Do irregular grids make a difference? Relaxing the spatial regularity assumption, in cellular models of social dynamics

This paper introduces irregular grids with variation in the structure and size of neighbourhoods between locations in the grid, and test robustness of two applications that are representative for two broad classes of CA models, migration dynamics and influence dynamics.

Abstract

Three decades of CA-modelling in the social sciences have shown that the cellular automata framework is a useful tool to explore the relationship between micro assumptions and macro outcomes in social dynamics. However, virtually all CA-applications in the social sciences rely on a potentially highly restrictive assumption, a rectangular grid structure. In this paper, we relax this assumption and introduce irregular grids with variation in the structure and size of neighbourhoods between locations in the grid. We test robustness of two applications from our previous work that are representative for two broad classes of CA models, migration dynamics and influence dynamics. We tentatively conclude that both influence dynamics and migration dynamics have important general properties that are robust to variation in the grid structure. At the same time, we find in both examples substantively interesting implications of the irregular grid that could not be identified with a regular grid structure.