  We study two ways of summing an infinite family of noncommutative spectral
triples. First, we propose a definition of the integration of spectral triples
and give an example using algebras of Toeplitz operators acting on weighted
Bergman spaces over the unit ball of $\mathbb{C}^n$. Secondly, we construct a
spectral triple associated to a general polygonal self-similar set in
$\mathbb{C}$ using algebras of Toeplitz operators on Hardy spaces. In this
case, we show that we can recover the Hausdorff dimension of the fractal set.
