Phyllotaxis is the geometric rule that governs where a plant places each new leaf, floret or seed around its growing tip (the apical meristem). Each new primordium appears rotated by a near-constant divergence angle from the previous one — empirically almost always close to the golden angle, 137.507764...°, derived from the golden ratio φ as 360°/φ². This single rule, repeated thousands of times, is enough to generate the interleaving spiral families (visible as "parastichies") counted in Fibonacci numbers on a real sunflower head or pinecone.
θ(n) = n · divergence
r(n) = C·√n (disc / capitulum — Vogel's model)
z(n) = n · rise (helix / leaf-bearing stem)
This simulation ports the exact recurrence used by the 2D original — r = C·√n at angle n·divergence, Vogel's classic model for a flat seed head — into real 3D space, and adds the general helical case: the same divergence angle, but each new organ climbs a fixed internode rise up a central stem instead of spreading outward on a flat disc. Real leaf phyllotaxis on a stem is exactly this helix; the flat capitulum is the special case where the growing tip itself is broad and flat instead of a narrow shoot.
- Divergence angle — away from the golden angle (137.5°), the packing breaks down into visible straight rays instead of interleaved spirals; this is why 137.5° is special, not 120° or 90°.
- Spacing constant C — sets how fast the disc spiral expands outward (Vogel's model, disc mode only).
- Internode rise — the vertical distance between successive leaves up the stem (helix mode only) — this is what turns a flat spiral into a climbing 3D helix.
- Growth pattern — toggle between the flat capitulum (sunflower/pinecone head) and the helical stem (ordinary leaf arrangement) — both driven by the same divergence-angle recurrence.