Self-Organized Societies: On the Sakoda Model of Social Interactions

Figure 9

(a) Plots of the rescaled interface edges versus the rescaled number of corners for all the types: are symbolized by and are symbolized by ■ and for case. The colors represent the five different vacancy concentrations: the cyan markers stand for , the red ones stand for , the green ones are for , blue ones stand for , and orange ones stand for . One notices that the correlation is linear: . The numerical simulation considers periodic lattice and includes the 45 different cases and 5 different initial fractions of vacancies. (b) plots the total rescaled number of edges versus ; (c) the total rescaled number of edges versus ; and finally (d) plots the total rescaled energy versus . In plots (b), (c), and (d) the surfaces were obtained after an interpolation with a quadratic fit of the form , where a, b, c, d, e, and f are fitting constants. The simulations were developed in a two-dimensional periodic lattice of size , considering short influence/long movement range evolution rule and with a running time of steps.

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(b)

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