The river follows the Howard-Knutson rule, where each centerline node migrates along its local normal at the rate
where κ is curvature, s is distance upstream, Ω = −1, Γ = 2.5, W = 100 m, and the memory length ℓ = 1/(αW) is the meander scale. When two banks come within the cutoff distance, the loop is cut off as an oxbow. Each step the channel is rasterized onto a grid, and a distance transform gives every floodplain cell its distance D to the river.
Households settle the grid with utility
with wd = 1 and C the number of settled neighbors (cohesion). A household the river erodes is relocated to the best open cell: forced migration. The worst-placed household moves to the best open cell when it gains more than the stubbornness μ: voluntary migration. Population is conserved.