Discrete symmetries of chaotic strings
  Chaotic strings are particular classes of coupled map lattices that can serve as models for vacuum fluctuations in stochastically quantized field theories. They have been previously shown to distinguish standard model coupling parameters as corresponding to states of strongest possible chaotic behaviour and vanishing nearest-neighbour correlation. In this paper we look at discrete symmetry transformations for chaotic strings. We show that several of the chaotic string dynamics can be transformed into each other by simple discrete coordinate transformations. We investigate how expectation values converge in the various coupling parameter regions and single out those stable zeros of the correlation function that correspond to ergodic states with well-defined convergence properties. 
Mirko Schaefer, Christian Beck