Each region holds a population share; a migration flux moves people from countryside to city every simulated year, gated by how strongly push and pull factors act on the still-rural share:
dU/dt = k · push · pull · (R/100) · (1 − U/Umax)
R = 100 − U
- Push factors — rural poverty, land scarcity, lack of local jobs; higher values shove more people out of the countryside each year.
- Pull factors — urban wages, services, agglomeration effects; higher values draw migrants in faster once they leave.
- Infrastructure overload — planned capacity (roads, housing, utilities) expands at a fixed, slow pace. When the city's actual population races ahead of that capacity, the overload index climbs nonlinearly and the skyline tints red.
Starting point mirrors the real trajectory: ~30% of the world lived in cities in 1950; today it is past 55%, with the UN projecting roughly 68% by 2050 — this model runs the same push/pull mechanics forward from that baseline.