Network Diffusion in Regional Science: From the Game of Life to Cellular Automata models
One of the main focuses in the course is the way how individuals’ decisions are influenced by their relationships with other people. Commonly, within a network, an individual’s actions are heavily dependent on other people’s decisions, explaining the occurrence of concepts like information cascade and network effects. Regarding the network structure, it is possible to expand the network model to other fields like ethology and regional science to understand and predict agent’s action patterns within the network. These kinds of models are referred to as Cellular Automata (CA) models in the field of regional science, in which the individual’s action (namely the “cellulars”) is based on their neighbors’ state.
The network model can be observed in nature. For example, each individual within a flock of birds or a school of fishes only has limited information regarding their surroundings. Since they can only observe their neighbors’ position and actions, these individuals within the society act based on their neighbors. An abstracted dynamic network named “Boids” simulates the flocking behavior, in which the individuals’ behavior is categorized into three rules: separation, alignment, and cohesion: they separate to avoid colliding with local flockmates; they steer to align with the average heading of local flockmates; they move to a cohesive position (center of mass) of the local flockmates.
A more well-known example of such a network model is Conway’s Game of Life. Within the plane, each grid represents an individual in the network, connected with its surrounding eight neighbors, and each grid’s state (live or death) depends on its neighbors. Conway’s Game of Life can be regarded as an oversimplified Cellular automata model of the natural world setting, that individuals die out due to local overcrowding or desertion, and reproduce with a favorable population density. Even with a simple set of rules, Conway’s Game of Life has exhibited unlimited potentials in simulating systems like computers and ecosystems. It has shed light on the exploratory path of using the Cellular Automata models to simulate and predict real-world scenarios – and it is often accurate and effective with adequate input of rules and initial conditions.
From the perspective of regional science, CA models are often used to simulate the change of land use over time. Land parcels at county or block level are similar to grids in Game of Life, and their status of development is highly related to their neighbors’ state. That is, if a parcel of land has multiple developed neighbors, it will be more likely to be developed in the next steps. In contrast, if the land parcel has no developed neighbors, it is not likely to become developed from barren land. This evolution process is similar to the network diffusion model discussed in class that a node is more likely to shift into a new state when it has more neighbors in the new state. An early adaption of the CA model was by W. R. Tobler in 1970, simulating the Urban Growth (population) in the Detroit region. Tobler’s assumption is slightly different from the network diffusion model. He claims that “everything is related to everything else, but closer neighbors have a stronger influence”. This assumption yields a complete graph formed by the neighborhoods in Detroit, and each edge between the vertices has a different weight based on their geographical distance. More closely-related grids are assumed to have a higher rate of population and development diffusion.
Source:
Keith C. Clarke, Cellular Automata and Agent-Based Models, https://link.springer.com/content/pdf/10.1007%2F978-3-642-23430-9_63.pdf
Reynolds, Craig (1987). Flocks, herds and schools: A distributed behavioral model. https://doi.org/10.1145%2F37401.37406