The mathematics of Schellings segregation model
- by Bruce
For those who don't know the model. You can read this pdf. I want to find what is the probability that 2 nodes are each others neighbors when the algorithm converges (i.e. when all nodes are happy).
Here's the model in a gist. You have
a grid (say 10x10). You have nodes of
two kind (red and green) 45 each. So
we have 10 empty spaces. We randomly
place the nodes on the grid. Now we
scan through this grid (Exact order
does not matter according to
Schelling). Each node wants a specific
percentage of people of same kind in
its Moore neighborhood (say b = 50%
for each red and green). We calculate
the happiness of each node (a = Number
of neighbors of same kind/Number of
neighbors of different kind). If a
node is unhappy (a < b) it moves to an
empty cell where it knows it will be
happy. This movement can change the
dynamics of old as well as new
neighborhood. Algorithm converges when
all nodes are happy.
PS - I am looking for links for any mathematical analysis of the Schelling's model.
