The analysis of natural hydraulic networks over a wide range of scales,:allowed by modem 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.