  I show that the motion of a closed string consisting of $n$ segments in
AdS$_3$ can be embedded into the mutation dynamics of the $Y^{n,0}$ brane
tiling. The determinant of the Kasteleyn matrix computes the spectral curve.
The dynamics is governed by a Y-system with additional constraints ensuring
that the string closes in target space. The constraints can be deformed by
coupling the worldsheet to a background two-form whose field strength is
proportional to the volume form.

High Energy Physics - Theory;Exactly Solvable and Integrable Systems