Ultrametric Cantor sets are classified by their Michon's graph,
which is a rooted weighted tree. Using the notion of Spectral Triple proposed in the eighties by A. Connes to describe the noncommutative analogs of Riemannian manifolds, such a space can be seen as a manifold with dimension given by the upper box dimension, the analog of a volume form and also a diffusion process generated by an analog of the Laplace-Beltrami operator. Potential applications will be discussed.