Spiral / Phyllotaxis Generator
Create phyllotaxis spirals like sunflowers. Use the golden angle to arrange points naturally.
Phyllotaxis describes how leaves, seeds, or petals arrange on a plant stem. The golden angle (137.507°) governs the spiral distribution in many plants. This generator visualizes phyllotaxis patterns: θ = n × 137.507° and r = c√n, where n is the point index. Export your spiral as a PNG for use in projects or education.
Generator
Settings
Adjust the controls to redraw the spiral instantly.
How Is It Calculated?
| Parameter | Formula | Typical Value |
|---|---|---|
| Golden Angle | 360° × (1 − 1/φ) | 137.507° |
| Angle of point n | θ(n) = n × 137.507° | θ(0)=0°, θ(1)=137.5° |
| Radius of point n | r(n) = c × √n | c ≈ 2–5 (scale) |
| Cartesian (x, y) | x = r cos(θ), y = r sin(θ) | Convert polar → rectangular |
The square root ensures equal area between consecutive rings. Without it, points cluster near the center. This spacing is observed in real sunflower seed distribution.
Example
Sunflower pattern with 1000 points
Parameters:
Points: 1000 | Angle: 137.507° | Scale: 1.0
Point 500:
θ(500) = 500 × 137.507° = 68,753.5° (mod 360°) = 233.5°
r(500) = 1.0 × √500 = 22.36
x = 22.36 × cos(233.5°) ≈ −13.4
y = 22.36 × sin(233.5°) ≈ −17.9
Each point's position is calculated, then rendered as a circle. The golden angle creates the natural-looking spiral arrangement.
Spiral Variations
FAQ
Why 137.507°?
This angle (360° × (1 − 1/φ)) ensures each new point is maximally distant from all previous points over a long sequence. It's derived from the golden ratio's mathematical properties and observed in sunflowers, pinecones, and spiral galaxies.
Can I change the angle?
Yes. Changing it creates different spirals. Angles close to 137.507° create tighter, more aesthetic spirals. Small deviations (±0.5°) produce visible changes in the pattern.
What does "scale" do?
Scale multiplies the radius formula: r(n) = scale × √n, and the result is normalised so the outermost point always stays inside the canvas. Higher scale spreads the pattern across more of the canvas; lower scale concentrates it near the centre. It does not change the spiral shape, only its size.
Can I export the pattern?
Yes. Use the Export PNG button to download the current canvas as a PNG image, suitable for web use, printing at canvas resolution, and quick sharing.
Updated: September 2026 | Golden Angle: 360° × (1 − 1/φ) = 137.5077...°