Nautilus Shell Spiral

Cephalopod chambered shell growth governed by the logarithmic equiangular spiral r = a*exp(b*theta), featuring internal curved septa walls and siphuncle canal.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Iridescent Rotation 0.4

Shell rotation speed

Septa Chambers 36

Number of internal camera walls

Mathematical Formulation

68 chars medium

Analytical Equation

r(\theta) = a e^{b \theta}, \quad b = \frac{\ln(\phi)}{2\pi} \approx 0.1759, \quad \alpha = \cot^{-1}(b)

Compact Formula

r = a * exp(0.1759 * θ), septum_arch = quadCurve(inPoint, outPoint)

Renderer Logic

const rOuter = a * Math.exp(b * theta1);
const rInner = theta2 > 0 ? a * Math.exp(b * theta2) : 0;
const outX = rOuter * Math.cos(theta1);
const outY = rOuter * Math.sin(theta1);

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#nautilus #spiral #logarithmic #creatures #golden-ratio #geometry

Author: Math Art Core Target: 60 FPS

Nautilus Shell Spiral

Live Parameters

Mathematical Formulation

Mathematical Tags

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