  The parameter regime in which a Brinkmann-Rice (BR) transition appears near
half-filling is investigated for a model of of one kind of electrons traversing
a plane randomly tiled with CuO_4 molecules, simulating the copper-oxide planes
of high-T_c superconductors. As the hole doping is increased, the BR transition
evolves continuously into a state characterized by Kauzmann-like plateaus in
the entropy vs. temperature curves. Despite clear analogies with the glass
transition, these are equilibrium properties of the model. This is because the
spin interactions, responsible for ordering in real space, are not included.
