  We discuss a general formalism for numerically evolving initial data in
general relativity in which the (complex) Ashtekar connection and the
Newman-Penrose scalars are taken as the dynamical variables. In the generic
case three gauge constraints and twelve reality conditions must be solved. The
analysis is applied to a Petrov type \{1111\} planar spacetime where we find a
spatially constant volume element to be an appropriate coordinate gauge choice.
