As the title suggest, I'm interested in depicting (if possible) the Cayley graph of the special linear group $SL_2(\mathbb{Z})$.
I know one has to start with a presentation of the group so $$SL_2(\mathbb{Z}) =\langle x,y \mid x^4=1 , x^2=y^3\rangle$$ but then stuff start to become really messy, I mean I start with the point representing the neutral element, and the presentation suggests me that I have a square attached to it by one of its vertices since $x^4=1$. Now by the fact that $y^3=x^2$ I can depict the diagonal from the identity to the vertex $x^2$ as the line $1-y-y^2-y^3=x^2$
But then how to go on? Is there a smarter way? are there some picture of it?