The Self-similar Structure Of The Translation Of Two Kind Of Cantor Sets

Many scholars have lucubrated on self similar sets with the overlap structure recently.The translation of the Cantor-like sets has been an activity topic for decades.They use different ways to compute the dimensions accurately or approximately.Thispaper considers concrete structure of the transaction from the self similar set.LetΓ_αbe the middleαCantor sets,α∈(1／3,1).This paper gives the concrete expression ofthe elements in the setΓ_α∩(Γ_α+t),then examines the setΓ_α∩(Γ_α+t) whether is aself similar set though the structure and expression of the general self similar set.givesthe sufficient and necessary condition so that the intersectionΓ_α∩(Γ_α+t) is a selfsimilar set.Then we will judge the IFS of the self similar set whether satisfies the OpenSet Condition.It is of direct importance to account the Hausdorff,Boxing dimensionof the self similar sets.We investigate some structures of the iterated function systemswhich generated the self similar sets.The questions and results are extended to thesimilar n Cantor set.