Mathematical properties [of branching model]

If an element c of the list b is real, so that there is a stem that goes straight up, then the limiting height of the center of the pattern is obtained by summing a geometric series, and is given by 1/(1-c). The overall limiting pattern will be finite so long as Abs[c]<1 for all elements of b. After n steps the total length of all stems is given by Apply[Plus,Abs[b]]^{n}. (See page 1006 for other properties.)