Phyllotaxis Spiral

Botanical sunflower spiral generated by the golden angle divergence formula theta = n * 137.508 degrees, scaling dynamically with radial distance.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Divergence Angle (°) 137.508

Golden ratio packing angle

Scale Factor (c) 6

Radial distribution density

Rotation Speed 0.5

Temporal rotation multiplier

Seed Count 1200

Total seed floret points

Mathematical Formulation

71 chars low

Analytical Equation

\theta_n = n \cdot 137.507764^{\circ}, \quad r_n = c \sqrt{n}

Compact Formula

θ = n * 137.508°, r = c * √n, x = r * cos(θ + t), y = r * sin(θ + t)

Renderer Logic

const theta = n * divergence + t * (1 + n * 0.0002);
const r = c * Math.sqrt(n) * (1 + 0.05 * Math.sin(t * 2 + n * 0.02));
const x = cx + r * Math.cos(theta);
const y = cy + r * Math.sin(theta);

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#golden-ratio #fibonacci #phyllotaxis #spiral #botany #polar

Author: Math Art Core Target: 60 FPS

Phyllotaxis Spiral

Live Parameters

Mathematical Formulation

Mathematical Tags

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