  Experiments on optical and STM injection of carriers in layered
$\mathrm{MX_2}$ materials revealed the formation of nanoscale patterns with
networks and globules of domain walls. This is thought to be responsible for
the metallization transition of the Mott insulator and for stabilization of a
"hidden" state. In response, here we present studies of the classical charged
lattice gas model emulating the superlattice of polarons ubiquitous to the
material of choice $1T-\mathrm{TaS_2}$. The injection pulse was simulated by
introducing a small random concentration of voids which subsequent evolution
was followed by means of Monte Carlo cooling. Below the detected phase
transition, the voids gradually coalesce into domain walls forming locally
connected globules and then the global network leading to a mosaic
fragmentation into domains with different degenerate ground states. The
obtained patterns closely resemble the experimental STM visualizations. The
surprising aggregation of charged voids is understood by fractionalization of
their charges across the walls' lines.
