Cantor sets arising from continued radicals

If a ₁,a ₂,a ₃,… are nonnegative real numbers and $f_{j}(x) = sqrt{a_{j}+x}$ , then lim _n→∞ f ₁°f ₂°?°f _n (0) is a continued radical with terms a ₁,a ₂,a ₃,…. The set of real numbers representable as a continued radical whose terms a _i are all from a set S={a,b} of two natural numbers is a Cantor set. We investigate the thickness, measure, and sums of such Cantor sets.