By a piecewise linear unimodal map,we described the mathematical of Feigenbaum attractor and proved that the quadratic family possessed a nest of proper Fμ cycles with period 2n which determined an attractive minimal Cantor set.The subsystem of the map on the set was topologically conjugate to a so-called "adding machine" on the symbol sequence space.Some supplements were added to the recent results and several proofs were simplified.