What is the nautilus, and how does it relate to Fibonacci?
What a nautilus is
The chambered nautilus is a cephalopod, a relative of squid and octopus, that lives in the deep waters of the Indo-Pacific. Unlike its cousins it carries a shell, coiled into a spiral and divided into chambers. The animal lives in the newest, outermost chamber. As it grows it moves forward, builds a new wall behind itself and adds a larger chamber, sealing off the old ones.
How it floats
A thin tube runs through every wall. Through it the nautilus fills the old chambers with gas or empties them of liquid, and so adjusts its buoyancy, rising and sinking with almost no effort.
How it relates to Fibonacci
Both are logarithmic spirals: every turn is larger than the last by the same factor, so the shape never changes as it grows. Start with 1 and 1, keep adding the last two numbers, and the ratio of neighbors settles toward 1.618, the golden ratio. Squares with those sides tile together, and a quarter circle in each makes the golden spiral, which widens by 1.618 every quarter turn.
The nautilus winds tighter. Its shell widens roughly three times per full turn, against almost seven for the golden spiral. So the nautilus is not a Fibonacci spiral, whatever you may have read. It is a cousin from the same family, and the family is the point: one simple growth rule, repeated, makes a shape that is the same at every size.
Where Volo comes in
Watch the line that stays when everything else fades. It is the last stretch of the nautilus, and it is the outer rocker of Volo’s frame. Laid over each other, the two curves are about one percent apart. Volo rocks the way the shell grows.
The mystery
Nobody told the nautilus, the sunflower or the galaxy to follow a rule. The same kind of curve keeps arriving in shells, seed heads and the arms of spiral galaxies. Look at it long enough and the question changes from what it is to why it keeps coming back.
One rule, repeated. The same shape at every size.
