What kind of studies are this? at this link there are quite a number of images reporting different patterns inside a circle: what kind of studies are this and does this belongs to a specific branch of the mathematics ?

It looks like what they're doing is making graphs on with vertex set $\{0,\ldots ,n-1\}$ and edges defined by $\{x,\;f(x)\bmod{n}\}$, where each image corresponds to a different $f(x)$.  I would say the area of math here is number theory, just represented in an interesting way using graphs.
There may also be some of them where the vertex set is a large sampling of points from $[0,1)$, with $f(x)$ taken $\bmod 1$.
