  Recent advances in emergent geometry have identified a new class of models
that represent spacetime as the graph obtained as the ground state of
interacting Ising spins. These models have many desirable features, including
stable excitations possessing many of the characteristics of a quantum
particle. We analyze the dynamics of such excitations, including a detailed
treatment of the edge states not previously addressed. Using a minimal
prescription for the interaction of defects we numerically investigate
approximate bounds to the speed of propagation of such a `particle'. We
discover, using numerical simulations, that there may be a Lieb-Robinson bound
to propagation that could point the way to how a causal structure could be
accommodated in this class of emergent geometry models.
