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🧪 2D Superformula — Gielis Curve Plotter

The flat polar cross-section behind the 3D Superformula: r(θ) = (|cos(mθ/4)/a|n2 + |sin(mθ/4)/b|n3)-1/n1, with six live sliders and a numeric readout of the curve's radius, area, perimeter and lobe count.

Drawing with Maths2DModerate60 FPS📱 Mobile-adapted⇄ 3D version
2d-dynamic-formula-visualization-three-dimensions ↗ Open standalone

This 2D companion evaluates the exact same Gielis superformula the 3D version uses to build its mesh, but only once per angle instead of twice — so instead of a rotating solid you get the flat polar curve it is built from, traced in real time. Six sliders (m for rotational symmetry, n1/n2/n3 for how sharply the curve pinches and rounds between lobes, and a/b for independent axis scaling) let you push the shape from a plain circle through stars, gears and flower petals, while a numeric panel reports the curve's minimum, maximum and mean radius, its enclosed area and perimeter (both computed directly from the sampled points via the shoelace formula and segment-length summation), and a live count of visible lobes — turning the abstract equation into something you can read off the screen as you drag.

⚙ Under the hood

2D polar plotter for Johan Gielis' superformula r(θ)=(|cos(mθ/4)/a|^n2+|sin(mθ/4)/b|^n3)^(-1/n1), sampled at 721 points per frame with live shoelace-area, perimeter and lobe-count readouts, and the same time-based auto-mutation as the 3D original.

superformulagielis curvepolar equationmathematical patternsdynamic visuals

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

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