Network Modeling with Cellular Automata: Revisiting the Issue of Dimensionality

Abstract

Bonacich (2003) explored how space dimensionality impacts upon networks modeled with N-dimensional cellular automata. This note revisits and complements his findings. Increasing dimensionality also modifies the geometric properties of the grid, influencing network properties in unexpected ways.

Keywords:

• cellular automata
• multidimensional space
• networks
• niche
• sphere packing

Acknowledgments

The author is grateful to the Editor of The Journal of Mathematical Sociology for his remarks, which helped make the article more comprehensive and better coupled with applications.

Notes

¹The thresholds may be different along dimensions. But equal salience weights and standardization (Assumptions 2 and 3) set these thresholds equal, implying cubic catchment areas.

²Figure 2 displays that volume change gradients alter with radius even along dimension ranges where volume changes monotonically. So dimension change has a differential impact on actors of different affiliation radii even along these ranges.

Source: Conway and Sloane (1998).