  We investigate the evolution of the density-density correlations in the
isoscalar critical condensate formed at the QCD critical point. The initial
equilibrium state of the system is characterized by a fractal measure
determining the distribution of isoscalar particles (sigmas) in configuration
space. Non-equilibrium dynamics is induced through a sudden symmetry breaking
leading gradually to the deformation of the initial fractal geometry. After
constructing an ensemble of configurations describing the initial state of the
isoscalar field we solve the equations of motion and show that remnants of the
critical state and the associated fractal geometry survive for time scales
larger than the time needed for the mass of the isoscalar particles to reach
the two-pion threshold. This result is more transparent in an event-by-event
analysis of the phenomenon. Thus, we conclude that the initial fractal
properties can eventually be transferred to the observable pion-sector through
the decay of the sigmas even in the case of a quench.
