Home▸Mathematics▸New Year Spiral: The Golden Ratio in Time

New Year Spiral: The Golden Ratio in Time — 2D

A real logarithmic (golden) spiral r = a·e^(bθ) plotted in 2D with pan/zoom, alongside a live Fibonacci-ratio convergence chart showing F(n+1)/F(n) approaching φ term by term.

Mathematics2DEasy60 FPS📱 Mobile-adapted⇄ 3D version

Details

CategoryMathematics

RenderingCanvas 2D

DifficultyEasy

Target FPS60

ControlsToggle to snap to the true golden spiral (k=phi per quarter turn); sliders for growth rate k and turn count; drag to pan and scroll to zoom the 2D spiral plot; slider for number of Fibonacci terms shown plus a step button and autoplay; fit-to-view button.

golden-ratiofibonaccilogarithmic-spiralmathematicsnew-year

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A 2D canvas plot of the logarithmic spiral r = a·e^(bθ), pannable and zoomable, next to a live Fibonacci sequence whose consecutive-term ratio F(n+1)/F(n) is genuinely computed and converges to the golden ratio φ as terms are added. Adjustable growth rate and turn count, with a one-click snap to the exact golden spiral (k = φ per quarter turn).

⚙ Under the hood

A real logarithmic spiral r = a·e^(bθ) plotted in 2D with pan/zoom, next to a live Fibonacci-ratio convergence chart approaching φ, with a one-click snap to the exact golden-spiral growth rate.

golden-ratiofibonaccilogarithmic-spiralmathematicsnew-year

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install