  The Horton-Strahler analysis is a graph-theoretic method to measure the
bifurcation complexity of branching patterns, by defining a number called the
order to each branch. The main result of this paper is a large deviation
theorem for the number of branches of each order in a random binary tree. The
rate function associated with a large deviation cannot be derived in a closed
form; instead, asymptotic forms of the rate function are given.
