The curling thread is a term that is very familiar to us. Ther are so many events that are related to the shapes of the curling threads. Usually, such events contain the meaning of annoyance, hopeless, and other disappointing, etc. Complicated problems are often analogous to the curling threads.
An interesting question, is why the curling threads have so complicated shapes? What kind of mechanism behind such shapes? If initially, the thread has a straight shape and then allowed to float freely, whether it maintains the straight shape or turns into curling?
We developed a physics model to explain such a phenomenon. This model was inspired by the shape of long-chain polymer that forms a shape like that of the curling threads. Therefore, it is logical to ask whether the process of the curling threads shape formation is similar to the process of forming long-chain polymer configurations. We borrowed the model that applies to long-chain polymers to explain the formation of curling threads. We found that the curling thread configuration resembles the configuration produced by the self-avoiding random walk (SAW) phenomenon. We also identified that the time-dependent process of thread curling from a straight state meets the one-dimensional crystallization equation. Those results have been published in the Journal of Statistical Mechanics: Theory and Experiment with the title: “Curling evolution of suspended threads replicates 2D self-avoiding walk phenomena and 1D crystallization process”.