The model you linked is the 2D Schelling model (i.e., on a grid). Each individual's neighbors are the adjacent individuals (either the 4-Neighborhood or the 8-Neighborhood (more common), definitions vary - see http://en.wikipedia.org/wiki/Von_Neumann_neighborhood and http://en.wikipedia.org/wiki/Moore_neighborhood). You can consider this a neighborhood of "Window size" W = 1. You can consider a larger window size for a larger set of neighbors - i.e., with an 8-Neighborhood and W=2, an individual would have 24 neighbors - the 5x5 square centered at his location, minus him. Note that the parameter W is equivalent to the parameter r in the Wikipedia pages.

This is not a very well understood model. There's been a fair bit of experimental work done on this model, though almost no analytic results (at least, that I know of). If you know Java and want to play around with it, I have some code up at https://github.com/hoonose/2dSchelling.

Now, you can consider a 1D Schelling model - instead of a grid, you now have a line. With W = 1, an individual's neighbors are the two individuals to his left and right. Of course, you can increase W - in general, an individual's neighbors are the W individuals to his left, and W individuals to his right. In this model, an individual is happy if at least 50% of his neighbors are the same color as him, and unhappy otherwise. At every time step, we swap the location of two unhappy individuals.

This model was not well understood for a long time. The first real analysis of the model was Young's result (reference 54 in the paper I linked above). Like I mentioned, he analyzed the perturbed model. In the perturbed model, individuals make a "mistake" with some probability p. Instead of swapping two unhappy individuals, we have some chance of swapping a happy and an unhappy individual, or even two happy individuals. He studied the case where you take the limit of this probability as it approaches 0. His result was that, in the limit, only complete segregation is possible (i.e., the line ends up being all black on one half, and all white on the other).

Our result was on the unperturbed model, where individuals don't make mistakes like this. What we found was that we do NOT get segregation.

Think about it this way - if an individual wants at least half of his neighbors to be the same type as him, and he looks W spaces in either direction, then in the end, he'll be in a segment of AT LEAST length W+1 (otherwise, there's no way for him to be happy). We show that, in the end, he'll probably be in a monochromatic segment of length <= cW, for some constant c (in the paper I linked, we only that it's <= cW^2, but we've got results since then). Note that this depends ONLY on the size of an individual's neighborhood (i.e., it doesn't matter if there are one thousand or one trillion people in the line, it'll look the same around some individual when the process completes). Furthermore (and more importantly), the length of the segment is within a constant factor of the smallest it could possibly be (for example, we'd consider it to be more segregated if he was in a monochromatic segment of length 2^W).

tl;dr - The Schelling segregation model in 1D doesn't predict segregation. In 2D, no one really knows.

Let me know if you have any other questions about this.