  We consider discrete Schr\"odinger operators with pattern Sturmian
potentials. This class of potentials strictly contains the class of Sturmian
potentials, for which the spectral properties of the associated Schr\"odinger
operators are well understood. In particular, it is known that for every
Sturmian potential, the associated Schr\"odinger operator has zero-measure
spectrum and purely singular continuous spectral measures. We conjecture that
the same statements hold in the more general class of pattern Sturmian
potentials. We prove partial results in support of this conjecture. In
particular, we confirm the conjecture for all pattern Sturmian potentials that
belong to the family of Toeplitz sequences.
