Phyllotaxis
the spirals are counted, not admired
Generator

spiral-at-growth

Fitting log r against angle on the drawn points returns 3.2000, and the model's worst residual is 9e-16 in log r.
A logarithmic spiral growing by 3.20× per turnFitting log r against angle on the drawn points returns 3.2000, and the model's worst residual is 9e-16 in log r.growth 3.20× per turnrecovered 3.200×

Drawn at its defaults, in shells and growth. It carries a slider over growth, so the claim in its caption strip is restated at every stop rather than at one. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 2 essays

the blast radius of changing it

Shells and growth

Growth as a rule

A logarithmic spiral is not a shape somebody admired. It is what a thing grows into when it adds material at its opening without changing shape, its one parameter is how much it grows per turn, and that parameter can be recovered from any drawn curve to the last digit.

 Shells and growth

The nautilus question

A golden spiral grows by 6.854 per turn. Measured nautilus sections give about 3.2. That is a factor of 2.14 — not a rounding error, not an artefact of where the centre is assumed to be, and not close.

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