Rivers form fractal shapes just like how Iterated Function Systems[1] and L-systems[2] form: by simple branching, carried out at varying levels of scale. A gentle reminder that fractals are nature's favorite building block.
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."
But rivers have been mathematical for only something less than ~60 years, no? Mandelbrot's paper on the length of the coastline of Albion was in the mid 60s or so, and the math that made rivers mathematical (fractals, chaos theory) came after that (within my lifetime!).
Rivers are mathematical only because we have so improved our mathematics in recent times (when my parents were born, they were random and non-deterministic, mysterious).
That questions makes no sense? What is "mathematical" as a property? It has it backwards. Accepting the property of being mathematical, isn't it caused effectively by how much we study and model it mathematically?
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.
Comments
Rivers form fractal shapes just like how Iterated Function Systems[1] and L-systems[2] form: by simple branching, carried out at varying levels of scale. A gentle reminder that fractals are nature's favorite building block.
[1] https://en.wikipedia.org/wiki/Iterated_function_system
[2] https://en.wikipedia.org/wiki/L-system
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."
But rivers have been mathematical for only something less than ~60 years, no? Mandelbrot's paper on the length of the coastline of Albion was in the mid 60s or so, and the math that made rivers mathematical (fractals, chaos theory) came after that (within my lifetime!).
Rivers are mathematical only because we have so improved our mathematics in recent times (when my parents were born, they were random and non-deterministic, mysterious).
That questions makes no sense? What is "mathematical" as a property? It has it backwards. Accepting the property of being mathematical, isn't it caused effectively by how much we study and model it mathematically?
"THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES" https://webhomes.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf
This is backwards cause-effect
Mathematical axioms are derived from sensory experience in this physical reality
The math is actually river-like
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.
It's not obvious that either way should work.