An Interactive Discovery

Nature writes in
spirals

From the unfurling fern to the sweep of a nautilus shell, a single number shapes the living world. Let's find it.

scroll to explore ↓

Three observations

Before any equation, let your eyes do the work. These patterns all trace the same curve.

Nautilus shell cross-section
01 · Chambered Nautilus

Logarithmic growth chambers

The nautilus adds ever-larger chambers as it grows. Each new chamber is roughly 1.618 times the size of the one before. The result: a shell that expands without ever changing shape.

Sunflower seed head
02 · Sunflower Head

Optimal seed packing

Sunflower seeds form two interlocking families of spirals: 34 clockwise, 55 counterclockwise. Adjacent Fibonacci numbers, arranged at the golden angle (137.5°) for maximum density.

Fern fiddlehead unfurling
03 · Fern Fiddlehead

Self-similar unfurling

A young fern frond unrolls from its base, each segment a miniature of the whole. This recursive, scale-invariant growth is nature's most efficient packaging strategy.

Nature's blueprint

a
b

When the ratio of a + b to a equals the ratio of a to b, both equal 1.618. This is the Golden Ratio (Φ), and it appears wherever growth must be continuous and undistorted.

(a + b) / a = a / b = Φ ≈ 1.618
The Fibonacci Sequence

Build the spiral

Drag the sliders. Watch what happens when the ratio shifts away from Φ.

Φ = 1.618 is the sweet spot where squares tile perfectly
21
Largest Square
1870
Total Area (px²)