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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

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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."

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