  We numerically test the correspondence between the scaling limit of
self-avoiding walks (SAW) in the plane and Schramm-Loewner evolution (SLE) with
k=8/3. We introduce a discrete-time process approximating SLE in the exterior
of the unit disc and compare the distribution functions for an internal point
in the SAW and a point at a fixed fractal variation on the SLE, finding good
agreement. This provides numerical evidence in favor of a conjecture by Lawler,
Schramm and Werner. The algorithm turns out to be an efficient way of computing
the position of an internal point in the SAW.
