DFT sort coefficients in Fourier Series

Question

On the website Drawing with DFT and Epicycles the author Amrit explains how to make the drawing with epicycles

I am studying through this site, and I have a question about sort.

What is the purpose of changing the order of coefficients from c_-100, c_-99, c_-98 ... to c_0, c_1, c_-1, c_2, c_-2 ?

if i sort by amplitude i get the same result as sorted image.

Even without sort it is possible to create the epicycles and draw.

Below are the gifs with and without sort.

sorted

unsorted

Answer 1

The series was placed in the usual order of the actual series, so c1 and c-1 are the same things as a1 and b1, they are the coefficients of cosine and sine next to each other.

With that, you start creating the circles with the lowest frequency terms (n=0, 1, 2, etc) and proceed to the highest ones. This is what increases the "stability" of the figure. The first circle, for example, corresponding to c_0 (or a_0), is stationary as it is the zero frequency term.