Natural Intelligence has developed an application called the "Ethnic Simulator" that models the residential behavior of people in the hypothetical ethnically diverse city of Metropolis....
The premise of the Ethnic Simulator is that ethnically distinct groups have a modest preference to live among their own kind.
Go here to read the details about the Ethnic Simulator and download a freeware copy of the application.
You will find that the different groups congregate relatively quickly in their separate enclaves -- within about ten years. It is important to note that this occurs without any assumption of discrimination by one group against another! All that is required is that each group have a modest preference for its own kind.
One of the counter-intuitive results is that the preferences of the dominant majority do not make as much difference as the preferences of the minorities. Blues are the largest group (about 65%), so that they will tend to have mostly Blues for neighbors, no matter their preferences. But the preference of a small minority will cause its families to clump quickly into segregated neighborhoods.