Animating infinity

A few weeks ago, we celebrated my son's second birthday. His name is Anant, which has its roots in Sanskrit and means "infinite." When my wife and I were deciding on his name, I mentioned that the uniqueness of Anant is that it has a mathematical symbol ??.

During my long travel, I pondered my son's name and how it could be related to mine. My name is Amit, also derived from Sanskrit, which means "boundless." Initially, boundless and infinite may seem synonymous, but they can have a functional relationship. Boundless can be an output of a function in the limits of infinity. For example, if a quantity greater than one is multiplied by itself in the limits of infinity, it becomes boundless. If this quantity is less than 1, the multiplication will result in bounded values (tends to zero). Therefore, Amit can be a function of Anant if operated by a specific function.

I also attempted to create an animation using cascading sine and cosine functions. Although it has corners unlike the smooth ending of the infinity symbol, it is simpler to program and animate. The shape can also be controlled to some extent by adjusting the contributions and amplitudes of sine and cosine.

Below is the program shared in a Google Drive folder.

MATLAB .m file for download

The next thing I would like to do is to synthesise this shape by adding multiple vectors rotating at multiple of original animation speeds (1, 2,..., n). This is essentially adding a Fourier series to generate a signal equivalent to the animated shape. Perhaps I will wait for my son to grow up and do it if he finds it interesting enough.

Thank you for reading my ramblings until the end.

Happy holidays, Merry Christmas, and a very happy new year to all of you.