The structure of a Cantor-like set with overlap

In this paper, for the contracting similarities S0(x)=x5, S1(x)=x+λ5, S2(x)=x+25, S3(x)=x+4-λ5 and S4(x)=x+45, where rational number λ∈[0,23], the Hausdorff dimension and the structure of Eλ, an invariant set with respect to S0, S1, S2, S3, S4 were studied and some new results were reported. Relation to El Naschie's quantum fractal is also discussed.