  It is shown that a group defined by forbidding all patterns of size s+1 that
do not appear in a given self-similar group of tree automorphisms is the
topological closure of a self-similar, countable, regular branch group,
branching over its level s stabilizer. As an application, it is shown that
there are no infinite, finitely constrained, topologically finitely generated
groups of binary tree automorphisms defined by forbidden patterns of size two.

Group Theory