  We show that the limit in our definition of tree shift topological entropy is
actually the infimum, as is the case for both the topological and
measure-theoretic entropies in the classical situation when the time parameter
is $\mathbb Z$. As a consequence, tree shift entropy becomes somewhat easier to
work with. For example, the statement that the topological entropy of a tree
shift defined by a one-dimensional subshift dominates the topological entropy
of the latter can now be extended from shifts of finite type to arbitrary
subshifts. Adapting to trees the strip method already used to approximate the
hard square constant on $\mathbb Z^2$, we show that the entropy of the hard
square tree shift on the regular $k$-tree increases with $k$, in contrast to
the case of $\mathbb Z^k$. We prove that the strip entropy approximations
increase strictly to the entropy of the golden mean tree shift for
$k=2,\dots,8$ and propose that this holds for all $k \geq 2$. We study the
dynamics of the map of the simplex that advances the vector of ratios of symbol
counts as the width of the approximating strip is increased, providing a fairly
complete description for the golden mean subshift on the $k$-tree for all $k$.
This map provides an efficient numerical method for approximating the entropies
of tree shifts defined by nearest neighbor restrictions. Finally, we show that
counting configurations over certain other patterns besides the natural finite
subtrees yields the same value of entropy for tree SFT's.
