  We give two new examples of groups of intermediate growth, by a method that
was first used by Bux and P\'erez. Our examples are the groups generated by the
automata with the kneading sequences 11(0) and 0(011). By results of
Nekrashevych, both of these groups are iterated monodromy groups of complex
post-critically finite quadratic polynomials. We include a complete, systematic
description of the Bux-P\'erez method. We also prove, as a sample application
of the method, that the groups determined by the automata with kneading
sequence 1(0^k) (k >= 2) have intermediate growth, although this result is
implicit in a survey article by Bartholdi, Grigorchuk, and Sunik. The paper
concludes with an example of a group with no admissible length function; i.e.,
the group in question admits no length function with the properties required by
the Bux-P\'erez method. Whether the group has intermediate growth appears to be
an open question.
