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(a)
(b)
FIGURE 2.8 Schelling's model: segregation from mild preferences to be amongst one's own kind.
(a) A random distribution of two kinds of agents - grey and white. (b) Segregation under mild conditions of
preferences for being similar.
neighbours and they begin to change their tastes accordingly. In fact, there are two ways of making
the change, either the resident might move to another cell to try to increase their number of like
neighbours or they might actually change their tastes to reflect their neighbours. We will adopt the
latter course in that we assume that if a resident with taste i finds himself or herself surrounded by
five or more neighbours with taste j , then they will assume that the vote has gone against them and
they will change their tastes accordingly.
Now let us see what happens when we start with a completely random configuration of tastes
but in the proportion 50:50 as illustrated in Figure 2.8a. Applying the transition rule, then after a
sufficient number of iterations (37 in this case), a new but highly segregated equilibrium emerges
which is shown in Figure 2.8b. What is remarkable about this structure is that although residents
will gladly coexist with an equal number of neighbours of either type - an even mix - this does
not occur. The local dynamics of the situation make any global equality impossible. You can
work this through by considering how more than four cells of either kind lead to a reinforcement
or positive feedback which increases segregation which, in random situations, is likely to be the
norm. Moreover, once this begins, the local repercussions throughout the system can turn what
is almost an even mix into a highly segregated pattern. Once again, this is a true property of
emergence in CA for it is impossible to deduce it from a knowledge of the local dynamics. It only
occurs when the local dynamics are writ large. It was first pointed out by Schelling (1978) as an
example of how micro-motives cannot be aggregated into macro-motives, which he illustrated
with respect to the emergence of highly segregated ethnic neighbourhoods in US cities. A similar
problem in which the residents move rather than change their tastes is worked through by Resnick
(1994), and a generalisation to wider models of segregation has been researched by Portugali et al.
(1994) and Benenson (2014).
2.9 APPLICATIONS TO CITIES AND RELATED ECOLOGIES
The application of CA to urban systems like CA itself can be traced back to the beginning, to the
first attempts to build mathematical models of urban systems which began in the 1950s. In the
postwar years, social physics was in full swing and models of spatial diffusion were an important
branch of these developments. Hagerstrand as early as 1950 was building diffusion models, specifi-
cally of human migration based on the excellent historical population record in Sweden, and these
models, although embodying action at a distance through gravitation effects, were close in spirit to
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