Long story short with no technicality behind it:
The Fibonacci Sequence is made up of numbers equal to the sum of the two previous numbers in that sequence. It essentially adds itself to itself, and so grows proportional to it’s previous self.
The most famous example of the nautilus she’ll is an example of a spiral-esque shape that slowly wants to expand it’s diameter to accommodate for an ever increasing living being while curling around itself. The current number/size of opening grows slightly larger than it was before over time.
If you look at the entire piece from outside you get a Fibonacci sequence-ish.
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