Phyllotaxis
Sunflowers, pinecones and pineapples pack their seeds by a single rule: each new seed is placed a fixed angle around from the last, stepping outward. When that angle is the golden angle, about 137.5 degrees, the seeds never line up into gaps and pack as tightly as possible, and your eye picks out sets of spiral arms whose counts are consecutive Fibonacci numbers. This tool grows the pattern seed by seed at whatever angle you choose. Nudge the angle a fraction of a degree off golden and the tight packing dissolves into ragged spokes, showing how special that one angle is. Colour the seeds by ring or spiral and export the result.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- Each seed sits at angle n·137.5° and radius √n from the centre, the model H. Vogel proposed for a sunflower head.
- The golden angle comes from the golden ratio, the “most irrational” number, so seed directions never repeat and the seeds avoid lining up into wasteful gaps.
- The visible spiral arms come in counts that are consecutive Fibonacci numbers (21 and 34, 34 and 55), a direct consequence of the golden angle.
- Runs 100% in your browser — simulations are computed locally on your device.
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