  We give the first example of a connected 4-regular graph whose Laplace
operator's spectrum is a Cantor set, as well as several other computations of
spectra following a common ``finite approximation'' method. These spectra are
simple transforms of the Julia sets associated to some quadratic maps. The
graphs involved are Schreier graphs of fractal groups of intermediate growth,
and are also ``substitutional graphs''. We also formulate our results in terms
of Hecke type operators related to some irreducible quasi-regular
representations of fractal groups and in terms of the Markovian operator
associated to noncommutative dynamical systems via which these fractal groups
were originally defined. In the computations we performed, the self-similarity
of the groups is reflected in the self-similarity of some operators; they are
approximated by finite counterparts whose spectrum is computed by an ad hoc
factorization process.
