Is $ mathrm {Cantor , set} times [0,1]$ self-similar?

Consider the Cantor set $ times $ l & # 39; interval $[0,1]$, that is to say that Cantor sets put "next to each other" to "cover" the place $[0,1]time [0,1]$ is this set similar, that is, the attractor of certain homotheties?