How erosion and feedback loops carve fractal drainage basins into the landscape.
From the air, rivers look like trees with branches at every scale — a fractal that looks the same whether you are looking at a hillside or a continent.
The structure comes from a feedback loop. Water erodes channels; deeper channels attract more water; more water erodes faster. The rich-get-richer dynamic organizes the basin into a hierarchical tree.
Strahler order: headwater rills are order 1; two order-1 streams merge into an order-2 stream. Horton found the bifurcation ratio $R_b = N_\omega / N_{\omega+1}$ stays between 3 and 5 across natural river systems regardless of terrain or climate.
Bars count stream segments; gap labels show R_b. Hover a bar to trace that order through the river network.
Figure 1. A simulated landscape under uniform rainfall. Watch as water (blue) carves channels into the terrain (brown). The hierarchical network that forms obeys the same scaling laws as real-world rivers.
The fractal pattern is a mathematical necessity for any system that drains a 2D surface through 1D channels while minimizing energy lost to friction and erosion.