How to read it
Every node gets a position in two lists. Q1 lists the tree top-down with siblings in their order, Q2 with siblings reversed. A node u reaches v exactly when u comes before v in both lists.
A new node needs two list insertions; the other positions stay as they are. Step through the build with the slider and watch it happen, edge by edge.
The method is described in E. Olgac, “Topology and Structure of Directed Trees: An Incremental Encoding”.