  An inhomogeneous random recursive lattice was constructed from the
multi-branched Husimi square lattice. The number of repeating units connected
on one vertex was randomly set to be 2 or 3 with a quenched ratio $P_2$ or
$P_3$ with $P_2+P_3=1$. The model was designed to describe complex
thermodynamic systems with variable coordinating neighbors, e.g. the
cross-dimensional range around the surface of a bulk materials. Classical
ferromagnetic spin-1 Ising model was solved on the lattice to achieve an
annealed solution via the local exact calculation technique. The model exhibits
distinct spontaneous magnetization similar to the deterministic system, with
however rigorous thermal fluctuations and significant singularities on the
entropy behavior around the critical temperature, indicating a complex
superheating and supercooling frustration in the cross-dimensional range
induced by the stochasticity. The critical temperature was found to be
exponentially correlated to the structural ratio $P$ with the coefficient
fitted as 0.53187, while the ground state energy presents linear relation to
$P$, implying a well-defined average property according to the structural
ratio.
