Interaction maximization and the observed distribution of urban populations: An agent-based model of humanity's metric condition

The very existence of urban formations on all inhabited continents and throughout the history of mankind since the 3rd millennium B.C. leads to suppose a tendency of some structured societies to maximize interaction by minimizing physical distance. Were this tendency unconstrained, it should eventually lead to the concentration of all of the society’s population into one single point: a situation only partially realized by the distribution of urban populations at the global scale. Models of constraints preventing its realization have thus to be proposed. We have set up one such model, using agent based simulation of food production and accessibility, in order to account for the structural constraints particular to the physical space. The simulations have notably shown that, while necessarily emerging from a society investing agricultural surplus into the upholding of specialists, an upper limit to city-growth is imposed by the phenomena of spatial friction.