Graph subshifts of finite type are defined via forbidden local patterns; those with only infinite graphs are either aperiodic or their period groups are not residually finite.
Tilings of the plane and Thurston semi-norm
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
We show that the problem of tiling the Euclidean plane with a finite set of polygons (up to translation) boils down to prove the existence of zeros of a non-negative convex function defined on a finite-dimensional simplex. This function is a generalisation, in the framework of branched surfaces, of the Thurston semi-norm originally defined for compact $3$-manifolds.
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Graph subshifts
Graph subshifts of finite type are defined via forbidden local patterns; those with only infinite graphs are either aperiodic or their period groups are not residually finite.