  The moving puncture method is analyzed for a single, non-spinning black hole.
It is shown that the puncture region is not resolved by current numerical
codes. As a result, the geometry near the puncture appears to evolve to an
infinitely long cylinder of finite areal radius. The puncture itself actually
remains at spacelike infinity throughout the evolution. In the limit of
infinite resolution the data never become stationary. However, at any
reasonable finite resolution the grid points closest to the puncture are
rapidly drawn into the black hole interior by the Gamma-driver shift condition.
The data can then evolve to a stationary state. These results suggest that the
moving puncture technique should be viewed as a type of "natural excision".
