(typically some fixed regular lattice) on which the CA are evolving according to a given fixed (typically local) CA-law, we are employing quite irregular, dynamic geometric structures called by us [cellular networks]{}, the main point being that connections ([edges]{} or [links]{}) between the respective [nodes]{} or [cells]{} can be created or annihilated according to a dynamical law which, in addition, determines the evolution of the local node- and edge-states.

To put it briefly, the ‘matter distribution’ (i.e. the global pattern of node-states) acts on the geometry of the network (the global pattern of active edges) and vice versa. Thus, as in general relativity, the network is supposed to find both its internal geometry and its matter-energy distribution with the help of a generalized dynamical law which intertwines the two aspects (cf. e.g. [@R1] or [@R2] and further references given there). Technically, the geometric substructure can be modelled by large, usually quite irregular ([random]{}) [graphs]{}.

To make our point clear, this approach should not be confused with e.g. the spin network approach in LQG or various forms of (dynamical) triangulations. Our networks are usually extremely irregular and wildly fluctuating on a microscopic scale, resembling rather Wheeler’s [space-time foam]{}, and smooth geometric 