MathVista 3D

Logarithmic spiral

x = a^u (1 + cos v) cos u y = a^u (1 + cos v) sin u z = a^u sin v

Domain X (±)Domain Y (±)DetailTheme

Speed (t)

3D Nautilus shell — logarithmic spiral

3D particle system

A nautilus is a logarithmic spiral: each turn scales by a constant a, so the shape is self-similar.

u runs along the tube, v around a cross-section. It is the classic model of golden-ratio growth.