  Simulations of the self-avoiding walk (SAW) are performed in a half-plane and
a cut-plane (the complex plane with the positive real axis removed) using the
pivot algorithm. We test the conjecture of Lawler, Schramm and Werner that the
scaling limit of the two-dimensional SAW is given by Schramm's Stochastic
Loewner Evolution (SLE). The agreement is found to be excellent. The
simulations also test the conformal invariance of the SAW since conformal
invariance would imply that if we map the walks in the cut-plane into the half
plane using the conformal map z -> sqrt(z), then the resulting walks will have
the same distribution as the SAW in the half plane. The simulations show
excellent agreement between the distributions.
