Does it have to do with something that involves cell/DNA formation, or other topics in biology/chemistry? Or is this based on coincidence?
In: 19
There are geometric reasons why the Fibonacci sequence turns up in places like pineapples, pine-cones, and sunflowers – it turns out that efficient packing of similar sized features (spiky bits on a pineapple, or seeds in a sunflower) ends up displaying a variety of Fibonacci numbers simply because other numbers wouldn’t fit. It’s a bit like how honeycomb is hexagonal – other shapes wouldn’t fit.
The golden ratio is a geometric consequence of Fibonacci numbers, so it can come out of certain cases where Fibonacci numbers are involved.
To combine the answers of /u/WarlandWriter and /u/Ares1935, the nautilus shell is grown outward at a certain rate in a spiral, but the size of each successive section is larger as the creature inside grows. If the rate of growth outward and the rate of growth around match about right, then you end up with the same “exponential plus delay” type growth rate (i.e. an analogue version of Fibonacci numbers leading to a golden spiral) One important feature of the golden spiral is self-similarity, meaning that if you take the first chunk of the growth and just make it bigger, you get exactly the same shape as the older shell (i.e. a 2 year old nautilus shell is the same shape as a 3 year old nautilus shell, just smaller) This means that the *shape* of the wee critter is the same and they don’t have to change shape as they grow. Anything that meant that the growth rates became mismatched would be rather inconvenient and the resulting organism would likely lose the Darwinian game an not survive to make more non-golden-spiral nautilus shells.
Mathologer has [a good video](https://www.youtube.com/watch?v=_GkxCIW46to) on the subject of Fibonacci numbers / golden ratio / spirals in nature. Numberphile also has some good Fibonacci / golden ratio / golden spiral videos you might want to watch, too 🙂
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