Meandering rivers show cyclic behavior because the channel is confined to its floodplain, where bends grow, cut off, and grow again. Despite these cycles, the river's behavior is complex and chaotic. The goal of this site is to think about potential biological behaviors in a computer simulation of meandering rivers.
We think three behaviors of the agents are important. First, agents are attracted to the river, their source of food, water, and transport. Second, they may be attracted to, or repelled by, each other. Third, the river destroys agents. We assume agents cannot stop a meandering river, which is blind to their dynamics.
Each panel below runs one behavior beside a toy river as a cellular automaton. We assume the population is conserved. Hover to play, or tap on phones.
The river follows the Howard-Knutson rule, a standard geometric model in geomorphology. Each centerline node migrates along its local normal at the rate
where κ is curvature, s is distance upstream, kl is the migration rate, 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.
N agents live on the same grid, one per cell, each with utility
where C is the number of agents in the eight neighboring cells, wd = 1, and the cohesion wc is positive for attraction and negative for repulsion. Each step, every agent on a cell the river now occupies dies, and as many new agents are born, each on the open cell of highest U next to an existing agent, so the population is conserved. Then, repeatedly, the agent with the lowest U moves to the best open cell, as long as that raises its U by more than the stubbornness μ.