  We perform dynamical and nonlinear numerical simulations to study critical
phenomena in the gravitational collapse of massless scalar fields in the
absence of spherical symmetry. We evolve axisymmetric sets of initial data and
examine the effects of deviation from spherical symmetry. For small deviations
we find values for the critical exponent and echoing period of the discretely
self-similar critical solution that agree well with established values;
moreover we find that such small deformations behave like damped oscillations
whose damping coefficient and oscillation frequencies are consistent with those
predicted in the linear perturbation calculations of Martin-Garcia and
Gundlach. However, we also find that the critical exponent and echoing period
appear to decrease with increasing departure from sphericity, and that, for
sufficiently large departures from spherical symmetry, the deviations become
unstable and grow, confirming earlier results by Choptuik et.al.. We find some
evidence that these growing modes lead to a bifurcation, similar to those
reported by Choptuik et.al., with two centers of collapse forming on the
symmetry axis above and below the origin. These findings suggest that nonlinear
perturbations of the critical solution lead to changes in the effective values
of the critical exponent, echoing period and damping coefficient, and may even
change the sign of the latter, so that perturbations that are stable in the
linear regime can become unstable in the nonlinear regime.
