  In this paper we perform a numerical study of the spectra, eigenstates, and
Lyapunov exponents of the skew-shift counterpart to Harper's equation. This
study is motivated by various conjectures on the spectral theory of these
'pseudo-random' models, which are reviewed in detail in the initial sections of
the paper. The numerics carried out at different scales are within agreement
with the conjectures and show a striking difference compared with the spectral
features of the Almost Mathieu model. In particular our numerics establish a
small upper bound on the gaps in the spectrum (conjectured to be absent).
