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🌀 Fibonacci Spiral

The Fibonacci spiral, the golden angle, and Fibonacci squares in nature. Interactive mathematical beauty. Age: 8+

Drawing with Maths3DEasy60 FPS

🐚 Fibonacci Spiral — Golden Ratio

Discover why sunflowers, pine cones, galaxies, and nautilus shells all share the same spiral. The Fibonacci sequence and Golden Ratio φ = 1.618… appear wherever things grow by adding to themselves.

🔬 What It Demonstrates

Sunflowers grow seeds at exactly 137.5° apart (the golden angle = 360°/φ²) — packing seeds most densely with no gaps. The Fibonacci sequence converges to φ as ratios of consecutive terms.

🎮 How to Use

Adjust the angle between seeds from 0° to 180°. Watch how rational angles create radial lines, irrational angles create spirals, and the specific golden angle creates the densest possible packing.

💡 Did You Know?

Sunflower heads always have Fibonacci numbers of spirals — 34 clockwise and 55 counter-clockwise (or 55 and 89 in larger flowers). These numbers are not coincidental — they are the mathematical inevitability of the golden angle.

⚙ Under the hood

Adjust the golden angle and point count to switch between spiral, sunflower and squares views of the Fibonacci sequence.

Fibonacci spiralgolden ratioFibonacci sequencephyllotaxis

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install