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