  We describe a numerical procedure to compute the so-called isospectral torus
of finite gap sets, that is, the set of Jacobi matrices whose essential
spectrum is composed of finitely many intervals. We also study numerically the
convergence of specific Jacobi matrices to their isospectral limit. We then
extend the analyis to the definition and computation of an "isospectral torus"
for Cantor sets in the family of Iterated Function Systems. This analysis is
developed with the ultimate goal of attacking numerically the conjecture that
the Jacobi matrices of I.F.S. measures supported on Cantor sets are
asymptotically almost-periodic.
