Combinatorial dynamics in quantum gravity

We describe the application of methods from the study of discrete dynamical systems to the study of histories of evolving spin networks. These have been found to describe the small scale structure of quantum general relativity and extensions of them have been conjectured to give background independent formulations of string theory. We explain why the the usual equilibrium second order critical phenomena may not be relevant for the problem of the continuum limit of such theories, and why the relevant critical phenomena analogue to the problem of the continuum limit is instead non-equilibrium critical phenomena such as directed percolation. The fact that such non-equilibrium critical phenomena may be self-organized implies the possibility that the classical limit of quantum theories of gravity may exist without fine tuning of parameters. email addresses: [email protected], [email protected]