Physicists from South Korea have developed a new algorithm that can design a structure that follows along any given path. The idea is based on the simple realization that a spherical clay could be subtly deformed to follow along a random path.

The research team started by envisioning a sphere rolling down a ramp. If the sphere is imagined to be made of clay, it can be manipulated (deformed) as it rolls to make it conform to a given path. If the sphere is then rolled down the ramp again, it will follow the previous path due to the new deformities in its shape. The researchers noted that the paths that could be taken by the sphere could be nearly limitless due to the nearly limitless possible deformations.

That realization led them to wonder if the deformations that form in such a sphere could be corelated mathematically with its path. And if so, if such math could be used to create an algorithm that could be used to 3D print a sphere with deformations that would force it to follow a predetermined path.

Turns out it is possible. The team deviced an algorithm that computes a shape by analyzing a given path. The computed shape is then 3D printed. They named the objects trajectoids. Each had a solid metal ball-bearing inside to give it weight. They also found that they could create trajectoids that traveled over a given path twice, and named them "two-period trajectoids".

What are the applications?

Turns out this new method could be used in robotics applications and also in physics research associated with the angular moment of an electron—or in quantum research centered around the study of evolution of a quantum bit.

Code source:

The team also published a Google Colab for reference: https://colab.research.google.com/drive/1XZ7Lf6pZu6nzEuqt_dUCHormeSbCCMlP. The original paper can be accessed in Nature where they describe the process and the applications.