  This note constructs a finitely generated group $W$ whose word-growth is
exponential, but for which the infimum of the growth rates over all finite
generating sets is 1 -- in other words, of non-uniformly exponential growth.
  This answers a question by Mikhael Gromov.
  The construction also yields a group of intermediate growth $V$ that locally
resembles $W$ in that (by changing the generating set of $W$) there are
isomorphic balls of arbitrarily large radius in $V$ and $W$'s Cayley graphs.
