  It is proposed that gravity may arise in the low energy limit of a model of
matter fields defined on a special kind of a dynamical random lattice. Time is
discretized into regular intervals, whereas the discretization of space is
random and dynamical. A triangulation is associated to each distribution of the
spacetime points using the flat metric of the embedding space. We introduce a
diffeomorphism invariant, bilinear scalar action, but no ``pure gravity''
action.
  Evidence for the existence of a non-trivial continuum limit is provided by
showing that the zero momentum scalar excitation has a finite energy in the
limit of vanishing lattice spacing. Assuming the existence of localized low
energy states which are described by a natural set of observables, we show that
an effective curved metric will be induced dynamically. The components of the
metric tensor are identified with quasi-local averages of certain microscopic
properties of the quantum spacetime. The Planck scale is identified with the
highest mass scale of the matter sector.
