Model, assumptions & sources
Construction. Seed i (counting from 0) sits at radius √(i + ½) and angle i × α, so every seed gets the same area, π square model units (Vogel's construction). The golden angle is 360° × (1 − 1/φ) ≈ 137.50776° with φ = (1 + √5)/2; the Golden preset uses that constant at full floating-point precision, not the rounded 137.508.
Spokes. If α is exactly p/q of a turn (120° = 1/3, 135° = 3/8), seed i + q lands on exactly the same ray as seed i. The page checks for exact fractions with denominators up to 360. Any decimal you type is a fraction too (137.3° = 1373/3600), but its repeat may lie far beyond the head.
Spiral families. For the outermost seed, the page finds which older seeds are nearest. Only continued-fraction approximations of α can be nearest neighbours, so those are the candidates. Offset q links seeds i, i+q, i+2q…, which makes exactly q strands. Drawn strands fade where that offset stops being a near-neighbour link. As the head grows the rim moves outward and the nearest offsets change, so the visible pair changes with seed count.
Neighbour gap. Mean nearest-neighbour distance over the outer three-quarters of seeds, divided by the gap of a perfect hexagonal packing at the same density (√(2π/√3) ≈ 1.905 units). It is a model metric, not a plant measurement.
Honest limits. No growth physics, no seed-size variation, no florets or petals; colour only marks placement order. In this model angles near the golden angle pack evenly, and other “noble” irrational angles such as ≈99.502° do too. That does not make the golden angle optimal for every plant: real divergence angles come from growth dynamics, vary, and real heads include non-Fibonacci patterns.
Keyboard: Space plays or pauses when focus is not in a control. Original code and procedural art by ExplainerTools.