  The reported spatial variation in the fine-structure constant at high
redshift, if physical, could be due to the presence of dilatonic domains, and
one or more domain walls inside our horizon. An absorption spectrum of an
object in a different domain from our own would be characterized by a different
value of alpha. We show that while a single wall solution is statically
comparable to a dipole fit, and is a big improvement over a weighted mean
(despite adding 3 parameters), a two-wall solution is a far better fit (despite
adding 3 parameters over the single wall solution). We derive a simple model
accounting for the two-domain wall solution. The goodness of these fits is
however dependent on the extra random error which was argued to account for the
large scatter in most of the data. When this error is omitted, all the above
solutions are poor fits to the data. When included, the solutions that exhibit
a spatial dependence agree with the data much more significantly than the
Standard Model; however, the Standard Model itself is not a terrible fit to the
data, having a p-value of ~ 20 %.
