  We describe the application of methods from the study of discrete dynanmical
systems to the problem of the continuum limit 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 critical phenomena may not be relevant for the problem of the
continuum limit of such theories and why, instead, the continuum limits of such
theories are likely to be governed by non-equilibrium critical phenomena such
as directed percolation. The fact that such non-equilibrium critical phenomena
can be self-organized implies the possibility that the classical limit of
quantum theories of gravity may exist without fine tuning of parameters.
