  We study the dynamics of genetic code evolution. The model of Vetsigian et
al. [1] and Vetsigian [2] uses the mechanism of horizontal gene transfer to
demonstrate convergence of the genetic code to a near universal solution. We
reproduce and analyze the algorithm as a dynamical system. All the parameters
used in the model are varied to assess their impact on convergence and
optimality score. We show that by allowing specific parameters to vary with
time, the solution exhibits attractor dynamics. Finally, we study automorphisms
of the genetic code arising due to this model. We use this to examine the
scaling of the solutions in order to re-examine universality and find that
there is a direct link to mutation rate.
