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Do Irregular Grids Make a Difference? Relaxing the Spatial Regularity Assumption in Cellular Models of Social Dynamics

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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.

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  • Andreas Flache & Rainer Hegselmann, 2001. "Do Irregular Grids Make a Difference? Relaxing the Spatial Regularity Assumption in Cellular Models of Social Dynamics," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 4(4), pages 1-6.
    • Handle: RePEc:jas:jasssj:2001-4-2
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    2. Bertazzi, Ilaria, 2014. "Transitivity matters. Norms Enforcement and diffusion using different neighborhoods in CAs," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201429, University of Turin.
    3. Daniel Stevens & Suzana Dragićević, 2007. "A GIS-Based Irregular Cellular Automata Model of Land-Use Change," Environment and Planning B, , vol. 34(4), pages 708-724, August.
    4. Bithell, M. & Macmillan, W.D., 2007. "Escape from the cell: Spatially explicit modelling with and without grids," Ecological Modelling, Elsevier, vol. 200(1), pages 59-78.
    5. Baetens, J.M. & Van der Weeën, P. & De Baets, B., 2012. "Effect of asynchronous updating on the stability of cellular automata," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 383-394.
    6. Jie Zhu & Yizhong Sun & Shuyin Song & Jing Yang & Hu Ding, 2021. "Cellular automata for simulating land-use change with a constrained irregular space representation: A case study in Nanjing city, China," Environment and Planning B, , vol. 48(7), pages 1841-1859, September.
    7. David O'Sullivan, 2009. "Changing Neighborhoods—Neighborhoods Changing," Sociological Methods & Research, , vol. 37(4), pages 498-530, May.
    8. Niandry Moreno & André Ménard & Danielle J Marceau, 2008. "VecGCA: A Vector-Based Geographic Cellular Automata Model Allowing Geometric Transformations of Objects," Environment and Planning B, , vol. 35(4), pages 647-665, August.
    9. Dan Miodownik & Britt Cartrite & Ravi Bhavnani, 2010. "Between Replication and Docking: "Adaptive Agents, Political Institutions, and Civic Traditions" Revisited," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 13(3), pages 1-1.
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    12. Yi Lu & Shawn Laffan & Chris Pettit & Min Cao, 2020. "Land use change simulation and analysis using a vector cellular automata (CA) model: A case study of Ipswich City, Queensland, Australia," Environment and Planning B, , vol. 47(9), pages 1605-1621, November.
    13. Itzhak Benenson & Erez Hatna & Ehud Or, 2009. "From Schelling to Spatially Explicit Modeling of Urban Ethnic and Economic Residential Dynamics," Sociological Methods & Research, , vol. 37(4), pages 463-497, May.
    14. José Manuel Galán & Luis R. Izquierdo & Segismundo S. Izquierdo & José Ignacio Santos & Ricardo del Olmo & Adolfo López-Paredes & Bruce Edmonds, 2009. "Errors and Artefacts in Agent-Based Modelling," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-1.
    15. Dirk Helbing & Anders Johansson, 2010. "Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach," PLOS ONE, Public Library of Science, vol. 5(10), pages 1-15, October.
    16. Elenna R Dugundji & László Gulyás, 2008. "Sociodynamic Discrete Choice on Networks in Space: Impacts of Agent Heterogeneity on Emergent Outcomes," Environment and Planning B, , vol. 35(6), pages 1028-1054, December.
    17. Simon Deichsel & Andreas Pyka, 2009. "A Pragmatic Reading of Friedman's Methodological Essay and What It Tells Us for the Discussion of ABMs," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(4), pages 1-6.
    18. Luis R. Izquierdo & Segismundo S. Izquierdo & José Manuel Galán & José Ignacio Santos, 2009. "Techniques to Understand Computer Simulations: Markov Chain Analysis," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-6.
    19. Heuermann, Daniel F. & Vom Berge, Philipp, 2024. "Unemployment, Segregation, and the Structure of Cities," IZA Discussion Papers 17058, Institute of Labor Economics (IZA).
    20. Clémentine Cottineau, 2022. "Modéliser les inégalités dans l’espace géographique," Post-Print halshs-03801388, HAL.
    21. Ortigoza, Gerardo M., 2015. "Unstructured triangular cellular automata for modeling geographic spread," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 520-536.
    22. Dirk Helbing & Attila Szolnoki & Matjaž Perc & György Szabó, 2010. "Evolutionary Establishment of Moral and Double Moral Standards through Spatial Interactions," PLOS Computational Biology, Public Library of Science, vol. 6(4), pages 1-9, April.

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