Black Forest

Coming back from a conference in Germany we passed the river Breg

whose water flows into the Danube and hence to the Black Sea, and close by the river Gutach

which joins the Rhine and hence the North Sea. (I read however that some of the water flowing towards the Danube is captured by the Rhine through underground channels.)

I was struck by the similarity between the graph of an endomorphism of a finite set, and a map of river systems. A river sytem is already a (partially discrete) abstraction of the flow of water over a landscape. A further discretization of space and time yields an endomorphism of a finite set.