[math-fun] Number-of-pieces question (in the limit)

Imagine a large unit circle C centered at the origin of the plane. Also assume the plane is endowed with the usual hexagonal tessellation T but after the tessellation has been uniformly shrunk toward the origin by a factor of f with 0 < f < 1, to obtain the tessellation we call fT. Given f, define H(f) = the union of the hexagons of fT lying entirely inside or on C. Now suppose that 50% of the hexagons of fT are selected independently at random. Call the *union* of these hexagons X. Questions: ---------- What is the expected number N(f) of connected components of X as a function of f ??? As f —> 0+, is N(f) asymptotic to (a constant times) some power f^p of f? —Dan