  We investigate numerically the behaviour of damage spreading in a Kauffman
cellular automaton with quenched rules on a dynamical $\phi^3$ graph, which is
equivalent to coupling the model to discretized 2D gravity. The model is
interesting from the cellular automaton point of view as it lies midway between
a fully quenched automaton with fixed rules and fixed connectivity and a
(soluble) fully annealed automaton with varying rules and varying connectivity.
In addition, we simulate the automaton on a fixed $\phi^3$ graph coming from a
2D gravity simulation as a means of exploring the graph geometry.
