  The smart kinetic self-avoiding walk (SKSAW) is a random walk which never
intersects itself and grows forever when run in the full-plane. At each time
step the walk chooses the next step uniformly from among the allowable nearest
neighbors of the current endpoint of the walk. In the full-plane a nearest
neighbor is allowable if it has not been visited before and there is a path
from the nearest neighbor to infinity through sites that have not been visited
before. It is well known that on the hexagonal lattice the SKSAW in a bounded
domain between two boundary points is equivalent to an interface in critical
percolation, and hence its scaling limit is the chordal Schramm-Loewner
evolution with kappa=6 (SLE_6). Like SLE there are variants of the SKSAW
depending on the domain and the initial and terminal points. On the hexagonal
lattice these variants have been shown to converge to the corresponding version
of SLE_6. We conjecture that the scaling limit of all these variants on any
regular lattice is the corresponding version of SLE_6. We test this conjecture
for the square lattice by simulating the SKSAW in the full-plane and find
excellent agreement with the predictions of full-plane SLE_6.
