  We present the first numerical simulations in null coordinates of the
collapse of nonspherical regular initial data to a black hole. We restrict to
twist-free axisymmetry, and re-investigate the critical collapse of a
non-spherical massless scalar field. We find that the Choptuik solution
governing scalar field critical collapse in spherical symmetry persists when
fine-tuning moderately non-spherical initial data to the threshold of black
hole formation. The non-sphericity evolves as an almost-linear perturbation
until the end of the self-similar phase, and becomes dominant only in the final
collapse to a black hole. We compare with numerical results of Choptuik et al,
Baumgarte, and Marouda et al, and conclude that they have been able to evolve
somewhat more non-spherical solutions. Future work with larger deviations from
spherical symmetry, and in particular vacuum collapse, will require a different
choice of radial coordinate that allows the null generators to reconverge
locally.
