Why are rivers so mathematical?

But IFS and L-systems don't help explain the phenomena (the "how"), just its expression. Fractals are not a building block, physical forces are. Where one or more physical forces are dominant over a range of spatial or temporal timescales, self-similar behavior can result.

I have no problem using the word "fractal" to communicate these shapes, but I'd like folks to realize that fractals are not a force, not a goal of nature, and do not answer "how."

It's not obvious that either way should work.

or: rivers obey physics with * absolute perfection, and "math" is a clumsy human constructed aproximation of certain conditions that will create a 2 dimensional image of something "river-like" but remain unconvincing to fish.

* humans are still unsure of exactly how much detail reality contains, or even if it's a constant, but we can be sure that all observable natural phenominon adhear to the laws of nature at the finest level that exists, and so in another article about "electric rain" it is shown that each drop of water in a cloud has a charge and can be considered as a physical component of lightning, and if left undischarged goes on to corrode cars, or interact in unknown ways as it becomes part of a river, to which I suggest getting some much higher, much bigger math to figure it out. Or ask a fish.