Abstract
The Schelling model of segregation allows for a general description of residential movements in an environment modeled by a lattice. The key factor is that occupants change positions until they are surrounded by a designated minimum number of similarly labeled residents. An analogy to the Ising model has been made in previous research, primarily due the assumption of state changes being dependent upon the adjacent cell positions. This allows for concepts produced in statistical mechanics to be applied to the Schelling model. Here is presented a methodology to estimate the entropy of the model for different states of the simulation. A Monte Carlo estimate is obtained for the set of macrostates defined as the different aggregate homogeneity satisfaction values across all residents, which allows for the entropy value to be produced for each state. This produces a trace of the estimated entropy value for the states of the lattice configurations to be displayed with each iteration. The results show that the initial random placements of residents have larger entropy values than the final states of the simulation when the overall homogeneity of the residential locality is increased.
Highlights
Human actors are very complex objects to model and the factors of the environment which affect their behavioral state is a challenge to encapsulate in a mathematical framework
This section explores the Schelling model in terms of the macrostate value at each iteration defined in Equation (7) and the entropy value estimated Set = k B Ω
The Monte Carlo sampling scheme required for Equation (10) is computationally demanding
Summary
Human actors are very complex objects to model and the factors of the environment which affect their behavioral state is a challenge to encapsulate in a mathematical framework. This difficulty is further increased when long term macroscopic changes are taken into account. A simulation continues to allocate random position reassignments until all residents have the required amount of identically labeled neighbors needed to cease their movements. This results in an iterative procedure of spatially orienting residents to be placed in a macroscopic set of labeled clusters. In the final iteration when the homogeneity satisfactions are met, the grid will look ‘organized’ as groups of labeled actors cluster together
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