2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71299Nekrashevych conjectured that the iterated monodromy groups of quadratic polynomials with preperiodic critical orbit have intermediate growth. We illustrate some of the difficulties that arise in attacking this conjecture and prove subexponential growth for the iterated monodromy group of $z^2+i$. This is the first non-trivial example supporting the conjecture.15 pages, 1 figure. Revised abstract and introductionGroup TheoryDynamical Systems20F65,37F20text