  We consider a Schelling model of self-organized segregation in an open system
that is equivalent to a zero-temperature Ising model with Glauber dynamics, or
an Asynchronous Cellular Automaton (ACA) with extended Moore neighborhoods.
Previous work has shown that if the intolerance parameter of the model $\tau\in
(\sim 0.488,\sim 0.512) \setminus \{1/2\}$, then for a sufficiently large
neighborhood of interaction $N$, any particle will end up in an exponentially
large monochromatic region almost surely.
  This paper extends the above result to the interval $\tau \in (\sim
0.433,\sim 0.567) \setminus \{1/2\}$. We also improve the bounds on the size of
the monochromatic region by exponential factors in $N$. Finally, we show that
when particles are placed on the infinite lattice $\mathbb{Z}^2$ rather than on
a flat torus, for the values of $\tau$ mentioned above, sufficiently large $N$,
and after a sufficiently long evolution time, any particle is contained in a
large monochromatic region of size exponential in $N$, almost surely. The new
proof, critically relies on a novel geometric construction related to the
formation of the monochromatic region.
