A thin film of water on a cold plate can grow ice that looks like flowers, yet the shapes are not decorative accidents. As water freezes from the edges inward, heat and dissolved gases must escape through the liquid, creating gradients of temperature and concentration that steer where new ice can form. The interface between solid and liquid becomes unstable, so tiny protrusions advance faster, splitting and spreading into familiar branching patterns.
Physicists describe this process with diffusion-limited aggregation and the Mullins–Sekerka instability, which also appear in snowflake formation and controlled crystal growth. Whenever particles or latent heat move mainly by diffusion and attach at a cold front, the growing edge amplifies small fluctuations, producing fractal geometry with repeated branching across scales. Change plate material, surface roughness, or cooling rate, and the pattern reorganizes, but the underlying equations stay the same.
Laboratory experiments tune these boundary conditions deliberately, while a kitchen plate does it by accident, yet both systems obey the same thermodynamics and entropy production constraints. The ice flowers on a plate are therefore not a household curiosity but a visible cross section of how order emerges from a simple phase transition under the quiet guidance of mathematical symmetry and instability.
