  Luo, Rao and Xiong [Topol. Appl. 322 (2022), 108271] conjectured that if a
planar self-similar iterated function system with the open set condition does
not involve rotations or reflections, then every connected component of the
attractor is locally connected. We create a homogeneous counterexample of
Lalley-Gatzouras type, which disproves this conjecture.
