Phyllotaxis Spiral Growth Screensaver
Phyllotaxis is the real botanical pattern behind sunflower heads, pinecones and pineapples — each new seed is placed at exactly the golden angle, about 137.5°, further round than the last, at a distance from center that grows with the square root of the seed's index. This screensaver grows that exact real pattern outward, one seed at a time.
How the Phyllotaxis Spiral Growth screensaver works
Every new point is placed at an angle exactly 137.5° — the golden angle, derived from the golden ratio — further around than the previous point.
Each point's distance from the center grows in proportion to the square root of how many points have been placed so far, which is what keeps the seeds evenly packed rather than bunching up.
Because 137.5° is an irrational fraction of a full circle, no two seeds ever line up exactly, which is exactly what prevents wasted gaps in the real packing.
The combination of these two real simple rules is what produces the interlocking spiral arm families visible in real sunflower heads and pinecones.
A worked example
Watch the count climb past a hundred seeds and multiple spiral arm families become visible at once — commonly 21, 34 or 55 arms, real neighboring Fibonacci numbers, exactly as counted on real sunflower heads.
Settings & tips
- Seed color recolours every placed point.
- The pattern regrows from the center once it fills the visible area.
- Try counting the visible spiral arms in both directions — they're almost always consecutive real Fibonacci numbers.
Frequently asked questions
- Is this the actual pattern real sunflowers use?
- Yes — the golden-angle placement rule is a well-documented real botanical model matching real seed-head packing in sunflowers, pinecones and more.
- Why the golden angle specifically?
- Its irrationality means no seed ever lines up radially with an earlier one, which real research shows minimizes wasted gaps as the head grows.
- Is a key needed?
- No — it's a pure local computation.
- Is it free?
- Yes — free, no download, in your browser.