The analysis of natural hydraulic networks over a wide range of scales, allowed by modern digital mapping technology, reveals extraordinary diversity of natural forms, and yet deep regularity and symmetry, regardless of geology, climate, vegetation or exposed lithology. River networks are indeed a paradigm of scale-invariant, or fractal, forms ubiquitous in nature, whereas tidal networks bear the both the signatures of scaling processes and of different dynamic origin and susceptibility to environmental factors. Here I review a subjective choice of linked results, suggesting that the dynamic origin of the recurrence of similar network forms in nature relates to a common mechanism of growth and stabilization of open, dissipative systems with many degrees of freedom.