Abstract
We discuss a general formalism for numerically evolving initial data in general relativity in which the (complex) Ashtekar connection and the Newman--Penrose conformal 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 
planar spacetime, where we find a spatially constant volume element to be an appropriate coordinate gauge choice.
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