There are several answers to this question ranging from the fundamental to the applied. On the fundamental side, patterns form at the interfaces between two phases, for example between a solid and its melt. The pattern forms because the system is driven out of equilibrium, for example by supercooling the melt. The evolution of the system then involves matching boundary condition at the moving interface. Moving-boundary-value problems have not been solved in general, and constitute a wide-open area of research in mathematical physics.

On the applied side, the patterns that form in systems such as solidifying steel can determine economically valuable properties of the final material. Dendritic crystalline microstructure formed during solidification makes steel tough and durable. Controlling the microstructural pattern formation through chemical composition, introduction of additives, and processing therefore determines the quality of the final product. Better understanding of the pattern formation process leads to better control over the product, therefore.

Pattern formation in colloidal systems provide an opportunity to watch the microscopic processes by which macroscopic patterns form. This is because individual colloidal particles are large enough to see with a conventional light microscope. They interact with each other and cooperatively form structures following many of the same rules that are believed to apply to atomic and molecular systems. Lessons learned from studying colloids therefore provide experimental insights both into the fundamental mechanisms underlying pattern formation in general and also into practical steps that may be taken to control pattern formation in real-world systems.

There are several answers to this question ranging from the fundamental to the applied. On the fundamental side, patterns form at the interfaces between two phases, for example between a solid and its melt. The pattern forms because the system is driven out of equilibrium, for example by supercooling the melt. The evolution of the system then involves matching boundary condition at the moving interface. Moving-boundary-value problems have not been solved in general, and constitute a wide-open area of research in mathematical physics.

On the applied side, the patterns that form in systems such as solidifying steel can determine economically valuable properties of the final material. Dendritic crystalline microstructure formed during solidification makes steel tough and durable. Controlling the microstructural pattern formation through chemical composition, introduction of additives, and processing therefore determines the quality of the final product. Better understanding of the pattern formation process leads to better control over the product, therefore.

Pattern formation in colloidal systems provide an opportunity to watch the microscopic processes by which macroscopic patterns form. This is because individual colloidal particles are large enough to see with a conventional light microscope. They interact with each other and cooperatively form structures following many of the same rules that are believed to apply to atomic and molecular systems. Lessons learned from studying colloids therefore provide experimental insights both into the fundamental mechanisms underlying pattern formation in general and also into practical steps that may be taken to control pattern formation in real-world systems.

The pattern formation study is very important for understanding the topology of interacting molecules and it may be a very efficient tool for understanding the basic mechanism of molecular interaction between interacting molecules as well.

You can get the diffusion kinetics i.e. nature of fluidity from it

The method of formation study is very signifecant to understand the topology of interacted molecules and it is a very efficient tool for understanding the basic mechanism of molecular interaction between interacting molecules as well.