  A zero-field Ising model with ferromagnetic coupling constants on the
so-called Labyrinth tiling is investigated. Alternatively, this can be regarded
as an Ising model on a square lattice with a quasi-periodic distribution of up
to eight different coupling constants. The duality transformation on this
tiling is considered and the self-dual couplings are determined. Furthermore,
we analyze the subclass of exactly solvable models in detail parametrizing the
coupling constants in terms of four rapidity parameters. For those, the
self-dual couplings correspond to the critical points which, as expected,
belong to the Onsager universality class.
