Alluvial rivers build their own bed with the sediment they transport. As
they do so, they spontaneously select their size and shape, and organize
themselves into beautifully ramified networks. Despite their apparent
randomness, these structures show remarkably constant geometrical
features: the streams' size and slope are tightly related to water
discharge, and they bifurcate at an angle of 72°. We will illustrate how
the physics of sediment transport and groundwater flow maintain these
features across scales ranging from that of a sand grain to the width of
the Amazon.