  We study the spectral decomposition of the Laplacian on a family of fractals
$\mathcal{VS}_n$ that includes the Vicsek set for $n=2$, extending earlier
research on the Sierpinski Gasket. We implement an algorithm [24] for spectral
decimation of eigenfunctions of the Laplacian, and explicitly compute these
eigenfunctions and some of their properties. We give an algorithm for computing
inner products of eigenfunctions. We explicitly compute solutions to the heat
equation and wave equation for Neumann boundary conditions. We study gaps in
the ratios of eigenvalues and eigenvalue clusters. We give an explicit formula
for the Green's function on $\mathcal{VS}_n$. Finally, we explain how the
spectrum of the Laplacian on $\mathcal{VS}_n$ converges as $n \to \infty$ to
the spectrum of the Laplacian on two crossed lines (the limit of the sets
$\mathcal{VS}_n$.)
