I understand $\pi _{3}(S^2)$ by the Hopf Fibration which is the map
$p(x_1,x_2,x_3,x_4)=(x_{1}^2+x_{2}^2-x_{3}^2-x_{4}^2, 2(x_1 x_4+x_2 x_3), 2(x_2 x_4-x_1 x_3))$.
These are disjoint circle in $\mathbb{R}^4$ mapped to points onto $S^2$. What is the map of $\pi _{4}(S^2)$?
I am trying to visualize $\pi _{4}(S^2)$ but I am having trouble. I have read Visualize Fourth Homotopy Group of $S^2$ but it is not coming to me. I think seeing a map like $p(x_1,x_2,x_3,x_4)$ will help.
Could someone please provide a map $p(x_1,x_2,x_3,x_4,x_5)$ for $\pi _{4}(S^2)$.