Monte Carlo simulation of entropy-driven pattern formation in two-dimensional system of rectangular particles

We simulated random walk of rectangular particles on a square lattice with periodic boundary conditions. Two kind of particles were investigated, viz., so-called `blind' and `myopic' particles. We found that steady state patterns occurred only for some values of the ratio $L_x/L_y$ where $L_x$ and $Ly$ are the linear sizes of the system and only for `needles', i.e., the particles of size $1 \times k$. Different patterns were observed for `blind' and `myopic' particles.