Geometry of branching stream networks

River networks have been a source of fascination for centuries. Yet, how these networks form and create these geometries remains elusive. Recently we have shown that streams branching in a diffusive field bifurcate at a characteristic angle of $\alpha=2\pi/5=72^\circ$. This result is obtained from Lowner dynamics by combining classical results of groundwater hydrology with the hypothesis that streams grow in the direction of maximal water flux into the channel's tip. Our theoretical results are umambigously consistent with field measurements we conducted in a 100 km$^2$ channel network on the Florida Panhandle. Here we extend our theory to include slope effects and apply our analysis to large drainage basins. We hypothesize that the extension of the network at the tip is driven by a diffusive process leading to a (slope corrected) $2\pi/5$ branching at the leaves of the network.