Given a binary tree, with parent node $O$, and each node having two children. Is there a prescription for what the coordinates of each node will be if I want to embed the tree in a Poincaré disc such that node $O$ is at the origin? Basically I want to construct an embedding that looks something like this. Is there a simple equation for the $x,y$ coordinates of each node? Or a deterministic algorithm to calculate it?
Thanks!