Generator
centre-sensitivity
A shell has no marked centre, so the fit needs one chosen. Getting it wrong by 25% of the radius moves the fitted factor by 55.9% — nowhere near enough to turn 3.2 into 6.85.
Drawn at its defaults, in shells and growth. 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 growthThe 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.