THE SHAWSTEAD GROUP

KEY CONCEPT

Inspired by phyllotaxis in plants, the golden spiral method (Vogel’s model) places points at an angle equal to the golden angle—2π·(1–1/φ) ≈ 137.5°—and adjusts radius by √(i/N) to ensure each new point occupies the same area as the last.

DISK ALGORITHM

For a flat disk, assign each point an index i + 0.5 (to center at mid‐cell) and compute:

r = MAX_RADIUS · √((i + 0.5) / N)
θ = (i + 0.5) · GOLDEN_ANGLE

SPHERE ALGORITHM

To distribute on a sphere’s surface, sample the polar angle via the inverse CDF of sin φ:

φ = acos(1 – 2·(i + 0.5)/N)
θ = (i + 0.5) · GOLDEN_ANGLE

MATHEMATICS

√(i/N) equalizes the differential ring areas (2πr dr), and the inverse‐CDF sampling for φ uses sin φ dφ to avoid polar clustering.

IMPLEMENTATION

I build an SVG of <circle> elements, apply <animate> tags for pulsing radius and opacity—offset by each point’s fractional position to create a wave effect.

APPLICATIONS

Ideal for generative art, data visualizations, computational geometry, or any scenario needing uniform sampling on circles or spheres.