The curve plotted here is r(θ) = a·e^(bθ), the logarithmic spiral, drawn directly in polar-to-Cartesian form on a flat 2D plane (no reprojection of a 3D model). Growth is parameterized as a multiplier k applied every quarter turn, so b = ln(k)/(π/2). k = φ = (1+√5)/2 ≈ 1.618034 gives the true golden spiral.
The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, …) is genuinely computed term by term; the chart plots the real ratio F(n+1)/F(n) at each step, which provably converges to φ. Use + next term to advance the sequence one step at a time and watch the ratio settle.
Honest note: the golden ratio's supposed presence in shells, galaxies or the human body is a popular myth without measured support — this page limits itself to the two facts that are actually provable: the spiral's geometry, and the Fibonacci-ratio convergence.
r(θ) = a·e^(bθ) b = ln(k)/(π/2)
F(n) = F(n-1)+F(n-2) F(n+1)/F(n) → φ as n→∞