BML model on non-orientable surfaces

Two-dimensional Biham–Middleton–Levine traffic model on a N×N square lattice embedded on a Klein bottle and a projective plane is investigated by computer simulations. The behavior of the model with these boundary conditions is compared with the model under toroidal boundary conditions. Our numerical results show that the phase diagram depends strongly on the underlying topology. We also investigate the influence of the ratio between the number of red and blue particles has over the speed of the system and conclude that the projective plane case differs considerably from the other cases reviewed here.