  We study the Monadic Second Order (MSO) Hierarchy over colourings of the
discrete plane, and draw links between classes of formula and classes of
subshifts. We give a characterization of existential MSO in terms of
projections of tilings, and of universal sentences in terms of combinations of
"pattern counting" subshifts. Conversely, we characterise logic fragments
corresponding to various classes of subshifts (subshifts of finite type, sofic
subshifts, all subshifts). Finally, we show by a separation result how the
situation here is different from the case of tiling pictures studied earlier by
Giammarresi et al.
