Axelrod culture dissemination

Field: political science · Zoo name: axelrod · Module: modelly.zoo.axelrod.model

Every site of a square grid holds a culture: features features, each one of traits values. At each event a random site and a random neighbour interact with probability equal to their overlap, the share of features on which they agree; when they do, the site copies one feature on which they differ. Similar neighbours grow more similar and neighbours with nothing in common never interact, so the grid freezes into regions of identical culture: one culture for few traits, many regions for many traits.

How it is written

The sites are the rows of a CellIndex over an OrthogonalVonNeumannGrid, and the cultures one (n_sites, features) integer array. Events stay sequential, as in the original, but each step draws its sites, their neighbours (CellIndex.random_neighbor) and the uniforms in three numpy calls, then runs events_per_step events on plain lists. After each step the model checks every bond at once; when no pair with partial overlap is left the map is frozen and running turns False. Regions are the connected components of the bonds with full overlap (scipy.sparse.csgraph).

from modelly.zoo.axelrod.model import Axelrod, AxelrodScenario

model = Axelrod(AxelrodScenario(rng=42, traits=15))
model.run()
model.n_regions(), model.time

Parameter	Default	Meaning
width, height	10, 10	grid size in sites
features	5	cultural features per site
traits	10	values each feature can take
events_per_step	2000	interactions attempted per step
steps	500	maximum run length of run()

Validation

tests/zoo/test_axelrod.py runs the 10 x 10, five-feature model of the original paper to its absorbing state with five seeds. Two traits end in a single region for at least four seeds of five; thirty traits leave more than 25 regions in every run; the mean number of regions grows from two to fifteen to sixty traits. It also checks the absorbing state (every bond has overlap 0 or features), the interaction rule on hand-made pairs, and that the same seed gives the same culture map.

References

• Axelrod, R. (1997). The dissemination of culture: a model with local convergence and global polarization. Journal of Conflict Resolution, 41(2), 203-226.

• Castellano, C., Marsili, M. and Vespignani, A. (2000). Nonequilibrium phase transition in a model for social influence. Physical Review Letters, 85(16), 3536-3539.

Start a project from it with modelly zoo copy axelrod my_cultures.