On the silhouette of binary search trees

A zero-one sequence describes a path through a rooted directed binary tree $T$; it also encodes a real number in $[0,1]$. We regard the level of the external node of $T$ along the path as a function on the unit interval, the silhouette of $T$. We investigate the asymptotic behavior of the resulting stochastic processes for sequences of trees that are generated by the binary search tree algorithm.