We define a function $f: \mathbb N \times \mathbb R \to \mathbb R$ such that $f_0(x)=1$ and for $n \ge 1$ $$f_n(x)=\prod_{j=1}^n \arctan(jx)$$ and then define a function $P: \mathbb N \times [0,2\pi] \to \mathbb R^2$ which correspond to a parameterization of paths over $\mathbb R^2$, where $$P_n(t)=(f_n(\cos(t)),f_n(\sin(t)))$$ So, the green path is just $P_5$ while $t$ ranges from $0$ to $2\pi$ and the pink lines are connected points represented by $P_k$ for each natural $k\le 5$ which emulates that kind of animation of drawing the green path.