  We suggest a generalization of the dynamical triangulation approach to
quantum gravity with both timelike and spacelike edges, which can serve as a
toy model for quantum gravity in the Lorentz sector in two dimensions. It is
possible to consider the model in a purely Lorentzian sector or to relax this
constraint and allow local signature changing moves. We show that, with
suitable conventions, the model is equivalent to an Ising model coupled to 2D
Euclidean quantum gravity and conduct a preliminary numerical simulation of the
Lorentz sector.
