest erupts from the cathode. Stannous chloride dissolved in acidified water carries Sn2+ ions. The instant you apply a few volts of DC, reduction begins at the negative electrode: Sn2+ + 2e- -> Sn But the metal doesn’t spread as a smooth film. It climbs outward as branching, fractal trees. The reason is instability. As tin plates out, it depletes Sn2+ inside a thin Nernst diffusion layer hugging the electrode. Any tiny protrusion pokes further into fresh, ion-rich solution and grows faster, while its sharpening tip concentrates the local electric field and pulls in still more ions. This runaway is the Mullins-Sekerka instability (1964): a flat deposition front is mathematically unstable, so noise amplifies into ramified structure. What emerges is a textbook case of diffusion-limited aggregation, the model Witten and Sander introduced in 1981. Ions random-walk toward the cluster and stick where they first make contact, statisti...