Golden-angle rose

Petals are placed with the golden angle α = π(3 − √5) ≈ 137.508°. Petal n is rotated by nα, so no two petals line up and the packing fills the disc as evenly as possible — the same rule sunflowers use for their seeds.

Each petal is a small parametric sheet in local coordinates [ρ, w, z] — radial distance, width offset, height — built from a bell-shaped width profile and rotated into place:

Pn(u,v) = Rotz(nα) · [ρ, w, z]T

Outer petals are larger and lower. Curl lifts their edges and tips, while Open lets the petals fall outward and flatten the bloom.