  The Biham-Middleton-Levine traffic model is perhaps the simplest system
exhibiting phase transitions and self-organization. Moreover, it is an
underpinning to extensive modern studies of traffic flow. The general belief is
that the system exhibits a sharp phase transition from freely flowing to fully
jammed, as a function of initial density of cars. However we discover
intermediate stable phases, where jams and freely flowing traffic coexist. The
geometric structure of such phases is highly regular, with bands of free
flowing traffic intersecting at jammed wavefronts that propagate smoothly
through the space. Instead of a phase transition as a function of density, we
see bifurcation points, where intermediate phases begin coexisting with the
more conventionally known phases. We show that the regular geometric structure
is in part a consequence of the finite size and aspect ratio of the underlying
lattice, and that for certain aspect ratios the asymptotic intermediate phase
is on a short periodic limit cycle (the exact microscopic configuration recurs
each tau timesteps, where tau is small compared to the system size). Aside from
describing these intermediate states, which previously were overlooked, we
derive simple equations to describe the geometric constraints, and predict
their asymptotic velocities.
